PORTFOLIO OF PROJECTS - Energy Storage using the Powell Unified Framework (Part 4)

In Part 4 we also change the 1-hot encoding of the decision variable to something more scalable. We will have a single decision variable ($x_{t,GB}$) where a positive value indicates the amount bought, a negative value the amount sold, and a zero value when neither happened. The $GB$ stands for ‘Grid-to-Battery’. When the flow is from grid to battery, $x_{t,GB}$ will have a positive value. When the flow is reversed, i.e. battery to grid, $x_{t,GB}$ will have a negative value. In the future, the number of decision variables will be increased as needed. Eventually we will have the decision vector:

$(x_{t,EL}, x_{t,EB}, x_{t,GL}, x_{t,GB}, x_{t,BL})$

In Part 4 we explore again the Bellman policy - in the Value Function Approximation (VFA) class. This policy will be based on Bellman’s exact dynamic programming approach making use of Backward Dynamic Programming (BDP). We also compare the Bellman policy with the earlier BuyLowSellHigh policy.

0 STRUCTURE & FRAMEWORK

The overall structure of this project and report follows the traditional CRISP-DM format. However, instead of the CRISP-DM’S “4 Modeling” section, we inserted the “6 step modeling process” of Dr. Warren Powell in section 4 of this document.

The example explored (but also modified) in this report comes from Dr. Warren Powell (formerly at Princeton). It was chosen as a template to create a POC for a client. It was important to understand this example thoroughly before embarking on creating the POC. Dr Powell’s unified framework shows great promise for unifying the formalisms of at least a dozen different fields. Using his framework enables easier access to thinking patterns in these other fields that might be beneficial and informative to the sequential decision problem at hand. Traditionally, this kind of problem would be approached from the reinforcement learning perspective. However, using Dr. Powell’s wider and more comprehensive perspective almost certainly provides additional value.

Here is information on Dr. Powell’s perspective on Sequential Decision Analytics.

The original code for this example can be found here.

In order to make a strong mapping between the code in this notebook and the mathematics in the Powell Unified Framework (PUF), we follow the following convention for naming Python identifier names:

Superscripts
- variable names have a double underscore to indicate a superscript
- $X^{\pi}$: has code X__pi, is read X pi
Subscripts
- variable names have a single underscore to indicate a subscript
- $S_t$: has code S_t, is read ‘S at t’
- $M^{Spend}_t$ has code M__Spend_t which is read: “MSpend at t”
Arguments
- collection variable names may have argument information added
- $X^{\pi}(S_t)$: has code X__piIS_tI, is read ‘X pi in S at t’
- the surrounding I’s are used to imitate the parentheses around the argument
Next time/iteration
- variable names that indicate one step in the future are quite common
- $R_{t+1}$: has code R_tt1, is read ‘R at t+1’
- $R^{n+1}$: has code R__nt1, is read ‘R at n+1’
Rewards
- State-independent terminal reward and cumulative reward
  - $F$: has code F for terminal reward
  - $\sum_{n}F$: has code cumF for cumulative reward
- State-dependent terminal reward and cumulative reward
  - $C$: has code C for terminal reward
  - $\sum_{t}C$: has code cumC for cumulative reward
Vectors where components use different names
- $S_t(R_t, p_t)$: has code S_t.R_t and S_t.p_t, is read ‘S at t in R at t, and, S at t in p at t’
- the code implementation is by means of a named tuple
  - self.State = namedtuple('State', SVarNames) for the ‘class’ of the vector
  - self.S_t for the ‘instance’ of the vector
Vectors where components reuse names
- $x_t(x_{t,GB}, x_{t,BL})$: has code x_t.x_t_GB and x_t.x_t_BL, is read ‘x at t in x at t for GB, and, x at t in x at t for BL’
- the code implementation is by means of a named tuple
  - self.Decision = namedtuple('Decision', xVarNames) for the ‘class’ of the vector
  - self.x_t for the ‘instance’ of the vector
Use of mixed-case variable names
- to reduce confusion, sometimes the use of mixed-case variable names are preferred (even though it is not a best practice in the Python community), reserving the use of underscores and double underscores for math-related variables

In order to make a strong mapping between the code in this notebook and the mathematics in the Powell Universal Framework (PUF), we follow the following convention for naming Python identifier names:

How to read/say
- var name & flavor first
- at t/n
- for entity OR of/with attribute
- $\hat{R}^{fail}_{t+1,a}$ has code Rhat__fail_tt1_a which is read: “Rhatfail at t+1 of/with (attribute) a”
Superscripts
- variable names have a double underscore to indicate a superscript
- $X^{\pi}$: has code X__pi, is read X pi
- when there is a ‘natural’ distinction between the variable symbol and the superscript (e.g. a change in case), the double underscore is sometimes omitted: Xpi instead of X__pi, or MSpend_t instead of M__Spend_t
Subscripts
- variable names have a single underscore to indicate a subscript
- $S_t$: has code S_t, is read ‘S at t’
- $M^{Spend}_t$ has code M__Spend_t which is read: “MSpend at t”
- $\hat{R}^{fail}_{t+1,a}$ has code Rhat__fail_tt1_a which is read: “Rhatfail at t+1 of/with (attribute) a” [RLSO-p436]
Arguments
- collection variable names may have argument information added
- $X^{\pi}(S_t)$: has code X__piIS_tI, is read ‘X pi in S at t’
- the surrounding I’s are used to imitate the parentheses around the argument
Next time/iteration
- variable names that indicate one step in the future are quite common
- $R_{t+1}$: has code R_tt1, is read ‘R at t+1’
- $R^{n+1}$: has code R__nt1, is read ‘R at n+1’
Rewards
- State-independent terminal reward and cumulative reward
  - $F$: has code F for terminal reward
  - $\sum_{n}F$: has code cumF for cumulative reward
- State-dependent terminal reward and cumulative reward
  - $C$: has code C for terminal reward
  - $\sum_{t}C$: has code cumC for cumulative reward
Vectors where components use different names
- $S_t(R_t, p_t)$: has code S_t.R_t and S_t.p_t, is read ‘S at t in R at t, and, S at t in p at t’
- the code implementation is by means of a named tuple
  - self.State = namedtuple('State', SVarNames) for the ‘class’ of the vector
  - self.S_t for the ‘instance’ of the vector
Vectors where components reuse names
- $x_t(x_{t,GB}, x_{t,BL})$: has code x_t.x_t_GB and x_t.x_t_BL, is read ‘x at t in x at t for GB, and, x at t in x at t for BL’
- the code implementation is by means of a named tuple
  - self.Decision = namedtuple('Decision', xVarNames) for the ‘class’ of the vector
  - self.x_t for the ‘instance’ of the vector
Use of mixed-case variable names
- to reduce confusion, sometimes the use of mixed-case variable names are preferred (even though it is not a best practice in the Python community), reserving the use of underscores and double underscores for math-related variables## 1 BUSINESS UNDERSTANDING

The following business description comes from the free book by Dr. Powell, Sequential Decision Analytics and Modeling:

New Jersey is looking to develop 3,500 megawatts (MW) of offshore wind generating power. A challenge is that wind (and especially offshore wind) can be highly variable, due in part to the property that wind power (over intermediate ranges) increases with the cube of wind speed. This variability is depicted in figure 9.1, developed from a study of offshore wind. Energy from wind power has become popular in regions where wind is high, such as the midwestern United States, coastal regions off of Europe, the northeast of Brazil, and northern regions of China (to name just a few). Sometimes communities (and companies) have invested in renewables (wind or solar) to help reduce their carbon footprint and minimize their dependence on the grid. It is quite rare, however, that these projects allow a community to eliminate the grid from their portfolio. Common practice is to let the renewable source (wind or solar) sell directly to the grid, while a company may purchase from the grid. This can be useful as a hedge since the company will make a lot of money during price spikes (prices may jump from $20 per megawatt-hour (MWh) to $300 per MWh or more) that offsets the cost of purchasing power during those periods.

A challenge with renewables is handling the variability. While one solution is to simply pump any energy from a renewable source into the grid and use the tremendous power of the grid to handle this variability, there has been considerable interest in using storage (in particular, battery storage) to smooth out the peaks and valleys. In addition to handling the variability in the renewable source, there has also been interest in using batteries to take advantage of price spikes, buying power when it is cheap (prices can even go negative) and selling it back when they are high. Exploiting the variability in power prices on the grid is known as battery arbitrage.

This problem will provide insights into virtually any inventory/storage problem, including - Holding cash in mutual funds A bank has to determine how much of its investment capital to hold in cash to meet requests for redemptions, versus investing the money in loans, stocks and bonds. - Retailers (including both online as well as bricksandmortar stores) have to manage inventories of the hundreds of thousands of products. - Auto dealers have to decide how many cars to hold to meet customer demand. - Consulting firms have to decide how many employees to keep on staff to meet the variable demand of different consulting projects.

Energy storage is a particularly rich form of inventory problem.

2 DATA UNDERSTANDING

# import pdb
from collections import namedtuple, defaultdict
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from copy import copy
import time
from scipy.ndimage.interpolation import shift
import pickle
from bisect import bisect
import math
from pprint import pprint
import matplotlib as mpl
pd.options.display.float_format = '{:,.4f}'.format
pd.set_option('display.max_columns', None)
pd.set_option('display.max_rows', None)
pd.set_option('display.max_colwidth', None)
! python --version
# 3.8.10; found it changed on 3/10/23

Python 3.10.12

DeprecationWarning: Please use `shift` from the `scipy.ndimage` namespace, the `scipy.ndimage.interpolation` namespace is deprecated.
  from scipy.ndimage.interpolation import shift

def process_raw_price_data(file, params):
    DISC_TYPE = "FROM_CUM"
    #DISC_TYPE = "OTHER"

    print("Processing raw price data. Constructing price change list and cdf using {}".format(DISC_TYPE))
    tS = time.time()

    # load energy price data from the Excel spreadsheet
    raw_data = pd.read_excel(file, sheet_name="Raw Data")

    # look at data spanning a week
    data_selection = raw_data.iloc[0:params['T'], 0:5]

    # rename columns to remove spaces (otherwise we can't access them)
    cols = data_selection.columns
    cols = cols.map(lambda x: x.replace(' ', '_') if isinstance(x, str) else x)
    data_selection.columns = cols

    # sort prices in ascending order
    sort_by_price = data_selection.sort_values('PJM_RT_LMP')
    #print(sort_by_price.head())

    hist_price = np.array(data_selection['PJM_RT_LMP'].tolist())
    #print(hist_price[0])

    max_price = pd.DataFrame.max(sort_by_price['PJM_RT_LMP'])
    min_price = pd.DataFrame.min(sort_by_price['PJM_RT_LMP'])
    print("Min price {:.2f} and Max price {:.2f}".format(min_price,max_price))

    # sort prices in ascending order
    sort_by_price = data_selection.sort_values('PJM_RT_LMP')

    # calculate change in price and sort values of change in price in ascending order
    data_selection['Price_Shift'] = data_selection.PJM_RT_LMP.shift(1)
    data_selection['Price_Change'] = data_selection['PJM_RT_LMP'] - data_selection['Price_Shift']
    sort_price_change = data_selection.sort_values('Price_Change')

    # discretize change in price and obtain f(p) for each price change
    max_price_change = pd.DataFrame.max(sort_price_change['Price_Change'])
    min_price_change = pd.DataFrame.min(sort_price_change['Price_Change'])
    print("Min price change {:.2f} and Max price change {:.2f}".format(min_price_change,max_price_change))

    # there are 191 values for price change
    price_changes_sorted = sort_price_change['Price_Change'].tolist()
    # remove the last NaN value
    price_changes_sorted.pop()

    if DISC_TYPE == "FROM_CUM":
    # discretize price change  by interpolating from cumulative distribution
        xp = price_changes_sorted
        fp = np.arange(len(price_changes_sorted) - 1) / (len(price_changes_sorted) - 1)
        cum_fn = np.append(fp, 1)

        # obtain 30 discrete prices
        discrete_price_change_cdf = np.linspace(0, 1, params['nPriceChangeInc'])
        discrete_price_change_list = []
        for i in discrete_price_change_cdf:
            interpolated_point = np.interp(i, cum_fn, xp)
            discrete_price_change_list.append(interpolated_point)
    else:
        price_change_range = max_price_change - min_price_change
        price_change_increment = price_change_range / params['nPriceChangeInc']
        discrete_price_change = np.arange(min_price_change, max_price_change, price_change_increment)
        discrete_price_change_list = list(np.append(discrete_price_change, max_price_change))

        f_p = np.arange(len(price_changes_sorted) - 1) / (len(price_changes_sorted) - 1)
        cum_fn = np.append(f_p, 1)
        discrete_price_change_cdf = []
        for c in discrete_price_change_list:
            interpolated_point = np.interp(c, price_changes_sorted, cum_fn)
            discrete_price_change_cdf.append(interpolated_point)

    price_changes_sorted = np.array(price_changes_sorted)
    discrete_price_change_list = np.array(discrete_price_change_list)
    discrete_price_change_cdf = np.array(discrete_price_change_cdf)
    discrete_price_change_pdf = discrete_price_change_cdf - shift(discrete_price_change_cdf,1,cval=0)

    mean_price_change = np.dot(discrete_price_change_list,discrete_price_change_pdf)

    #print("discrete_price_change_list ", discrete_price_change_list)
    #print("discrete_price_change_cdf", discrete_price_change_cdf)
    #print("discrete_price_change_pdf", discrete_price_change_pdf)

    print("Finishing processing raw price data in {:.2f} secs. Expected price change is {:.2f}. Hist_price len is {}".format(time.time()-tS,mean_price_change,len(hist_price)))
    #input("enter any key to continue...")

    exog_params = {
        "hist_price": hist_price,
        "price_changes_sorted": price_changes_sorted,
        "discrete_price_change_list": discrete_price_change_list,
        "discrete_price_change_cdf": discrete_price_change_cdf}
    return exog_params

seed = 189654913
file = 'Parameters.xlsx'

# NOTE:
# R__max: unit is MWh which is an energy unit
# R_0:    unit is MWh which is an energy unit
parDf = pd.read_excel(f'{base_dir}/{file}', sheet_name='ParamsModel', index_col=0); print(f'{parDf}')
parDict = parDf.T.to_dict('list') #.
PARAMS = {key:v for key, value in parDict.items() for v in value}
PARAMS['seed'] = seed
PARAMS['T'] = min(PARAMS['T'], 192); print(f'{PARAMS=}')

                    0
Index                
Algorithm  BackwardDP
T                 195
eta            0.9000
R__max              1
R_0                 1
PARAMS={'Algorithm': 'BackwardDP', 'T': 192, 'eta': 0.9, 'R__max': 1, 'R_0': 1, 'seed': 189654913}

parDf = pd.read_excel(f'{base_dir}/{file}', sheet_name='GridSearch', index_col=0); print(parDf)
parDict = parDf.T.to_dict('list')
paramsPolicy = {key:v for key, value in parDict.items() for v in value}; print(f'{paramsPolicy=}')
PARAMS.update(paramsPolicy); pprint(f'{PARAMS=}')

                  0
Index              
theta_sell_min   10
theta_sell_max  100
theta_buy_min    10
theta_buy_max   100
theta_inc         1
paramsPolicy={'theta_sell_min': 10, 'theta_sell_max': 100, 'theta_buy_min': 10, 'theta_buy_max': 100, 'theta_inc': 1}
("PARAMS={'Algorithm': 'BackwardDP', 'T': 192, 'eta': 0.9, 'R__max': 1, 'R_0': "
 "1, 'seed': 189654913, 'theta_sell_min': 10, 'theta_sell_max': 100, "
 "'theta_buy_min': 10, 'theta_buy_max': 100, 'theta_inc': 1}")

parDf = pd.read_excel(f'{base_dir}/{file}', sheet_name='BackwardDP', index_col=0); print(parDf)
parDict = parDf.T.to_dict('list')
paramsPolicy = {key:v for key, value in parDict.items() for v in value}; print(f'{paramsPolicy=}')
PARAMS.update(paramsPolicy); pprint(f'{PARAMS=}')

                      0
Index                  
nPriceChangeInc      50
priceDiscSet     1, 0.5
run3D             False
paramsPolicy={'nPriceChangeInc': 50, 'priceDiscSet': '1, 0.5', 'run3D': False}
("PARAMS={'Algorithm': 'BackwardDP', 'T': 192, 'eta': 0.9, 'R__max': 1, 'R_0': "
 "1, 'seed': 189654913, 'theta_sell_min': 10, 'theta_sell_max': 100, "
 "'theta_buy_min': 10, 'theta_buy_max': 100, 'theta_inc': 1, "
 "'nPriceChangeInc': 50, 'priceDiscSet': '1, 0.5', 'run3D': False}")

if isinstance(PARAMS['priceDiscSet'], str):
    price_disc_list = PARAMS['priceDiscSet'].split(",")
    price_disc_list = [float(e) for e in price_disc_list]
else:
    price_disc_list = [float(PARAMS['priceDiscSet'])]
PARAMS['price_disc_list'] = price_disc_list; print(f'{price_disc_list=}')

price_disc_list=[1.0, 0.5]

pprint(f"{PARAMS=}")

("PARAMS={'Algorithm': 'BackwardDP', 'T': 192, 'eta': 0.9, 'R__max': 1, 'R_0': "
 "1, 'seed': 189654913, 'theta_sell_min': 10, 'theta_sell_max': 100, "
 "'theta_buy_min': 10, 'theta_buy_max': 100, 'theta_inc': 1, "
 "'nPriceChangeInc': 50, 'priceDiscSet': '1, 0.5', 'run3D': False, "
 "'price_disc_list': [1.0, 0.5]}")

EXOG_PARAMS = process_raw_price_data(f'{base_dir}/{file}', PARAMS) #SDAM-9.3.3

Processing raw price data. Constructing price change list and cdf using FROM_CUM
Min price 0.00 and Max price 107.34
Min price change -54.40 and Max price change 65.81
Finishing processing raw price data in 1.97 secs. Expected price change is 1.28. Hist_price len is 192

print("Ingesting raw price data for understanding.")
# load energy price data from the Excel spreadsheet
raw_data = pd.read_excel(f'{base_dir}/{file}', sheet_name="Raw Data")

# look at data spanning a week
df_raw = raw_data.iloc[0:PARAMS['T'], 0:5]

# rename columns to remove spaces (otherwise we can't access them)
cols = df_raw.columns
cols = cols.map(lambda x: x.replace(' ', '_') if isinstance(x, str) else x)
df_raw.columns = cols
df_raw.head()

Ingesting raw price data for understanding.

	Time	Day	Hour	PJM_DA_LMP	PJM_RT_LMP
0	1.0000	2005-01-01 00:00:00	1.0000	25.7200	18.9100
1	2.0000	2005-01-01 01:00:00	2.0000	23.0800	14.2700
2	3.0000	2005-01-01 02:00:00	3.0000	21.0000	9.6700
3	4.0000	2005-01-01 03:00:00	4.0000	20.0000	17.6800
4	5.0000	2005-01-01 04:00:00	5.0000	20.0400	11.8800

def plot_data(df):
  n_charts = 2
  ylabelsize = 16
  fig, axs = plt.subplots(n_charts, sharex=True)
  fig.set_figwidth(10); fig.set_figheight(7)
  fig.suptitle('PRICE OF ELECTRICITY [$/MWh]', fontsize=20)
  i = 0
  axs[i].set_ylim(auto=True); axs[i].spines['top'].set_visible(False); axs[i].spines['right'].set_visible(True); axs[i].spines['bottom'].set_visible(True)
  axs[i].plot(df['PJM_DA_LMP'], 'r')
  axs[i].set_ylabel('$\mathrm{PJM\ DA\ LMP}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
  i = 1
  axs[i].set_ylim(auto=True); axs[i].spines['top'].set_visible(False); axs[i].spines['right'].set_visible(True); axs[i].spines['bottom'].set_visible(True)
  axs[i].plot(df['PJM_RT_LMP'], 'g')
  axs[i].set_ylabel('$\mathrm{PJM\ RT\ LMP}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
  axs[i].set_xlabel('$t\ \mathrm{[hours]}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
plot_data(df_raw)

# PARAMETERS
SNAMES = [ #state variable names
    'R_t',   #resource
    'p_t',   #price
]
xNAMES = ['x_t'] #decision variable names
eNAMES = [ #entity variable names
  # 'EL', #Wind to Load ('EC': Wind to Consumer)
  # 'EB', #Wind to Battery ('WS': Wind to Storage)
  # 'GL', #Grid to Load ('GC': Grid to Consumer)
  'GB', #Grid to Battery ('GS': Grid to Storage)
  # 'BL', #Battery to Load ('SC': Storage to Consumer)
]
piNAMES = ['X__BuyLowSellHigh', 'X__Bellman']
thNAMES = ['thLo', 'thHi'] #theta names

POSSIBLE_DECISIONS = [-1., 0, 1.]

N_SAMPLEPATHS = 3
N_TRANSITIONS = 192

INIT_RESOURCE = {eNAMES[0]: PARAMS['R_0']}
INIT_PRICE = {eNAMES[0]: EXOG_PARAMS['hist_price'][0]}
S_0_INFO = {
  'R_t': {en: INIT_RESOURCE[en] for en in eNAMES},
  'p_t': {en: INIT_PRICE[en] for en in eNAMES},
}

#        'GB'
TH_HI = {eNAMES[0]: (PARAMS['theta_sell_min'], PARAMS['theta_sell_max'], PARAMS['theta_inc'])}
TH_LO = {eNAMES[0]: (PARAMS['theta_buy_min'], PARAMS['theta_buy_max'], PARAMS['theta_inc'])}

3 DATA PREPARATION

The most important aspect of data preparation will be to create an empirical distribution rather than to try and fit the data to a parametric distribution. This involves the computation of a cumulative distribution from the data. We first sort the prices from smallest to largest. Let this ordered sequence be represented by $\tilde{p}_t$ where $\tilde{p}_{t-1} \le \tilde{p}_t$. Also, let $T$ be the number of time periods. The percentage of time periods with a price less than $\tilde{p}_t$ is then $t/T$. The empirical cumulative distribution is given by \[ F_P(\tilde{p}_t) = \frac{t}{T} \]

df_hist_price = pd.DataFrame({'hist_price': EXOG_PARAMS['hist_price']});
print(df_hist_price.shape)
# df_hist_price.plot('hist_price');
# df_hist_price.plot();
df_hist_price[:10]

(192, 1)

	hist_price
0	18.9100
1	14.2700
2	9.6700
3	17.6800
4	11.8800
5	2.0800
6	0.0000
7	18.0000
8	14.4800
9	17.8800

df_price_changes_sorted = pd.DataFrame({'price_changes_sorted': EXOG_PARAMS['price_changes_sorted']});
print(df_price_changes_sorted.shape)
df_price_changes_sorted.plot(figsize=(10,5));
df_price_changes_sorted[:10]

(191, 1)

	price_changes_sorted
0	-54.4000
1	-51.4900
2	-42.1100
3	-41.0800
4	-41.0100
5	-39.2400
6	-38.6900
7	-35.9800
8	-25.1700
9	-21.2800

df_discrete_price_change_list = pd.DataFrame(
  {'discrete_price_change_list': EXOG_PARAMS['discrete_price_change_list']})
print(df_discrete_price_change_list.shape)
df_discrete_price_change_list.plot(figsize=(10,5));
df_discrete_price_change_list[:10]

(50, 1)

	discrete_price_change_list
0	-54.4000
1	-41.0186
2	-27.8173
3	-19.6308
4	-14.7080
5	-10.8080
6	-9.7151
7	-8.3486
8	-7.8090
9	-7.1051

df_discrete_price_change_cdf = pd.DataFrame(
  {'discrete_price_change_cdf': EXOG_PARAMS['discrete_price_change_cdf']})
print(df_discrete_price_change_cdf.shape)
# df_discrete_price_change_cdf.plot(figsize=(10,5));
df_discrete_price_change_cdf[:10]

(50, 1)

	discrete_price_change_cdf
0	0.0000
1	0.0204
2	0.0408
3	0.0612
4	0.0816
5	0.1020
6	0.1224
7	0.1429
8	0.1633
9	0.1837

4 MODELING

4.1 Narrative

There has been an interest making use of batteries to exploit electricity price spikes. Power is bought when the price is low and power is sold when the price is high. This is known as battery arbitrage.

This project hightlights some interesting aspects of this kind of problem. Among these are:

Electricity prices on the grid can be very volatile (varies between about $20/MWh to about $1,000/MWh or even $10,000/MWh for brief periods)
Prices change every 5 minutes
We assume that we can observe the price and then decide if we want to buy or sell
We can only buy or sell for an entire 5-minute interval at a maximum rate of 0.01 MW
Wind energy can be forecasted but not very well. Rolling forecasts can be used.
Energy demand is variable but quite predictable. It depends on:
- temperature (primarily)
- humidity (less)
Energy may be bought from or sold to the grid at current grid prices.
There is a 5% to 10% loss when converting power from AC (grid) to DC (to store in battery).

The next figure shows how the system components interact:

Figure 1 Components of the Energy Storage System

4.2 Core Elements

This section attempts to answer three important questions: - What metrics are we going to track? - What decisions do we intend to make? - What are the sources of uncertainty?

For this problem, the only metric we are interested in is the amount of profit we make after each decision window. A single type of decision needs to be made at the start of each window - how much energy to buy or sell. The only source of uncertainty is the price of energy.

4.3 Mathematical Model | SUM Design

A Python class is used to implement the model for the SUS (System-Under-Steer):

class Model():
  def __init__(self, S_0_info):
    ...
    ...

4.3.1 State variables

The state variables represent what we need to know.

$R_t$
- amount of energy stored in the battery at time $t$
- measured in kWh or MWh
$p_t$
- price of energy on the grid

The state is:

$S_t = (R_t,p_t)$

The state variables are represented by the following variables in the Model class:

self.State = namedtuple('State', SNAMES) # 'class'
self.S_t = self.build_state(info) # 'instance'

where

SNAMES = [ #state variable names
    'R_t',   #resource
    'p_t',   #price
]

4.3.2 Decision variables

The decision variables represent what we control.

$x_t$
- amount of energy bought from ($x_t>0$) or sold to ($x_t<0$) the grid
Losses
- When energy is transferred to or from the battery a loss is incurred
- Assume the loss into the battery is the same as the loss out of the battery
- $\eta$ is the fraction of the energy retained
- $1 - \eta$ is the loss
Constraints
- buy from grid $(x_t>0)$:
  - $x_t \le \frac{1}{\eta}(R^{max} - R_t)$
- sell to grid $(x_t<0)$:
  - $-x_t \le R_t$, which comes to
  - $x_t \ge -R_t$
Decisions are made with a policy (TBD below):
- $X^{\pi}(S_t)$

The decision variables are represented by the following variables in the Model class:

self.Decision = namedtuple('Decision', xNAMES) # 'class'

where

xNAMES = ['x_t'] #decision variable names
eNAMES = [ #entity variable names
  # 'EL', #Wind to Load ('EC': Wind to Consumer)
  # 'EB', #Wind to Battery ('WS': Wind to Storage)
  # 'GL', #Grid to Load ('GC': Grid to Consumer)
  'GB', #Grid to Battery ('GS': Grid to Storage)
  # 'BL', #Battery to Load ('SC': Storage to Consumer)
]

4.3.3 Exogenous information variables

The exogenous information variables represent what we did not know (when we made a decision). These are the variables that we cannot control directly. The information in these variables become available after we make the decision $x_t$.

When we assume that the price in each time period is revealed, without any model to predict the price based on past prices, we have, using approach 1:

\[ p_{t+1} = W_{t+1} \]

Alternatively, when we assume that we observe the change in price $\hat{p}_{t+1}=p_{t+1}-p_{t}$, we have, using approach 2:

\[ \begin{aligned} p_{t+1} &= p_t + W_{t+1} \\ &= p_t + \hat{p}_{t+1} \end{aligned} \]

We will make use of approach 2 which means that the exogenous information, $W_{t+1}$, is the observed change in price of the share.

The exogenous information have been preprocessed and is captured in:

EXOG_PARAMS['hist_price']
EXOG_PARAMS['price_changes_sorted']
EXOG_PARAMS['discrete_price_change_list']
EXOG_PARAMS['discrete_price_change_cdf']

The latest exogenous information can be accessed by calling the W_fn() method from class Model().

4.3.4 Transition function

The transition function describe how the state variables evolve over time. Because we currently have two state variables in the state, $S_t=(R_t,p_t)$, we have the equations:

\[ \begin{aligned} R_{t+1} &= R_t + \eta x_t \\ p_{t+1} &= p_t + \hat{p}_{t+1} \end{aligned} \]

Collectively, they represent the general transition function:

\[ S_{t+1} = S^M(S_t,X^{\pi}(S_t)) \]

4.3.5 Objective function

The objective function captures the performance metrics of the solution to the problem. It is given by:

\[ \max_{\pi} \mathbb{E} \sum_{t=0}^T C(S_t,x_t) \]

where \[ C(S_t,x_t) = -p_tx_t \]

4.3.6 Implementation of the System-Under-Steer (SUS) Model

class Model():
    def __init__(
        self, S_0_info, W_fn=None, S__M_fn=None, C_fn=None):
        self.S_0_info = S_0_info
        self.State = namedtuple('State', SNAMES) #. 'class'
        self.S_t = self.build_state(S_0_info) #. 'instance'
        self.Decision = namedtuple('Decision', xNAMES) #. 'class'
        self.prng = np.random.RandomState(PARAMS['seed'])
        self.Ccum = 0.0 #. cumulative reward

    def reset(self):
        self.Ccum = 0.0
        self.S_t = self.build_state(self.S_0_info)

    def build_state(self, info):
        return self.State(*[info[sn] for sn in SNAMES])

    def build_decision(self, info):
        return self.Decision(*[info[xn] for xn in xNAMES])

    def W_fn(self, t):
        W_tt1 = EXOG_PARAMS['hist_price'][t]
        return W_tt1

    def S__M_fn(self, t, S_t, x_t, W_tt1):
        # print(f'...in S__M_fn()...\n\t{x_t=}')
        # R_t
        R_tt1 = {}
        for en in eNAMES:
          R_tt1[en] = S_t.R_t[en] + x_t.x_t[en]

        # p_t
        p_tt1 = {}
        p_tt1['GB'] = W_tt1

        if len(SNAMES) == 2:
            S_tt1 = self.build_state({'R_t': R_tt1, 'p_t': p_tt1})
        elif len(SNAMES) == 3:
            S_tt1 = self.build_state({'R_t': R_tt1, 'p_t': p_tt1, 'p_t_1': self.S_t.p_t['GB']})
        return S_tt1

    def C_fn(self, S_t, x_t, W_tt1):
        # print(f'...in C_fn()...\n\t{x_t=}')
        C_t = S_t.p_t['GB']*( -PARAMS['eta']*x_t.x_t['GB'] )#. C(S_t, x_t, W_t+1); x_t_GB>0 for buy, <0 for sell
        return C_t

    def step(self, t, x_t):
        INDENT = '\t\t'
        # print(f"{INDENT}..... M. step() .....")
        # print(f'{INDENT}{x_t=}')
        W_tt1 = self.W_fn(t)
        self.Ccum += self.C_fn(self.S_t, x_t, W_tt1)
        self.S_t = self.S__M_fn(t, self.S_t, x_t, W_tt1)
        return (self.S_t, self.Ccum, x_t) #. for plotting

4.4 Uncertainty Model

As mentioned above in section 3, we make use of an empirical distribution rather than to try and fit the data to a parametric distribution. This involves the computation of a cumulative distribution from the data. We first sort the prices from smallest to largest. Let this ordered sequence be represented by $\tilde{p}_t$ where $\tilde{p}_{t-1} \le \tilde{p}_t$. Also, let $T$ be the number of time periods. The percentage of time periods with a price less than $\tilde{p}_t$ is then $t/T$. The empirical cumulative distribution is given by \[ F_P(\tilde{p}_t) = \frac{t}{T} \]

4.5 Policy Design

There are two main meta-classes of policy design. Each of these has two subclasses: - Policy Search - Policy Function Approximations (PFAs) - Cost Function Approximations (CFAs) - Lookahead - Value Function Approximations (VFAs) - Direct Lookaheads (DLAs)

In this project we will use two approaches: - A simple buy low, sell high parameterized policy (from the PFA class) - A Bellman policy (from the VFA class)

4.5.1 Implementation of Policy Design

import random
class Policy():
  def __init__(self, model):
    self.model = model
    self.Policy = namedtuple('Policy', piNAMES) #. 'class'
    self.Theta = namedtuple('Theta', thNAMES) #. 'class'

  def build_policy(self, info):
    return self.Policy(*[info[pin] for pin in piNAMES])

  def build_theta(self, info):
    return self.Theta(*[info[thn] for thn in thNAMES])

  def X__BuyLowSellHigh(self, t, S_t, theta): #. SDAM-9.4.1
    info = {
        'x_t': {en: 0 for en in eNAMES} #default is hold
    }
    if t >= T:
      print(f"ERROR: t={t} should not reach or exceed the max steps ({T})")
      return self.model.build_decision(info)
    if t == T - 1: #Last time period - sell
      info['x_t_GB'] = -S_t.R_t['GB'] #sell the whole inventory
      # print(f'last t for this sample-path: selling all ...')
    else:
      #. (SDAM-eq9.11): X^lohi(S_t|theta)
      theta__buy = theta.thLo['GB'] # theta__buy
      theta__sell = theta.thHi['GB'] # theta__sell
      if S_t.p_t['GB'] <= theta__buy: # BUY if p_t <= theta__buy
        info['x_t']['GB'] = (PARAMS['R__max'] - S_t.R_t['GB'])/PARAMS['eta']
      elif S_t.p_t['GB'] >= theta__sell: # SELL if p_t >= theta__sell
        info['x_t']['GB'] = -S_t.R_t['GB'] #sell the whole inventory
      else: # HOLD if theta__buy < p_t < theta__sell
        info['x_t']['GB'] = 0
    return self.model.build_decision(info)

  def X__Bellman(self, t, S_t, bellmanModel, T): #. SDAM-9.4.2
      INDENT = '\t'
      # print(f"{INDENT}..... P.X__Bellman() .....")
      info = {
          'x_t': {en: 0 for en in eNAMES} #default is hold
      }
      p_t = S_t.p_t['GB']
      R_t = S_t.R_t['GB']
      # print(f'{INDENT}X_bellman invocation: {R_t=:.2f}, {p_t=:.2f}')
      vMax = -np.inf #.
      dMax = None #.
      F_P = EXOG_PARAMS['discrete_price_change_cdf']
      for d in POSSIBLE_DECISIONS: #. for each x_t, relates to discrete_energy, R_t
          C_t = S_t.p_t['GB']*( -PARAMS['eta']*d )#. C(S_t, x_t, W_t+1); x_t_GB>0 for buy, <0 for sell
          Sum_w = 0
          w_idx = 0
          for w in EXOG_PARAMS['discrete_price_change_list']: #. for each w
              f__W = F_P[w_idx] if w_idx == 0 else F_P[w_idx] - F_P[w_idx - 1]
              # //////////////////////////////
              # non-en version:
              tmpS_t = self.model.build_state({'R_t': S_t.R_t['GB'], 'p_t': S_t.p_t['GB']})
              # S_tt1 = bellmanModel.S__M(S_t, d, w)
              S_tt1 = bellmanModel.S__M(tmpS_t, d, w)
              # \\\\\\\\\\
              try:
                  V_tt1 = bellmanModel.V_tIS_tI[t+1][S_tt1] if t < bellmanModel.time else bellmanModel.terminalContribution
              except KeyError as ke:
                  # print(f'Key {ke} Not Found in V_tIS_tI[{t + 1}][{S_tt1}]')
                  # print(f'&&&&&&&&&&& {t=}, {S_t=}, {S_tt1=}, {d=}, {w=}'); #print('.', end='')
                  # V_tt1 = 0.0 #no
                  # V_tt1 = 100.0 #less so
                  V_tt1 = 1_000.0 #promising
                  # V_tt1 = 10_000.0 #less so
                  # continue #no
              Sum_w += f__W*V_tt1
              w_idx += 1
          # print(f"{w_idx=}")
          v = C_t + Sum_w #.
          # print(f'{INDENT}  {d=}, {v=:.0f}, {vMax=:.0f}, {dMax=}')
          if (v > vMax):
              # print(f'{INDENT}    {v=:.0f} is greater than {vMax=:.0f}')
              vMax = v; #print(f'{INDENT}    new {vMax=:.0f}')
              dMax = d; #print(f'{INDENT}    new {dMax=}')
      # return maxDec
      if dMax > 0: #BUY
          info['x_t']['GB'] = min(dMax, (PARAMS['R__max'] - S_t.R_t['GB'])/PARAMS['eta'])
      elif dMax < 0: #SELL
          info['x_t']['GB'] = max(-S_t.R_t['GB'], dMax) #sell the whole inventory
      else:
          # print(f'{INDENT}### {dMax=}')
          info['x_t']['GB'] = 0.0 #HOLD
      return self.model.build_decision(info)

  def X__Bellman_random(self, t, S_t, bellmanModel, T): #. SDAM-9.4.2
      info = {
          'x_t_EL': 0, #Wind to Load ('EC': Wind to Consumer)
          'x_t_EB': 0, #Wind to Battery ('WS': Wind to Storage)
          'x_t_GL': 0, #Grid to Load ('GC': Grid to Consumer)
          'x_t_GB': 0, #Grid to Battery ('GS': Grid to Storage); can be negative to reverse flow (sell back to Grid)
          'x_t_BL': 0, #Battery to Load ('SC': Storage to Consumer)
      }
      p_t = S_t.p_t #price
      R_t = S_t.R_t #energy_amount
      dMax = random.choice(POSSIBLE_DECISIONS); print(f'X__bellman_random: {dMax=}')
      if dMax > 0: #BUY
          info['x_t_GB'] = (PARAMS['R__max'] - S_t.R_t)/PARAMS['eta']
      elif dMax < 0: #SELL
          info['x_t_GB'] = -S_t.R_t #sell the whole inventory
      else:
          # print(f'{dMax=}')
          info['x_t_GB'] = 0.0
      return self.model.build_decision(info)

  def grid_search_thetas_2(self, thetasLo, thetasHi):
    thetas = [
    self.build_theta({'thLo': {eNAMES[0]: th0}, 'thHi': {eNAMES[0]: th1}})
    for th0 in thetasLo[eNAMES[0]]
      for th1 in thetasHi[eNAMES[0]]
    ]
    return thetas

  def run_grid_sample_paths(self, theta, piName, record):
      CcumIomega__lI = []
      for l in list(range(L)): #for each sample-path
          # print(f'%%% {l=}')
          M = copy(self.model)
          record_l = [piName, theta, l]
          for t in range(T): #for each transition/step
              # print(f'\t%%% {t=}')
              x_t = getattr(self, piName)(t, M.S_t, theta)

              S_t, Ccum, x_t = M.step(t, x_t)

              record_t = [t] + \
                [S_t.R_t[en] for en in eNAMES] + [S_t.p_t[en] for en in eNAMES] + \
                [Ccum] + \
                [x_t.x_t[en] for en in eNAMES]
              record.append(record_l + record_t)
          CcumIomega__lI.append(M.Ccum) #. just above (SDAM-eq2.9) #. Fhat for this sample-path is in model_copy.cumC
      return CcumIomega__lI

  def perform_grid_search_sample_paths(self, piName, thetas, exploitSym=True):
      Cbarcum = defaultdict(float)
      Ctilcum = defaultdict(float)
      expCbarcum = defaultdict(float)
      expCtilcum = defaultdict(float)
      numThetas = len(thetas)
      record = []
      print(f'{numThetas=}'); print(f'{thetas=}')
      nth = 500
      i = 0; print(f'... printing every {nth}th theta ...')
      for theta in thetas:
        # theta=({'AAA': 168.0, 'BBB': 72.0}, {'AAA': 200.0, 'BBB': 90.0})
        # a dict cannot be used as a key, so we define
        # theta_key = ((168.0, 72.0), (200.0, 90.0)):
        theta_key = tuple(tuple(itm.values()) for itm in theta)
        # theta_key = theta

        # exploit symmetry to half compute time
        if exploitSym and (theta.thLo['GB'] >= theta.thHi['GB']):
          Cbarcum[theta_key], Ctilcum[theta_key] = 0, 0
        else:
          # print(f'\n=== {theta=} ===')
          if i%nth == 0: print(f'=== ({i:,} / {numThetas:,}), theta={theta} ===')

          CcumIomega__lI = self.run_grid_sample_paths(theta, piName, record)

          Cbarcum_tmp = np.array(CcumIomega__lI).mean()
          Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)

          Cbarcum[theta_key] = Cbarcum_tmp
          Ctilcum[theta_key] = np.sqrt(Ctilcum_tmp/L)

          expCbarcum_tmp = pd.Series(CcumIomega__lI).expanding().mean()
          expCbarcum[theta_key] = expCbarcum_tmp

          expCtilcum_tmp = pd.Series(CcumIomega__lI).expanding().std()
          expCtilcum[theta_key] = expCtilcum_tmp
          i += 1
      best_theta = max(Cbarcum, key=Cbarcum.get)
      worst_theta = min(Cbarcum, key=Cbarcum.get)

      best_Cbarcum = Cbarcum[best_theta]
      best_Ctilcum = Ctilcum[best_theta]

      worst_Cbarcum = Cbarcum[worst_theta]
      worst_Ctilcum = Ctilcum[worst_theta]

      thetaStar_expCbarcum = expCbarcum[best_theta]
      thetaStar_expCtilcum = expCtilcum[best_theta]
      thetaStar_expCtilcum[0] = 0 #set NaN to 0

      # best_theta_w_enames = tuple(( ({eNAMES[0]: itm[0], eNAMES[1]: itm[1]})) for itm in best_theta)
      best_theta_w_enames = tuple(( ({eNAMES[0]: itm[0]})) for itm in best_theta)
      best_theta_en = self.build_theta({'thLo': best_theta_w_enames[0], 'thHi': best_theta_w_enames[1]})
      print(f'best_theta_en:\n{best_theta_en}\n{best_Cbarcum=:.2f}\n{best_Ctilcum=:.2f}')

      # worst_theta_w_enames = tuple(( ({eNAMES[0]: itm[0], eNAMES[1]: itm[1]})) for itm in worst_theta)
      worst_theta_w_enames = tuple(( ({eNAMES[0]: itm[0]})) for itm in worst_theta)
      worst_theta_en = self.build_theta({'thLo': worst_theta_w_enames[0], 'thHi': worst_theta_w_enames[1]})
      print(f'worst_theta_en:\n{worst_theta_en}\n{worst_Cbarcum=:.2f}\n{worst_Ctilcum=:.2f}')

      return \
        thetaStar_expCbarcum, thetaStar_expCtilcum, \
        Cbarcum, Ctilcum, \
        best_theta_en, worst_theta_en, \
        best_Cbarcum, worst_Cbarcum, \
        best_Ctilcum, worst_Ctilcum, \
        record

  def run_bellman_sample_paths(self, inc, piInfo, piName, record): #. piInfo is bdp
      INDENT = '\t'
      print(f"{INDENT}..... P.run_bellman_sample_paths() .....")
      CcumIomega__lI = []
      for l in list(range(L)): #for each sample-path
          print(f"{INDENT}{l=}")
          M = copy(self.model)
          T = PARAMS['T']
          record_l = [piName, inc, l]
          for t in range(T): #for each transition/step
              x_t = getattr(self, piName)(t, M.S_t, piInfo, T) #. piInfo is bdp

              S_t, Ccum, x_t = M.step(t, x_t)

              record_t = [t] + \
                [S_t.R_t[en] for en in eNAMES] + [S_t.p_t[en] for en in eNAMES] + \
                [Ccum] + \
                [x_t.x_t[en] for en in eNAMES]
              record.append(record_l + record_t)
          CcumIomega__lI.append(M.Ccum)
      return CcumIomega__lI

  def perform_bellman_search_sample_paths(self, piName, R__disc, minPrice, maxPrice, incs):
      INDENT = ''
      print(f"{INDENT}..... P.perform_bellman_search_sample_paths() .....")
      Cbarcum = defaultdict(float)
      Ctilcum = defaultdict(float)
      bdp = {}
      expCbarcum = defaultdict(float)
      expCtilcum = defaultdict(float)
      best_inc_evolving = -np.inf
      best_Cbarcum_evolving = -np.inf
      best_bdp_evolving = None
      numIncs = len(incs)
      record = []
      print(f'{numIncs=}'); print(f'{incs=}')
      nth = 1
      i = 0; print(f'{INDENT}printing every {nth}th inc')
      for inc in incs: #for each discretization
          inc_key = inc

          # print(f'\n=== {inc=} ===')
          if i%nth == 0: print(f'{INDENT}=== ({i:,} / {numIncs - 1:,}), inc={inc} ===')

          p__disc = np.arange(minPrice, maxPrice + inc, inc)
          # print(f"{INDENT}Starting BackwardDP 2D for price discretization with inc={inc}")
          test_2D_bdp = BDP(
              p__disc=p__disc, #discrete prices
              R__disc=R__disc, #discrete energy
              stop_time=T,
              model=copy(M))
          test_2D_bdp.compute_value_function()

          CcumIomega__lI = self.run_bellman_sample_paths(inc, test_2D_bdp, piName, record)

          Cbarcum_tmp = np.array(CcumIomega__lI).mean()
          Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)

          Cbarcum[inc_key] = Cbarcum_tmp
          bdp[inc_key] = test_2D_bdp
          Ctilcum[inc_key] = np.sqrt(Ctilcum_tmp/L)

          expCbarcum_tmp = pd.Series(CcumIomega__lI).expanding().mean()
          expCbarcum[inc_key] = expCbarcum_tmp

          expCtilcum_tmp = pd.Series(CcumIomega__lI).expanding().std()
          expCtilcum[inc_key] = expCtilcum_tmp

          if(Cbarcum_tmp > best_Cbarcum_evolving):
              best_inc_evolving  = inc
              best_Cbarcum_evolving = Cbarcum_tmp
              best_bdp_evolving = test_2D_bdp
          print(f"{INDENT}Finishing inc {inc} with {best_inc_evolving=}, {best_Cbarcum_evolving=}")
          i += 1
      print(f"FOR COMPARISON (final evolving values): \n{best_inc_evolving=}, {best_Cbarcum_evolving=}")

      best_inc = max(Cbarcum, key=Cbarcum.get)
      worst_inc = min(Cbarcum, key=Cbarcum.get)

      best_Cbarcum = Cbarcum[best_inc]
      best_Ctilcum = Ctilcum[best_inc]

      worst_Cbarcum = Cbarcum[worst_inc]
      worst_Ctilcum = Ctilcum[worst_inc]

      incStar_expCbarcum = expCbarcum[best_inc]
      incStar_expCtilcum = expCtilcum[best_inc]
      incStar_expCtilcum[0] = 0 #set NaN to 0

      best_bdp = bdp[best_inc]

      return \
          incStar_expCbarcum, incStar_expCtilcum, \
          Cbarcum, Ctilcum, \
          best_inc, worst_inc, \
          best_Cbarcum, worst_Cbarcum, \
          best_Ctilcum, worst_Ctilcum, \
          bdp, \
          best_bdp, \
          record

  ############################################################################
  ### PLOTTING
  ############################################################################
  def round_theta(self, complex_theta):
    thetas_rounded = []
    for theta in complex_theta:
      evalues_rounded = []
      for _, evalue in theta.items():
        evalues_rounded.append(float(f"{evalue:f}"))
      thetas_rounded.append(tuple(evalues_rounded))
    return str(tuple(thetas_rounded))

  def plot_Fhat_map_2(self, FhatI_theta_I, thetasX, thetasY, labelX, labelY, title):
      Fhat_values = [
        FhatI_theta_I[
          # (thetaX,thetaY)
          ((thetaX,),(thetaY,))
        ]
          for thetaY in thetasY for thetaX in thetasX
      ]
      Fhats = np.array(Fhat_values)
      increment_count = len(thetasX)
      Fhats = np.reshape(Fhats, (-1, increment_count))#.

      fig, ax = plt.subplots()
      im = ax.imshow(Fhats, cmap='hot', origin='lower', aspect='auto')
      # create colorbar
      cbar = ax.figure.colorbar(im, ax=ax)
      # cbar.ax.set_ylabel(cbarlabel, rotation=-90, va="bottom")

      ax.set_xticks(np.arange(0, len(thetasX), 5))#.
      # ax.set_xticks(np.arange(len(thetasX)))

      ax.set_yticks(np.arange(0, len(thetasY), 5))#.
      # ax.set_yticks(np.arange(len(thetasY)))

      # NOTE: round tick labels, else very messy
      # function round() does not work, have to do this way
      thetasX_form = [f'{th:.0f}' for th in thetasX]
      thetasY_form = [f'{th:.0f}' for th in thetasY]

      ax.set_xticklabels(thetasX[::5])
      # ax.set_xticklabels(thetasX); ax.set_xticklabels(thetasX_form)

      ax.set_yticklabels(thetasY[::5])
      # ax.set_yticklabels(thetasY); ax.set_yticklabels(thetasY_form)

      # rotate the tick labels and set their alignment.
      #plt.setp(ax.get_xticklabels(), rotation=45, ha="right",rotation_mode="anchor")

      ax.set_title(title)
      ax.set_xlabel(labelX)
      ax.set_ylabel(labelY)

      #fig.tight_layout()
      plt.show()
      return True

  # color_style examples: 'r-', 'b:', 'g--'
  def plot_Fhat_chart(self, FhatI_theta_I, thetasX, labelX, labelY, title, color_style, thetaStar):
      mpl.rcParams['lines.linewidth'] = 1.2
      xylabelsize = 16
      # plt.figure(figsize=(13, 9))
      plt.figure(figsize=(13, 4))
      plt.title(title, fontsize=20)
      Fhats = FhatI_theta_I.values()
      plt.plot(thetasX, Fhats, color_style)
      plt.axvline(x=thetaStar, color='k', linestyle=':')
      plt.xlabel(labelX, rotation=0, labelpad=10, ha='right', va='center', fontweight='bold', size=xylabelsize)
      plt.ylabel(labelY, rotation=0, labelpad=1, ha='right', va='center', fontweight='normal', size=xylabelsize)
      plt.show()

  # expanding Fhat chart
  def plot_expFhat_chart(self, df, labelX, labelY, title, color_style):
    mpl.rcParams['lines.linewidth'] = 1.2
    xylabelsize = 16
    plt.figure(figsize=(13, 4))
    plt.title(title, fontsize=20)
    plt.plot(df, color_style)
    plt.xlabel(labelX, rotation=0, labelpad=10, ha='right', va='center', fontweight='bold', size=xylabelsize)
    plt.ylabel(labelY, rotation=0, labelpad=1, ha='right', va='center', fontweight='normal', size=xylabelsize)
    plt.show()

  # expanding Fhat charts
  def plot_expFhat_charts(self, means, stdvs, labelX, labelY, suptitle, pars=defaultdict(str)):
    n_charts = 2
    xlabelsize = 14
    ylabelsize = 14
    mpl.rcParams['lines.linewidth'] = 1.2
    default_colors = plt.rcParams['axes.prop_cycle'].by_key()['color']
    fig, axs = plt.subplots(n_charts, sharex=True)
    fig.set_figwidth(13); fig.set_figheight(9)
    fig.suptitle(suptitle, fontsize=18)

    xi = 0
    legendlabels = []
    axs[xi].set_title(r"$exp\bar{C}^{cum}(\theta^*)$", loc='right', fontsize=16)
    for i,itm in enumerate(means.items()):
      axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
      leg = axs[xi].plot(itm[1], color=pars['colors'][i]); #print(f"{pars['colors'][i]}")
      legendlabels.append(itm[0])
    axs[xi].set_ylabel(labelY, rotation=0, ha='right', va='center', fontweight='normal', size=ylabelsize)

    xi = 1
    axs[xi].set_title(r"$exp\tilde{C}^{cum}(\theta^*)$", loc='right', fontsize=16)
    for i,itm in enumerate(stdvs.items()):
      axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
      # leg = axs[xi].plot(itm[1], default_colors[i], linestyle='--')
      leg = axs[xi].plot(itm[1], pars['colors'][i], linestyle='--')
    axs[xi].set_ylabel(labelY, rotation=0, ha='right', va='center', fontweight='normal', size=ylabelsize)

    fig.legend(
          # [leg],
          labels=legendlabels,
          title="Policies",
          loc='upper right',
          fancybox=True,
          shadow=True,
          ncol=1)
    plt.xlabel(labelX, rotation=0, labelpad=10, ha='right', va='center', fontweight='normal', size=xlabelsize)
    plt.show()

  def plot_records(self, df, df_non, pars=defaultdict(str)):
    # legendlabels = []
    n_e = len(eNAMES) #number of entities
    n_charts = 3*n_e + 1
    ylabelsize = 14
    mpl.rcParams['lines.linewidth'] = 1.2
    mycolors = ['g', 'b']
    fig, axs = plt.subplots(n_charts, sharex=True)
    fig.set_figwidth(13); fig.set_figheight(9)
    fig.suptitle(pars['suptitle'], fontsize=14)

    xi = 0
    for i,e in enumerate(eNAMES):
      axs[xi+i].set_ylim(auto=True); axs[xi+i].spines['top'].set_visible(False); axs[xi+i].spines['right'].set_visible(True); axs[xi+i].spines['bottom'].set_visible(False)
      axs[xi+i].step(df[f'x_t_{e}'], 'm-', where='post')
      if not df_non is None: axs[xi+i].step(df_non[f'x_t_{e}'], 'c-.', where='post')
      axs[xi+i].axhline(y=0, color='k', linestyle=':')
      # y1ab = '$x_{t}$'
      y1ab = '$x_{t,'+f'{e}'+'}$'
      axs[xi+i].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
      for j in range(df.shape[0]//T): axs[xi+i].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = n_e
    for i,e in enumerate(eNAMES):
      axs[xi+i].set_ylim(auto=True); axs[xi+i].spines['top'].set_visible(False); axs[xi+i].spines['right'].set_visible(True); axs[xi+i].spines['bottom'].set_visible(False)
      axs[xi+i].step(df[f'p_t_{e}'], mycolors[xi%len(mycolors)], where='post')
      if not df_non is None: axs[xi+i].step(df_non[f'p_t_{e}'], 'c-.', where='post')
      # axs[xi+i].axhline(y=0, color='k', linestyle=':')
      if(pars['thetaLo']): axs[xi+i].text(-4, pars['thetaLo'][e], r'$\theta^{Lo}$' + f"={pars['thetaLo'][e]:.1f}", size=10, color='m')
      if(pars['thetaLo']): axs[xi+i].axhline(y=pars['thetaLo'][e], color='m', linestyle=':')
      if(pars['thetaHi']): axs[xi+i].text(-4, pars['thetaHi'][e], r'$\theta^{Hi}$' + f"={pars['thetaHi'][e]:.1f}", size=10, color='m')
      if(pars['thetaHi']): axs[xi+i].axhline(y=pars['thetaHi'][e], color='m', linestyle=':')

      if(pars['thetaLoNon']): axs[xi+i].text(-4, pars['thetaLoNon'][e], r'$\theta^{Lo}$' + f"={pars['thetaLoNon'][e]:.1f}", size=10, color='c')
      if(pars['thetaLoNon']): axs[xi+i].axhline(y=pars['thetaLoNon'][e], color='c', linestyle=':')
      if(pars['thetaHiNon']): axs[xi+i].text(-4, pars['thetaHiNon'][e], r'$\theta^{Hi}$' + f"={pars['thetaHiNon'][e]:.1f}", size=10, color='c')
      if(pars['thetaHiNon']): axs[xi+i].axhline(y=pars['thetaHiNon'][e], color='c', linestyle=':')
      y1ab = '$p_{t,'+f'{e}'+'}$'
      axs[xi+i].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
      for j in range(df.shape[0]//T): axs[xi+i].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = 2*n_e
    for i,e in enumerate(eNAMES):
      axs[xi+i].set_ylim(auto=True); axs[xi+i].spines['top'].set_visible(False); axs[xi+i].spines['right'].set_visible(True); axs[xi+i].spines['bottom'].set_visible(False)
      axs[xi+i].step(df[f'R_t_{e}'], 'm-', where='post')
      if not df_non is None: axs[xi+i].step(df_non[f'R_t_{e}'], 'c-.', where='post')
      axs[xi+i].axhline(y=0, color='k', linestyle=':')
      y1ab = '$R_{t,'+f'{e}'+'}$'
      axs[xi+i].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
      for j in range(df.shape[0]//T): axs[xi+i].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = 3*n_e
    axs[xi].set_ylim(auto=True); axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
    axs[xi].step(df['Ccum'], 'm-', where='post')
    if not df_non is None: axs[xi].step(df_non['Ccum'], 'c-.', where='post')
    axs[xi].axhline(y=0, color='k', linestyle=':')
    axs[xi].set_ylabel('$C^{cum}$'+'\n'+'$\mathrm{(Profit)}$'+'\n'+''+'$\mathrm{[\$]}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
    for j in range(df.shape[0]//T): axs[xi].axvline(x=(j+1)*T, color='grey', ls=':')

    axs[xi].set_xlabel('$t\ \mathrm{[decision\ windows]}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
    # fig.legend(labels=legendlabels, loc='lower left', fontsize=16)

  def plot_evalu_comparison(self, df1, df2, df3, pars=defaultdict(str)):
    legendlabels = ['X__BuyLowSellHigh', 'X__Bellman']
    n_charts = 4
    ylabelsize = 14
    mpl.rcParams['lines.linewidth'] = 1.2
    fig, axs = plt.subplots(n_charts, sharex=True)
    fig.set_figwidth(13); fig.set_figheight(9)
    thetaStarStr = []
    for cmp in pars["thetaStar"]: thetaStarStr.append(f'{cmp:.1f}')
    thetaStarStr = '(' + ', '.join(thetaStarStr) + ')'
    fig.suptitle(pars['suptitle'], fontsize=16)

    xi = 0
    axs[xi].set_ylim(auto=True); axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
    axs[xi].step(df1[f'x_t_GB'], 'r-', where='post')
    axs[xi].step(df2[f'x_t_GB'], 'g-.', where='post')
    # axs[xi].step(df3[f'x_t'], 'b:', where='post')
    axs[xi].axhline(y=0, color='k', linestyle=':')
    y1ab = '$x_{t,GB}$'
    axs[xi].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
    for j in range(df1.shape[0]//T): axs[xi].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = 1
    axs[xi].set_ylim(auto=True); axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
    axs[xi].step(df1[f'R_t_GB'], 'r-', where='post')
    axs[xi].step(df2[f'R_t_GB'], 'g-.', where='post')
    # axs[xi].step(df3[f'R_t_GB'], 'b:', where='post')
    axs[xi].axhline(y=0, color='k', linestyle=':')
    y1ab = '$R_{t,GB}$'
    axs[xi].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
    for j in range(df1.shape[0]//T): axs[xi].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = 2
    axs[xi].set_ylim(auto=True); axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
    axs[xi].step(df1[f'p_t_GB'], 'r-', where='post')
    axs[xi].step(df2[f'p_t_GB'], 'g-.', where='post')
    # axs[xi].step(df3[f'p_t'], 'b:', where='post')
    axs[xi].axhline(y=0, color='k', linestyle=':')

    if(pars['lower_non']): axs[xi].text(-4, pars['lower_non'], r'$\theta^{lower}$' + f"={pars['lower_non']:.1f}", size=10, color='c')
    if(pars['lower_non']): axs[xi].axhline(y=pars['lower_non'], color='c', linestyle=':')

    if(pars['upper_non']): axs[xi].text(-4, pars['upper_non'], r'$\theta^{upper}$' + f"={pars['upper_non']:.1f}", size=10, color='c')
    if(pars['upper_non']): axs[xi].axhline(y=pars['upper_non'], color='c', linestyle=':')

    if(pars['lower']): axs[xi].text(-4, pars['lower'], r'$\theta^{lower}$' + f"={pars['lower']:.1f}", size=10, color='m')
    if(pars['lower']): axs[xi].axhline(y=pars['lower'], color='m', linestyle=':')

    if(pars['upper']): axs[xi].text(-4, pars['upper'], r'$\theta^{upper}$' + f"={pars['upper']:.1f}", size=10, color='m')
    if(pars['upper']): axs[xi].axhline(y=pars['upper'], color='m', linestyle=':')

    if(pars['alpha_non']): axs[xi].text(-4, pars['alpha_non'], r'$\theta^{alpha}$' + f"={pars['alpha_non']:.1f}", size=10, color='c')
    if(pars['alpha_non']): axs[xi].axhline(y=pars['alpha_non'], color='c', linestyle=':')

    if(pars['trackSignal_non']): axs[xi].text(-4, pars['trackSignal_non'], r'$\theta^{trackSignal}$' + f"={pars['trackSignal_non']:.1f}", size=10, color='c')
    if(pars['trackSignal_non']): axs[xi].axhline(y=pars['trackSignal_non'], color='c', linestyle=':')

    if(pars['alpha']): axs[xi].text(-4, pars['alpha'], r'$\theta^{alpha}$' + f"={pars['alpha']:.1f}", size=10, color='m')
    if(pars['alpha']): axs[xi].axhline(y=pars['alpha'], color='m', linestyle=':')

    if(pars['trackSignal']): axs[xi].text(-4, pars['trackSignal'], r'$\theta^{trackSignal}$' + f"={pars['trackSignal']:.1f}", size=10, color='m')
    if(pars['trackSignal']): axs[xi].axhline(y=pars['trackSignal'], color='m', linestyle=':')

    y1ab = '$p_{t,GB}$'
    axs[xi].set_ylabel(y1ab, rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize)
    for j in range(df1.shape[0]//T): axs[xi].axvline(x=(j+1)*T, color='grey', ls=':')

    xi = 3
    axs[xi].set_ylim(auto=True); axs[xi].spines['top'].set_visible(False); axs[xi].spines['right'].set_visible(True); axs[xi].spines['bottom'].set_visible(False)
    axs[xi].step(df1['Ccum'], 'r-', where='post')
    axs[xi].step(df2['Ccum'], 'g-.', where='post')
    # axs[xi].step(df3['Ccum'], 'b:', where='post')
    axs[xi].axhline(y=0, color='k', linestyle=':')
    axs[xi].set_ylabel('$C^{cum}$'+'\n'+'$\mathrm{(Profit)}$'+'\n'+''+'$\mathrm{[\$]}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
    axs[xi].set_xlabel('$t\ \mathrm{[decision\ windows]}$', rotation=0, ha='right', va='center', fontweight='bold', size=ylabelsize);
    for j in range(df1.shape[0]//T): axs[xi].axvline(x=(j+1)*T, color='grey', ls=':')

    fig.legend(
          # [leg],
          labels=legendlabels,
          # labels=labels,
          title="Policies",
          loc='upper right',
          fontsize=14,
          fancybox=True,
          shadow=True,
          ncol=1)

class BDP(): #. SDAM-9.4.2: Backward Dynamic Programming; SDAM-fig9.6; RLSO-fig14.3
    def __init__(self, p__disc, R__disc, stop_time, model):
        self.R__disc = R__disc #discrete energy
        self.p__disc = p__disc #discrete prices
        self.time = stop_time - 1
        self.model = model
        self.terminalContribution = 0
        self.V_tIS_tI = None #this will store the vfas; computed by the method bellman_2D or bellman_3D

    def S__M(self, S_t, x_t, exogInfo):
        """
        this function tells us what state we transition to if we are in some state and make a decision
        (restricted to states in possible_states)
        :param state: namedtuple - the state of the model at a given time
        :param decision: namedtuple - contains all decision info
        :param exog_info: any exogenous info
        :return: new state object
        """
        R_tt1 = self.model.S_t.R_t['GB'] + PARAMS['eta']*x_t #. x_t here is number
        R_tt1_adjusted = math.ceil(R_tt1)

        if len(S_t) == 2:
            p_tt1 = S_t.p_t + exogInfo
        elif len(S_t) == 3:
            p_tt1 = 0.5*S_t.p_t_1 + 0.5*S_t.p_t + exogInfo

        if p_tt1 <= min(self.p__disc):
            p_tt1_adjusted = min(self.p__disc)
        elif p_tt1 >= max(self.p__disc):
            p_tt1_adjusted = max(self.p__disc)
        else:
            index = bisect(self.p__disc, p_tt1)
            p_tt1_adjusted = self.p__disc[index]

        if len(S_t) == 2:
            S_tt1 = self.model.build_state({'R_t': R_tt1_adjusted, 'p_t': p_tt1_adjusted})
        elif len(S_t) == 3:
            p_t = S_t.p_t #.
            if p_t <= min(self.p__disc):
                p_t_adjusted = min(self.p__disc)
            elif p_t >= max(self.p__disc):
                p_t_adjusted = max(self.p__disc)
            else:
                index = bisect(self.p__disc, p_t)
                p_t_adjusted = self.p__disc[index]
            S_tt1 = self.model.build_state({ #.
                'R_t': R_tt1_adjusted,
                'p_t': p_tt1_adjusted,
                'p_t_1': p_t_adjusted
            })
        return S_tt1

    def compute_value_function(self): #does not use eNAMES
        """
        this function computes the value function using Bellman's equation for a 2D state variable
        :return: list - list of contribution values
        """
        INDENT = '\t'
        print(f"{INDENT}..... BDP.compute_value_function() .....")
        # make list of all possible 2D states using discretized values
        self.possibleStates = []
        if len(SNAMES) == 2:
            for price in self.p__disc:
                for energy in self.R__disc:
                    S_t = self.model.build_state({'R_t': energy, 'p_t': price})
                    self.possibleStates.append(S_t)
        else:
            for p in self.p__disc:
                for prev_p in self.p__disc:
                    for energy in self.R__disc:
                        S_t = self.model.build_state({'R_t': energy, 'p_t': p, 'p_t_1': prev_p})
                        self.possibleStates.append(S_t)

        print(f"{INDENT}State dimension: {len(SNAMES)}. \
          State space size: {len(self.possibleStates)}. \
          Exogenous info size: {len(EXOG_PARAMS['discrete_price_change_list'])}")
        print(f'{INDENT}{self.p__disc=}')
        print(f'{INDENT}{self.R__disc=}')
        print(f'{INDENT}{self.possibleStates=}')

        t = self.time # T - 1
        V_tIS_tI = defaultdict(dict) #.
        F_P = EXOG_PARAMS['discrete_price_change_cdf'] #.
        while t != -1: #. for each t
            # print(f'{INDENT}{t=}', end='\r')
            # print(t, end='\r')
            if t%10 == 0: print(f'{INDENT}{t=}')
            maxDict = {} #.
            for S_t in self.possibleStates: #. for each S_t
                p_t = S_t.p_t #.
                R_t = S_t.R_t #.
                vList = []
                for d in POSSIBLE_DECISIONS: #. for each x_t
                    C_t = S_t.p_t*( -PARAMS['eta']*d )#. C(S_t, x_t, W_t+1); x_t_GB>0 for buy, <0 for sell
                    Sum_w = 0 #.
                    w_idx = 0
                    for w in EXOG_PARAMS['discrete_price_change_list']: #. for each w
                        f__W = F_P[w_idx] if w_idx == 0 else F_P[w_idx] - F_P[w_idx - 1]
                        S_tt1 = self.S__M(S_t, d, w); #print(f'{INDENT}###{next_state=}') #.
                        # print(f'{INDENT}&&&&&&&&&&& {t=}, {S_t=}, {S_tt1=}, {d=}, {w=}')
                        # time.sleep(1)
                        try:
                            V_tt1 = V_tIS_tI[t + 1][S_tt1] if t < self.time else self.terminalContribution
                        except KeyError as ke:
                            # print(f'{INDENT}Key {ke} Not Found in V_tIS_tI[{t + 1}][{S_tt1}]')
                            # print(f'{INDENT}&&&&&&&&&&& {t=}, {S_t=}, {S_tt1=}, {d=}, {w=}'); # print('.', end='')
                            V_tt1 = 0.0
                        Sum_w += f__W*V_tt1
                        w_idx += 1
                    v = C_t + Sum_w #.
                    vList.append(v)
                maxValue = max(vList)
                # print(f'{INDENT}{maxDict=}, {maxValue=}, {S_t=}')
                maxDict.update({S_t: maxValue}) #.
            V_tIS_tI[t] = maxDict; #self.V_tIS_tI = V_tIS_tI #REMOVE
            t -= 1
        self.V_tIS_tI = V_tIS_tI
        return #. returns None

    def compute_value_function_with_en(self): #use eNAMES
    # still bug with maxDict.update({S_t: maxValue}) coz keys cannot have a
    # nested dict
        """
        this function computes the value function using Bellman's equation for a 2D state variable
        :return: list - list of contribution values
        """
        # make list of all possible 2D states using discretized values
        self.possibleStates = []
        if len(SNAMES) == 2:
            for price in self.discretePrices:
                p_t = {} #.
                p_t['GB'] = price #.
                for energy in self.discreteEnergy:
                    R_t = {} #.
                    R_t['GB'] = energy #.
                    S_t = self.model.build_state({'R_t': R_t, 'p_t': p_t}) #.
                    self.possibleStates.append(S_t) #.
        else:
            for p in self.discretePrices:
                p_t = {} #.
                p_t['GB'] = p #.
                for prev_p in self.discretePrices:
                    p_t_1 = {} #.
                    p_t_1['GB'] = prev_p #.
                    for energy in self.discreteEnergy:
                        R_t = {} #.
                        R_t['GB'] = energy #.
                        S_t = self.model.build_state({'R_t': R_t, 'p_t': p_t, 'p_t_1': p_t_1}) #.
                        self.possibleStates.append(S_t) #.

        print("State dimension: {}. State space size: {}. Exogenous info size: {}".format(len(SNAMES),len(self.possibleStates),len(self.discretePriceChanges)))
        print(f'{self.discretePrices=}')
        print(f'{self.discreteEnergy=}')
        print(f'{self.possibleStates=}') #.

        t = self.time
        V_tIS_tI = defaultdict(dict) #.
        while t != -1: #. for each t
            # print(f'{t=}', end='\r')
            # print(t, end='\r')
            if t%10 == 0: print(f'{t}')
            maxDict = {} #.
            for S_t in self.possibleStates: #. for each S_t
                # p_t = S_t.p_t #.
                p_t = S_t.p_t['GB'] #.
                # R_t = S_t.R_t #.
                R_t = S_t.R_t['GB'] #.
                vList = []
                for d in POSSIBLE_DECISIONS: #. for each x_t
                    # C_t = S_t.p_t*( -PARAMS['eta']*d )#. C(S_t, x_t, W_t+1); x_t_GB>0 for buy, <0 for sell
                    C_t = S_t.p_t['GB']*( -PARAMS['eta']*d )#. C(S_t, x_t, W_t+1); x_t_GB>0 for buy, <0 for sell
                    Sum_w = 0 #.
                    w_idx = 0
                    # for w in self.discretePriceChanges: #. for each w
                    for w in EXOG_PARAMS['discrete_price_change_list']: #. for each w
                        f__W = self.f_p[w_idx] if w_idx == 0 else self.f_p[w_idx] - self.f_p[w_idx - 1]
                        S_tt1 = self.S__M(S_t, d, w); #print(f'###{next_state=}') #.
                        # print(f'&&&&&&&&&&& {t=}, {S_t=}, {S_tt1=}, {d=}, {w=}')
                        # time.sleep(1)
                        try:
                            V_tt1 = V_tIS_tI[t + 1][S_tt1] if t < self.time else self.terminalContribution
                        except KeyError as ke:
                            # print(f'Key {ke} Not Found in V_tIS_tI[{t + 1}][{S_tt1}]')
                            # print(f'&&&&&&&&&&& {t=}, {S_t=}, {S_tt1=}, {d=}, {w=}'); # print('.', end='')
                            V_tt1 = 0.0
                            # return V_tIS_tI
                        Sum_w += f__W*V_tt1
                        w_idx += 1
                    v = C_t + Sum_w #.
                    vList.append(v)
                maxValue = max(vList)
                print(f'{maxDict=}, {maxValue=}, {S_t=}')
                maxDict.update({S_t: maxValue}) #.
            V_tIS_tI[t] = maxDict; #self.V_tIS_tI = V_tIS_tI #REMOVE
            t -= 1
        self.V_tIS_tI = V_tIS_tI
        return #. returns None

# example of max_dict for t=7, i.e. V_tIS_tI[7]
# {
    # State(R_t=0.0, p_t=0.0): 110.04629159565617,
    # State(R_t=1.0, p_t=0.0): 110.04629159565617,
    # State(R_t=0.0, p_t=1.0): 108.98857668111593,
    # State(R_t=1.0, p_t=1.0): 110.09968779222704,
    # State(R_t=0.0, p_t=2.0): 107.93584162127829,
    # State(R_t=1.0, p_t=2.0): 110.15806384350051,
    # State(R_t=0.0, p_t=3.0): 106.8882655782204,
    # ...
    # State(R_t=0.0, p_t=106.0): 39.65253639870996,
    # State(R_t=1.0, p_t=106.0): 135.05253639870998,
    # State(R_t=0.0, p_t=107.0): 39.56669555911158,
    # State(R_t=1.0, p_t=107.0): 135.86669555911158,
    # State(R_t=0.0, p_t=108.0): 39.49186057994566,
    # State(R_t=1.0, p_t=108.0): 136.69186057994565}
# }

4.6 Policy Evaluation

4.6.1 Training/Tuning

4.6.1.1 X__BuyLowSellHigh

# setup labels to plot info
R_t_labels = ['R_t_'+en for en in eNAMES]
p_t_labels = ['p_t_'+en for en in eNAMES]
x_t_labels = ['x_t_'+en for en in eNAMES]
labels = ['piName', 'theta', 'l'] + \
  ['t'] + R_t_labels + p_t_labels + \
  ['Ccum'] + x_t_labels
labels

['piName', 'theta', 'l', 't', 'R_t_GB', 'p_t_GB', 'Ccum', 'x_t_GB']

N_SAMPLEPATHS, N_TRANSITIONS

(3, 192)

PARAMS['R_0'], EXOG_PARAMS['hist_price'][0]

(1, 18.91)

%%time
#GridSearch #. SDAM-9.4.1
L = 50 #N_SAMPLEPATHS
T = 100 #N_TRANSITIONS
first_n_t = 4*T
last_n_t = 4*T

M = Model(S_0_INFO)
P = Policy(M)

th_lo = {en: np.arange(TH_LO[en][0], TH_LO[en][1], TH_LO[en][2]) for en in eNAMES}
th_hi = {en: np.arange(TH_HI[en][0], TH_HI[en][1], TH_HI[en][2]) for en in eNAMES}
thetas = P.grid_search_thetas_2(th_lo, th_hi)

thetaStar_expCbarcum_BuyLowSellHigh, thetaStar_expCtilcum_BuyLowSellHigh, \
Cbarcum_BuyLowSellHigh, Ctilcum_BuyLowSellHigh, \
best_theta_BuyLowSellHigh, worst_theta_BuyLowSellHigh, \
best_Cbarcum_BuyLowSellHigh, worst_Cbarcum_BuyLowSellHigh, \
best_Ctilcum_BuyLowSellHigh, worst_Ctilcum_BuyLowSellHigh, \
record_BuyLowSellHigh = \
  P.perform_grid_search_sample_paths("X__BuyLowSellHigh", thetas)
f'{thetaStar_expCbarcum_BuyLowSellHigh.iloc[-1]=:.2f}'
df_first_n_t = pd.DataFrame.from_records(record_BuyLowSellHigh[:first_n_t], columns=labels)
df_last_n_t = pd.DataFrame.from_records(record_BuyLowSellHigh[-last_n_t:], columns=labels)

numThetas=8100
thetas=[Theta(thLo={'GB': 10}, thHi={'GB': 10}), Theta(thLo={'GB': 10}, thHi={'GB': 11}), Theta(thLo={'GB': 10}, thHi={'GB': 12}), Theta(thLo={'GB': 10}, thHi={'GB': 13}), Theta(thLo={'GB': 10}, thHi={'GB': 14}), Theta(thLo={'GB': 10}, thHi={'GB': 15}), Theta(thLo={'GB': 10}, thHi={'GB': 16}), Theta(thLo={'GB': 10}, thHi={'GB': 17}), Theta(thLo={'GB': 10}, thHi={'GB': 18}), Theta(thLo={'GB': 10}, thHi={'GB': 19}), Theta(thLo={'GB': 10}, thHi={'GB': 20}), Theta(thLo={'GB': 10}, thHi={'GB': 21}), Theta(thLo={'GB': 10}, thHi={'GB': 22}), Theta(thLo={'GB': 10}, thHi={'GB': 23}), Theta(thLo={'GB': 10}, thHi={'GB': 24}), Theta(thLo={'GB': 10}, thHi={'GB': 25}), Theta(thLo={'GB': 10}, thHi={'GB': 26}), Theta(thLo={'GB': 10}, thHi={'GB': 27}), Theta(thLo={'GB': 10}, thHi={'GB': 28}), Theta(thLo={'GB': 10}, thHi={'GB': 29}), Theta(thLo={'GB': 10}, thHi={'GB': 30}), Theta(thLo={'GB': 10}, thHi={'GB': 31}), Theta(thLo={'GB': 10}, thHi={'GB': 32}), Theta(thLo={'GB': 10}, thHi={'GB': 33}), Theta(thLo={'GB': 10}, thHi={'GB': 34}), Theta(thLo={'GB': 10}, thHi={'GB': 35}), Theta(thLo={'GB': 10}, thHi={'GB': 36}), Theta(thLo={'GB': 10}, thHi={'GB': 37}), Theta(thLo={'GB': 10}, thHi={'GB': 38}), Theta(thLo={'GB': 10}, thHi={'GB': 39}), Theta(thLo={'GB': 10}, thHi={'GB': 40}), Theta(thLo={'GB': 10}, thHi={'GB': 41}), Theta(thLo={'GB': 10}, thHi={'GB': 42}), Theta(thLo={'GB': 10}, thHi={'GB': 43}), Theta(thLo={'GB': 10}, thHi={'GB': 44}), Theta(thLo={'GB': 10}, thHi={'GB': 45}), Theta(thLo={'GB': 10}, thHi={'GB': 46}), Theta(thLo={'GB': 10}, thHi={'GB': 47}), Theta(thLo={'GB': 10}, thHi={'GB': 48}), Theta(thLo={'GB': 10}, thHi={'GB': 49}), Theta(thLo={'GB': 10}, thHi={'GB': 50}), Theta(thLo={'GB': 10}, thHi={'GB': 51}), Theta(thLo={'GB': 10}, thHi={'GB': 52}), Theta(thLo={'GB': 10}, thHi={'GB': 53}), Theta(thLo={'GB': 10}, thHi={'GB': 54}), Theta(thLo={'GB': 10}, thHi={'GB': 55}), Theta(thLo={'GB': 10}, thHi={'GB': 56}), Theta(thLo={'GB': 10}, thHi={'GB': 57}), Theta(thLo={'GB': 10}, thHi={'GB': 58}), Theta(thLo={'GB': 10}, thHi={'GB': 59}), Theta(thLo={'GB': 10}, thHi={'GB': 60}), Theta(thLo={'GB': 10}, thHi={'GB': 61}), Theta(thLo={'GB': 10}, thHi={'GB': 62}), Theta(thLo={'GB': 10}, thHi={'GB': 63}), Theta(thLo={'GB': 10}, thHi={'GB': 64}), Theta(thLo={'GB': 10}, thHi={'GB': 65}), Theta(thLo={'GB': 10}, thHi={'GB': 66}), Theta(thLo={'GB': 10}, thHi={'GB': 67}), Theta(thLo={'GB': 10}, thHi={'GB': 68}), Theta(thLo={'GB': 10}, thHi={'GB': 69}), Theta(thLo={'GB': 10}, thHi={'GB': 70}), Theta(thLo={'GB': 10}, thHi={'GB': 71}), Theta(thLo={'GB': 10}, thHi={'GB': 72}), Theta(thLo={'GB': 10}, thHi={'GB': 73}), Theta(thLo={'GB': 10}, thHi={'GB': 74}), Theta(thLo={'GB': 10}, thHi={'GB': 75}), Theta(thLo={'GB': 10}, thHi={'GB': 76}), Theta(thLo={'GB': 10}, thHi={'GB': 77}), Theta(thLo={'GB': 10}, thHi={'GB': 78}), Theta(thLo={'GB': 10}, thHi={'GB': 79}), Theta(thLo={'GB': 10}, thHi={'GB': 80}), Theta(thLo={'GB': 10}, thHi={'GB': 81}), Theta(thLo={'GB': 10}, thHi={'GB': 82}), Theta(thLo={'GB': 10}, thHi={'GB': 83}), Theta(thLo={'GB': 10}, thHi={'GB': 84}), Theta(thLo={'GB': 10}, thHi={'GB': 85}), Theta(thLo={'GB': 10}, thHi={'GB': 86}), Theta(thLo={'GB': 10}, thHi={'GB': 87}), Theta(thLo={'GB': 10}, thHi={'GB': 88}), Theta(thLo={'GB': 10}, thHi={'GB': 89}), Theta(thLo={'GB': 10}, thHi={'GB': 90}), Theta(thLo={'GB': 10}, thHi={'GB': 91}), Theta(thLo={'GB': 10}, thHi={'GB': 92}), Theta(thLo={'GB': 10}, thHi={'GB': 93}), Theta(thLo={'GB': 10}, thHi={'GB': 94}), Theta(thLo={'GB': 10}, thHi={'GB': 95}), Theta(thLo={'GB': 10}, thHi={'GB': 96}), Theta(thLo={'GB': 10}, thHi={'GB': 97}), Theta(thLo={'GB': 10}, thHi={'GB': 98}), Theta(thLo={'GB': 10}, thHi={'GB': 99}), Theta(thLo={'GB': 11}, thHi={'GB': 10}), Theta(thLo={'GB': 11}, thHi={'GB': 11}), Theta(thLo={'GB': 11}, thHi={'GB': 12}), Theta(thLo={'GB': 11}, thHi={'GB': 13}), Theta(thLo={'GB': 11}, thHi={'GB': 14}), Theta(thLo={'GB': 11}, thHi={'GB': 15}), Theta(thLo={'GB': 11}, thHi={'GB': 16}), Theta(thLo={'GB': 11}, thHi={'GB': 17}), Theta(thLo={'GB': 11}, thHi={'GB': 18}), Theta(thLo={'GB': 11}, thHi={'GB': 19}), Theta(thLo={'GB': 11}, thHi={'GB': 20}), Theta(thLo={'GB': 11}, thHi={'GB': 21}), Theta(thLo={'GB': 11}, thHi={'GB': 22}), Theta(thLo={'GB': 11}, thHi={'GB': 23}), Theta(thLo={'GB': 11}, thHi={'GB': 24}), Theta(thLo={'GB': 11}, thHi={'GB': 25}), Theta(thLo={'GB': 11}, thHi={'GB': 26}), Theta(thLo={'GB': 11}, thHi={'GB': 27}), Theta(thLo={'GB': 11}, thHi={'GB': 28}), Theta(thLo={'GB': 11}, thHi={'GB': 29}), Theta(thLo={'GB': 11}, thHi={'GB': 30}), Theta(thLo={'GB': 11}, thHi={'GB': 31}), Theta(thLo={'GB': 11}, thHi={'GB': 32}), Theta(thLo={'GB': 11}, thHi={'GB': 33}), Theta(thLo={'GB': 11}, thHi={'GB': 34}), Theta(thLo={'GB': 11}, thHi={'GB': 35}), Theta(thLo={'GB': 11}, thHi={'GB': 36}), Theta(thLo={'GB': 11}, thHi={'GB': 37}), Theta(thLo={'GB': 11}, thHi={'GB': 38}), Theta(thLo={'GB': 11}, thHi={'GB': 39}), Theta(thLo={'GB': 11}, thHi={'GB': 40}), Theta(thLo={'GB': 11}, thHi={'GB': 41}), Theta(thLo={'GB': 11}, thHi={'GB': 42}), Theta(thLo={'GB': 11}, thHi={'GB': 43}), Theta(thLo={'GB': 11}, thHi={'GB': 44}), Theta(thLo={'GB': 11}, thHi={'GB': 45}), Theta(thLo={'GB': 11}, thHi={'GB': 46}), Theta(thLo={'GB': 11}, thHi={'GB': 47}), Theta(thLo={'GB': 11}, thHi={'GB': 48}), Theta(thLo={'GB': 11}, thHi={'GB': 49}), Theta(thLo={'GB': 11}, thHi={'GB': 50}), Theta(thLo={'GB': 11}, thHi={'GB': 51}), Theta(thLo={'GB': 11}, thHi={'GB': 52}), Theta(thLo={'GB': 11}, thHi={'GB': 53}), Theta(thLo={'GB': 11}, thHi={'GB': 54}), Theta(thLo={'GB': 11}, thHi={'GB': 55}), Theta(thLo={'GB': 11}, thHi={'GB': 56}), Theta(thLo={'GB': 11}, thHi={'GB': 57}), Theta(thLo={'GB': 11}, thHi={'GB': 58}), Theta(thLo={'GB': 11}, thHi={'GB': 59}), Theta(thLo={'GB': 11}, thHi={'GB': 60}), Theta(thLo={'GB': 11}, thHi={'GB': 61}), Theta(thLo={'GB': 11}, thHi={'GB': 62}), Theta(thLo={'GB': 11}, thHi={'GB': 63}), Theta(thLo={'GB': 11}, thHi={'GB': 64}), Theta(thLo={'GB': 11}, thHi={'GB': 65}), Theta(thLo={'GB': 11}, thHi={'GB': 66}), Theta(thLo={'GB': 11}, thHi={'GB': 67}), Theta(thLo={'GB': 11}, thHi={'GB': 68}), Theta(thLo={'GB': 11}, thHi={'GB': 69}), Theta(thLo={'GB': 11}, thHi={'GB': 70}), Theta(thLo={'GB': 11}, thHi={'GB': 71}), Theta(thLo={'GB': 11}, thHi={'GB': 72}), Theta(thLo={'GB': 11}, thHi={'GB': 73}), Theta(thLo={'GB': 11}, thHi={'GB': 74}), Theta(thLo={'GB': 11}, thHi={'GB': 75}), Theta(thLo={'GB': 11}, thHi={'GB': 76}), Theta(thLo={'GB': 11}, thHi={'GB': 77}), Theta(thLo={'GB': 11}, thHi={'GB': 78}), Theta(thLo={'GB': 11}, thHi={'GB': 79}), Theta(thLo={'GB': 11}, thHi={'GB': 80}), Theta(thLo={'GB': 11}, thHi={'GB': 81}), Theta(thLo={'GB': 11}, thHi={'GB': 82}), Theta(thLo={'GB': 11}, thHi={'GB': 83}), Theta(thLo={'GB': 11}, thHi={'GB': 84}), Theta(thLo={'GB': 11}, thHi={'GB': 85}), Theta(thLo={'GB': 11}, thHi={'GB': 86}), Theta(thLo={'GB': 11}, thHi={'GB': 87}), Theta(thLo={'GB': 11}, thHi={'GB': 88}), Theta(thLo={'GB': 11}, thHi={'GB': 89}), Theta(thLo={'GB': 11}, thHi={'GB': 90}), Theta(thLo={'GB': 11}, thHi={'GB': 91}), Theta(thLo={'GB': 11}, thHi={'GB': 92}), Theta(thLo={'GB': 11}, thHi={'GB': 93}), Theta(thLo={'GB': 11}, thHi={'GB': 94}), Theta(thLo={'GB': 11}, thHi={'GB': 95}), Theta(thLo={'GB': 11}, thHi={'GB': 96}), Theta(thLo={'GB': 11}, thHi={'GB': 97}), Theta(thLo={'GB': 11}, thHi={'GB': 98}), Theta(thLo={'GB': 11}, thHi={'GB': 99}), Theta(thLo={'GB': 12}, thHi={'GB': 10}), Theta(thLo={'GB': 12}, thHi={'GB': 11}), Theta(thLo={'GB': 12}, thHi={'GB': 12}), Theta(thLo={'GB': 12}, thHi={'GB': 13}), Theta(thLo={'GB': 12}, thHi={'GB': 14}), Theta(thLo={'GB': 12}, thHi={'GB': 15}), Theta(thLo={'GB': 12}, thHi={'GB': 16}), Theta(thLo={'GB': 12}, thHi={'GB': 17}), Theta(thLo={'GB': 12}, thHi={'GB': 18}), Theta(thLo={'GB': 12}, thHi={'GB': 19}), Theta(thLo={'GB': 12}, thHi={'GB': 20}), Theta(thLo={'GB': 12}, thHi={'GB': 21}), Theta(thLo={'GB': 12}, thHi={'GB': 22}), Theta(thLo={'GB': 12}, thHi={'GB': 23}), Theta(thLo={'GB': 12}, thHi={'GB': 24}), Theta(thLo={'GB': 12}, thHi={'GB': 25}), Theta(thLo={'GB': 12}, thHi={'GB': 26}), Theta(thLo={'GB': 12}, thHi={'GB': 27}), Theta(thLo={'GB': 12}, thHi={'GB': 28}), Theta(thLo={'GB': 12}, thHi={'GB': 29}), Theta(thLo={'GB': 12}, thHi={'GB': 30}), Theta(thLo={'GB': 12}, thHi={'GB': 31}), Theta(thLo={'GB': 12}, thHi={'GB': 32}), Theta(thLo={'GB': 12}, thHi={'GB': 33}), Theta(thLo={'GB': 12}, thHi={'GB': 34}), Theta(thLo={'GB': 12}, thHi={'GB': 35}), Theta(thLo={'GB': 12}, thHi={'GB': 36}), Theta(thLo={'GB': 12}, thHi={'GB': 37}), Theta(thLo={'GB': 12}, thHi={'GB': 38}), Theta(thLo={'GB': 12}, thHi={'GB': 39}), Theta(thLo={'GB': 12}, thHi={'GB': 40}), Theta(thLo={'GB': 12}, thHi={'GB': 41}), Theta(thLo={'GB': 12}, thHi={'GB': 42}), Theta(thLo={'GB': 12}, thHi={'GB': 43}), Theta(thLo={'GB': 12}, thHi={'GB': 44}), Theta(thLo={'GB': 12}, thHi={'GB': 45}), Theta(thLo={'GB': 12}, thHi={'GB': 46}), Theta(thLo={'GB': 12}, thHi={'GB': 47}), Theta(thLo={'GB': 12}, thHi={'GB': 48}), Theta(thLo={'GB': 12}, thHi={'GB': 49}), Theta(thLo={'GB': 12}, thHi={'GB': 50}), Theta(thLo={'GB': 12}, thHi={'GB': 51}), Theta(thLo={'GB': 12}, thHi={'GB': 52}), Theta(thLo={'GB': 12}, thHi={'GB': 53}), Theta(thLo={'GB': 12}, thHi={'GB': 54}), Theta(thLo={'GB': 12}, thHi={'GB': 55}), Theta(thLo={'GB': 12}, thHi={'GB': 56}), Theta(thLo={'GB': 12}, thHi={'GB': 57}), Theta(thLo={'GB': 12}, thHi={'GB': 58}), Theta(thLo={'GB': 12}, thHi={'GB': 59}), Theta(thLo={'GB': 12}, thHi={'GB': 60}), Theta(thLo={'GB': 12}, thHi={'GB': 61}), Theta(thLo={'GB': 12}, thHi={'GB': 62}), Theta(thLo={'GB': 12}, thHi={'GB': 63}), Theta(thLo={'GB': 12}, thHi={'GB': 64}), Theta(thLo={'GB': 12}, thHi={'GB': 65}), Theta(thLo={'GB': 12}, thHi={'GB': 66}), Theta(thLo={'GB': 12}, thHi={'GB': 67}), Theta(thLo={'GB': 12}, thHi={'GB': 68}), Theta(thLo={'GB': 12}, thHi={'GB': 69}), Theta(thLo={'GB': 12}, thHi={'GB': 70}), Theta(thLo={'GB': 12}, thHi={'GB': 71}), Theta(thLo={'GB': 12}, thHi={'GB': 72}), Theta(thLo={'GB': 12}, thHi={'GB': 73}), Theta(thLo={'GB': 12}, thHi={'GB': 74}), Theta(thLo={'GB': 12}, thHi={'GB': 75}), Theta(thLo={'GB': 12}, thHi={'GB': 76}), Theta(thLo={'GB': 12}, thHi={'GB': 77}), Theta(thLo={'GB': 12}, thHi={'GB': 78}), Theta(thLo={'GB': 12}, thHi={'GB': 79}), Theta(thLo={'GB': 12}, thHi={'GB': 80}), Theta(thLo={'GB': 12}, thHi={'GB': 81}), Theta(thLo={'GB': 12}, thHi={'GB': 82}), Theta(thLo={'GB': 12}, thHi={'GB': 83}), Theta(thLo={'GB': 12}, thHi={'GB': 84}), Theta(thLo={'GB': 12}, thHi={'GB': 85}), Theta(thLo={'GB': 12}, thHi={'GB': 86}), Theta(thLo={'GB': 12}, thHi={'GB': 87}), Theta(thLo={'GB': 12}, thHi={'GB': 88}), Theta(thLo={'GB': 12}, thHi={'GB': 89}), Theta(thLo={'GB': 12}, thHi={'GB': 90}), Theta(thLo={'GB': 12}, thHi={'GB': 91}), Theta(thLo={'GB': 12}, thHi={'GB': 92}), Theta(thLo={'GB': 12}, thHi={'GB': 93}), Theta(thLo={'GB': 12}, thHi={'GB': 94}), Theta(thLo={'GB': 12}, thHi={'GB': 95}), Theta(thLo={'GB': 12}, thHi={'GB': 96}), Theta(thLo={'GB': 12}, thHi={'GB': 97}), Theta(thLo={'GB': 12}, thHi={'GB': 98}), Theta(thLo={'GB': 12}, thHi={'GB': 99}), Theta(thLo={'GB': 13}, thHi={'GB': 10}), Theta(thLo={'GB': 13}, thHi={'GB': 11}), Theta(thLo={'GB': 13}, thHi={'GB': 12}), Theta(thLo={'GB': 13}, thHi={'GB': 13}), Theta(thLo={'GB': 13}, thHi={'GB': 14}), Theta(thLo={'GB': 13}, thHi={'GB': 15}), Theta(thLo={'GB': 13}, thHi={'GB': 16}), Theta(thLo={'GB': 13}, thHi={'GB': 17}), Theta(thLo={'GB': 13}, thHi={'GB': 18}), Theta(thLo={'GB': 13}, thHi={'GB': 19}), Theta(thLo={'GB': 13}, thHi={'GB': 20}), Theta(thLo={'GB': 13}, thHi={'GB': 21}), Theta(thLo={'GB': 13}, thHi={'GB': 22}), Theta(thLo={'GB': 13}, thHi={'GB': 23}), Theta(thLo={'GB': 13}, thHi={'GB': 24}), Theta(thLo={'GB': 13}, thHi={'GB': 25}), Theta(thLo={'GB': 13}, thHi={'GB': 26}), Theta(thLo={'GB': 13}, thHi={'GB': 27}), Theta(thLo={'GB': 13}, thHi={'GB': 28}), Theta(thLo={'GB': 13}, thHi={'GB': 29}), Theta(thLo={'GB': 13}, thHi={'GB': 30}), Theta(thLo={'GB': 13}, thHi={'GB': 31}), Theta(thLo={'GB': 13}, thHi={'GB': 32}), Theta(thLo={'GB': 13}, thHi={'GB': 33}), Theta(thLo={'GB': 13}, thHi={'GB': 34}), Theta(thLo={'GB': 13}, thHi={'GB': 35}), Theta(thLo={'GB': 13}, thHi={'GB': 36}), Theta(thLo={'GB': 13}, thHi={'GB': 37}), Theta(thLo={'GB': 13}, thHi={'GB': 38}), Theta(thLo={'GB': 13}, thHi={'GB': 39}), Theta(thLo={'GB': 13}, thHi={'GB': 40}), Theta(thLo={'GB': 13}, thHi={'GB': 41}), Theta(thLo={'GB': 13}, thHi={'GB': 42}), Theta(thLo={'GB': 13}, thHi={'GB': 43}), Theta(thLo={'GB': 13}, thHi={'GB': 44}), Theta(thLo={'GB': 13}, thHi={'GB': 45}), Theta(thLo={'GB': 13}, thHi={'GB': 46}), Theta(thLo={'GB': 13}, thHi={'GB': 47}), Theta(thLo={'GB': 13}, thHi={'GB': 48}), Theta(thLo={'GB': 13}, thHi={'GB': 49}), Theta(thLo={'GB': 13}, thHi={'GB': 50}), Theta(thLo={'GB': 13}, thHi={'GB': 51}), Theta(thLo={'GB': 13}, thHi={'GB': 52}), Theta(thLo={'GB': 13}, thHi={'GB': 53}), Theta(thLo={'GB': 13}, thHi={'GB': 54}), Theta(thLo={'GB': 13}, thHi={'GB': 55}), Theta(thLo={'GB': 13}, thHi={'GB': 56}), Theta(thLo={'GB': 13}, thHi={'GB': 57}), Theta(thLo={'GB': 13}, thHi={'GB': 58}), Theta(thLo={'GB': 13}, thHi={'GB': 59}), Theta(thLo={'GB': 13}, thHi={'GB': 60}), Theta(thLo={'GB': 13}, thHi={'GB': 61}), Theta(thLo={'GB': 13}, thHi={'GB': 62}), Theta(thLo={'GB': 13}, thHi={'GB': 63}), Theta(thLo={'GB': 13}, thHi={'GB': 64}), Theta(thLo={'GB': 13}, thHi={'GB': 65}), Theta(thLo={'GB': 13}, thHi={'GB': 66}), Theta(thLo={'GB': 13}, thHi={'GB': 67}), Theta(thLo={'GB': 13}, thHi={'GB': 68}), Theta(thLo={'GB': 13}, thHi={'GB': 69}), Theta(thLo={'GB': 13}, thHi={'GB': 70}), Theta(thLo={'GB': 13}, thHi={'GB': 71}), Theta(thLo={'GB': 13}, thHi={'GB': 72}), Theta(thLo={'GB': 13}, thHi={'GB': 73}), Theta(thLo={'GB': 13}, thHi={'GB': 74}), Theta(thLo={'GB': 13}, thHi={'GB': 75}), Theta(thLo={'GB': 13}, thHi={'GB': 76}), Theta(thLo={'GB': 13}, thHi={'GB': 77}), Theta(thLo={'GB': 13}, thHi={'GB': 78}), Theta(thLo={'GB': 13}, thHi={'GB': 79}), Theta(thLo={'GB': 13}, thHi={'GB': 80}), Theta(thLo={'GB': 13}, thHi={'GB': 81}), Theta(thLo={'GB': 13}, thHi={'GB': 82}), Theta(thLo={'GB': 13}, thHi={'GB': 83}), Theta(thLo={'GB': 13}, thHi={'GB': 84}), Theta(thLo={'GB': 13}, thHi={'GB': 85}), Theta(thLo={'GB': 13}, thHi={'GB': 86}), Theta(thLo={'GB': 13}, thHi={'GB': 87}), Theta(thLo={'GB': 13}, thHi={'GB': 88}), Theta(thLo={'GB': 13}, thHi={'GB': 89}), Theta(thLo={'GB': 13}, thHi={'GB': 90}), Theta(thLo={'GB': 13}, thHi={'GB': 91}), Theta(thLo={'GB': 13}, thHi={'GB': 92}), Theta(thLo={'GB': 13}, thHi={'GB': 93}), Theta(thLo={'GB': 13}, thHi={'GB': 94}), Theta(thLo={'GB': 13}, thHi={'GB': 95}), Theta(thLo={'GB': 13}, thHi={'GB': 96}), Theta(thLo={'GB': 13}, thHi={'GB': 97}), Theta(thLo={'GB': 13}, thHi={'GB': 98}), Theta(thLo={'GB': 13}, thHi={'GB': 99}), Theta(thLo={'GB': 14}, thHi={'GB': 10}), Theta(thLo={'GB': 14}, thHi={'GB': 11}), Theta(thLo={'GB': 14}, thHi={'GB': 12}), Theta(thLo={'GB': 14}, thHi={'GB': 13}), Theta(thLo={'GB': 14}, thHi={'GB': 14}), Theta(thLo={'GB': 14}, thHi={'GB': 15}), Theta(thLo={'GB': 14}, thHi={'GB': 16}), Theta(thLo={'GB': 14}, thHi={'GB': 17}), Theta(thLo={'GB': 14}, thHi={'GB': 18}), Theta(thLo={'GB': 14}, thHi={'GB': 19}), Theta(thLo={'GB': 14}, thHi={'GB': 20}), Theta(thLo={'GB': 14}, thHi={'GB': 21}), Theta(thLo={'GB': 14}, thHi={'GB': 22}), Theta(thLo={'GB': 14}, thHi={'GB': 23}), Theta(thLo={'GB': 14}, thHi={'GB': 24}), Theta(thLo={'GB': 14}, thHi={'GB': 25}), Theta(thLo={'GB': 14}, thHi={'GB': 26}), Theta(thLo={'GB': 14}, thHi={'GB': 27}), Theta(thLo={'GB': 14}, thHi={'GB': 28}), Theta(thLo={'GB': 14}, thHi={'GB': 29}), Theta(thLo={'GB': 14}, thHi={'GB': 30}), Theta(thLo={'GB': 14}, thHi={'GB': 31}), Theta(thLo={'GB': 14}, thHi={'GB': 32}), Theta(thLo={'GB': 14}, thHi={'GB': 33}), Theta(thLo={'GB': 14}, thHi={'GB': 34}), Theta(thLo={'GB': 14}, thHi={'GB': 35}), Theta(thLo={'GB': 14}, thHi={'GB': 36}), Theta(thLo={'GB': 14}, thHi={'GB': 37}), Theta(thLo={'GB': 14}, thHi={'GB': 38}), Theta(thLo={'GB': 14}, thHi={'GB': 39}), Theta(thLo={'GB': 14}, thHi={'GB': 40}), Theta(thLo={'GB': 14}, thHi={'GB': 41}), Theta(thLo={'GB': 14}, thHi={'GB': 42}), Theta(thLo={'GB': 14}, thHi={'GB': 43}), Theta(thLo={'GB': 14}, thHi={'GB': 44}), Theta(thLo={'GB': 14}, thHi={'GB': 45}), Theta(thLo={'GB': 14}, thHi={'GB': 46}), Theta(thLo={'GB': 14}, thHi={'GB': 47}), Theta(thLo={'GB': 14}, thHi={'GB': 48}), Theta(thLo={'GB': 14}, thHi={'GB': 49}), Theta(thLo={'GB': 14}, thHi={'GB': 50}), Theta(thLo={'GB': 14}, thHi={'GB': 51}), Theta(thLo={'GB': 14}, thHi={'GB': 52}), Theta(thLo={'GB': 14}, thHi={'GB': 53}), Theta(thLo={'GB': 14}, thHi={'GB': 54}), Theta(thLo={'GB': 14}, thHi={'GB': 55}), Theta(thLo={'GB': 14}, thHi={'GB': 56}), Theta(thLo={'GB': 14}, thHi={'GB': 57}), Theta(thLo={'GB': 14}, thHi={'GB': 58}), Theta(thLo={'GB': 14}, thHi={'GB': 59}), Theta(thLo={'GB': 14}, thHi={'GB': 60}), Theta(thLo={'GB': 14}, thHi={'GB': 61}), Theta(thLo={'GB': 14}, thHi={'GB': 62}), Theta(thLo={'GB': 14}, thHi={'GB': 63}), Theta(thLo={'GB': 14}, thHi={'GB': 64}), Theta(thLo={'GB': 14}, thHi={'GB': 65}), Theta(thLo={'GB': 14}, thHi={'GB': 66}), Theta(thLo={'GB': 14}, thHi={'GB': 67}), Theta(thLo={'GB': 14}, thHi={'GB': 68}), Theta(thLo={'GB': 14}, thHi={'GB': 69}), Theta(thLo={'GB': 14}, thHi={'GB': 70}), Theta(thLo={'GB': 14}, thHi={'GB': 71}), Theta(thLo={'GB': 14}, thHi={'GB': 72}), Theta(thLo={'GB': 14}, thHi={'GB': 73}), Theta(thLo={'GB': 14}, thHi={'GB': 74}), Theta(thLo={'GB': 14}, thHi={'GB': 75}), Theta(thLo={'GB': 14}, thHi={'GB': 76}), Theta(thLo={'GB': 14}, thHi={'GB': 77}), Theta(thLo={'GB': 14}, thHi={'GB': 78}), Theta(thLo={'GB': 14}, thHi={'GB': 79}), Theta(thLo={'GB': 14}, thHi={'GB': 80}), Theta(thLo={'GB': 14}, thHi={'GB': 81}), Theta(thLo={'GB': 14}, thHi={'GB': 82}), Theta(thLo={'GB': 14}, thHi={'GB': 83}), Theta(thLo={'GB': 14}, thHi={'GB': 84}), Theta(thLo={'GB': 14}, thHi={'GB': 85}), Theta(thLo={'GB': 14}, thHi={'GB': 86}), Theta(thLo={'GB': 14}, thHi={'GB': 87}), Theta(thLo={'GB': 14}, thHi={'GB': 88}), Theta(thLo={'GB': 14}, thHi={'GB': 89}), Theta(thLo={'GB': 14}, thHi={'GB': 90}), Theta(thLo={'GB': 14}, thHi={'GB': 91}), Theta(thLo={'GB': 14}, thHi={'GB': 92}), Theta(thLo={'GB': 14}, thHi={'GB': 93}), Theta(thLo={'GB': 14}, thHi={'GB': 94}), Theta(thLo={'GB': 14}, thHi={'GB': 95}), Theta(thLo={'GB': 14}, thHi={'GB': 96}), Theta(thLo={'GB': 14}, thHi={'GB': 97}), Theta(thLo={'GB': 14}, thHi={'GB': 98}), Theta(thLo={'GB': 14}, thHi={'GB': 99}), Theta(thLo={'GB': 15}, thHi={'GB': 10}), Theta(thLo={'GB': 15}, thHi={'GB': 11}), Theta(thLo={'GB': 15}, thHi={'GB': 12}), Theta(thLo={'GB': 15}, thHi={'GB': 13}), Theta(thLo={'GB': 15}, thHi={'GB': 14}), Theta(thLo={'GB': 15}, thHi={'GB': 15}), Theta(thLo={'GB': 15}, thHi={'GB': 16}), Theta(thLo={'GB': 15}, thHi={'GB': 17}), Theta(thLo={'GB': 15}, thHi={'GB': 18}), Theta(thLo={'GB': 15}, thHi={'GB': 19}), Theta(thLo={'GB': 15}, thHi={'GB': 20}), Theta(thLo={'GB': 15}, thHi={'GB': 21}), Theta(thLo={'GB': 15}, thHi={'GB': 22}), Theta(thLo={'GB': 15}, thHi={'GB': 23}), Theta(thLo={'GB': 15}, thHi={'GB': 24}), Theta(thLo={'GB': 15}, thHi={'GB': 25}), Theta(thLo={'GB': 15}, thHi={'GB': 26}), Theta(thLo={'GB': 15}, thHi={'GB': 27}), Theta(thLo={'GB': 15}, thHi={'GB': 28}), Theta(thLo={'GB': 15}, thHi={'GB': 29}), Theta(thLo={'GB': 15}, thHi={'GB': 30}), Theta(thLo={'GB': 15}, thHi={'GB': 31}), Theta(thLo={'GB': 15}, thHi={'GB': 32}), Theta(thLo={'GB': 15}, thHi={'GB': 33}), Theta(thLo={'GB': 15}, thHi={'GB': 34}), Theta(thLo={'GB': 15}, thHi={'GB': 35}), Theta(thLo={'GB': 15}, thHi={'GB': 36}), Theta(thLo={'GB': 15}, thHi={'GB': 37}), Theta(thLo={'GB': 15}, thHi={'GB': 38}), Theta(thLo={'GB': 15}, thHi={'GB': 39}), Theta(thLo={'GB': 15}, thHi={'GB': 40}), Theta(thLo={'GB': 15}, thHi={'GB': 41}), Theta(thLo={'GB': 15}, thHi={'GB': 42}), Theta(thLo={'GB': 15}, thHi={'GB': 43}), Theta(thLo={'GB': 15}, thHi={'GB': 44}), Theta(thLo={'GB': 15}, thHi={'GB': 45}), Theta(thLo={'GB': 15}, thHi={'GB': 46}), Theta(thLo={'GB': 15}, thHi={'GB': 47}), Theta(thLo={'GB': 15}, thHi={'GB': 48}), Theta(thLo={'GB': 15}, thHi={'GB': 49}), Theta(thLo={'GB': 15}, thHi={'GB': 50}), Theta(thLo={'GB': 15}, thHi={'GB': 51}), Theta(thLo={'GB': 15}, thHi={'GB': 52}), Theta(thLo={'GB': 15}, thHi={'GB': 53}), Theta(thLo={'GB': 15}, thHi={'GB': 54}), Theta(thLo={'GB': 15}, thHi={'GB': 55}), Theta(thLo={'GB': 15}, thHi={'GB': 56}), Theta(thLo={'GB': 15}, thHi={'GB': 57}), Theta(thLo={'GB': 15}, thHi={'GB': 58}), Theta(thLo={'GB': 15}, thHi={'GB': 59}), Theta(thLo={'GB': 15}, thHi={'GB': 60}), Theta(thLo={'GB': 15}, thHi={'GB': 61}), Theta(thLo={'GB': 15}, thHi={'GB': 62}), Theta(thLo={'GB': 15}, thHi={'GB': 63}), Theta(thLo={'GB': 15}, thHi={'GB': 64}), Theta(thLo={'GB': 15}, thHi={'GB': 65}), Theta(thLo={'GB': 15}, thHi={'GB': 66}), Theta(thLo={'GB': 15}, thHi={'GB': 67}), Theta(thLo={'GB': 15}, thHi={'GB': 68}), Theta(thLo={'GB': 15}, thHi={'GB': 69}), Theta(thLo={'GB': 15}, thHi={'GB': 70}), Theta(thLo={'GB': 15}, thHi={'GB': 71}), Theta(thLo={'GB': 15}, thHi={'GB': 72}), Theta(thLo={'GB': 15}, thHi={'GB': 73}), Theta(thLo={'GB': 15}, thHi={'GB': 74}), Theta(thLo={'GB': 15}, thHi={'GB': 75}), Theta(thLo={'GB': 15}, thHi={'GB': 76}), Theta(thLo={'GB': 15}, thHi={'GB': 77}), Theta(thLo={'GB': 15}, thHi={'GB': 78}), Theta(thLo={'GB': 15}, thHi={'GB': 79}), Theta(thLo={'GB': 15}, thHi={'GB': 80}), Theta(thLo={'GB': 15}, thHi={'GB': 81}), Theta(thLo={'GB': 15}, thHi={'GB': 82}), Theta(thLo={'GB': 15}, thHi={'GB': 83}), Theta(thLo={'GB': 15}, thHi={'GB': 84}), Theta(thLo={'GB': 15}, thHi={'GB': 85}), Theta(thLo={'GB': 15}, thHi={'GB': 86}), Theta(thLo={'GB': 15}, thHi={'GB': 87}), Theta(thLo={'GB': 15}, thHi={'GB': 88}), Theta(thLo={'GB': 15}, thHi={'GB': 89}), Theta(thLo={'GB': 15}, thHi={'GB': 90}), Theta(thLo={'GB': 15}, thHi={'GB': 91}), Theta(thLo={'GB': 15}, thHi={'GB': 92}), Theta(thLo={'GB': 15}, thHi={'GB': 93}), Theta(thLo={'GB': 15}, thHi={'GB': 94}), Theta(thLo={'GB': 15}, thHi={'GB': 95}), Theta(thLo={'GB': 15}, thHi={'GB': 96}), Theta(thLo={'GB': 15}, thHi={'GB': 97}), Theta(thLo={'GB': 15}, thHi={'GB': 98}), Theta(thLo={'GB': 15}, thHi={'GB': 99}), Theta(thLo={'GB': 16}, thHi={'GB': 10}), Theta(thLo={'GB': 16}, thHi={'GB': 11}), Theta(thLo={'GB': 16}, thHi={'GB': 12}), Theta(thLo={'GB': 16}, thHi={'GB': 13}), Theta(thLo={'GB': 16}, thHi={'GB': 14}), Theta(thLo={'GB': 16}, thHi={'GB': 15}), Theta(thLo={'GB': 16}, thHi={'GB': 16}), Theta(thLo={'GB': 16}, thHi={'GB': 17}), Theta(thLo={'GB': 16}, thHi={'GB': 18}), Theta(thLo={'GB': 16}, thHi={'GB': 19}), Theta(thLo={'GB': 16}, thHi={'GB': 20}), Theta(thLo={'GB': 16}, thHi={'GB': 21}), Theta(thLo={'GB': 16}, thHi={'GB': 22}), Theta(thLo={'GB': 16}, thHi={'GB': 23}), Theta(thLo={'GB': 16}, thHi={'GB': 24}), Theta(thLo={'GB': 16}, thHi={'GB': 25}), Theta(thLo={'GB': 16}, thHi={'GB': 26}), Theta(thLo={'GB': 16}, thHi={'GB': 27}), Theta(thLo={'GB': 16}, thHi={'GB': 28}), Theta(thLo={'GB': 16}, thHi={'GB': 29}), Theta(thLo={'GB': 16}, thHi={'GB': 30}), Theta(thLo={'GB': 16}, thHi={'GB': 31}), Theta(thLo={'GB': 16}, thHi={'GB': 32}), Theta(thLo={'GB': 16}, thHi={'GB': 33}), Theta(thLo={'GB': 16}, thHi={'GB': 34}), Theta(thLo={'GB': 16}, thHi={'GB': 35}), Theta(thLo={'GB': 16}, thHi={'GB': 36}), Theta(thLo={'GB': 16}, thHi={'GB': 37}), Theta(thLo={'GB': 16}, thHi={'GB': 38}), Theta(thLo={'GB': 16}, thHi={'GB': 39}), Theta(thLo={'GB': 16}, thHi={'GB': 40}), Theta(thLo={'GB': 16}, thHi={'GB': 41}), Theta(thLo={'GB': 16}, thHi={'GB': 42}), Theta(thLo={'GB': 16}, thHi={'GB': 43}), Theta(thLo={'GB': 16}, thHi={'GB': 44}), Theta(thLo={'GB': 16}, thHi={'GB': 45}), Theta(thLo={'GB': 16}, thHi={'GB': 46}), Theta(thLo={'GB': 16}, thHi={'GB': 47}), Theta(thLo={'GB': 16}, thHi={'GB': 48}), Theta(thLo={'GB': 16}, thHi={'GB': 49}), Theta(thLo={'GB': 16}, thHi={'GB': 50}), Theta(thLo={'GB': 16}, thHi={'GB': 51}), Theta(thLo={'GB': 16}, thHi={'GB': 52}), Theta(thLo={'GB': 16}, thHi={'GB': 53}), Theta(thLo={'GB': 16}, thHi={'GB': 54}), Theta(thLo={'GB': 16}, thHi={'GB': 55}), Theta(thLo={'GB': 16}, thHi={'GB': 56}), Theta(thLo={'GB': 16}, thHi={'GB': 57}), Theta(thLo={'GB': 16}, thHi={'GB': 58}), Theta(thLo={'GB': 16}, thHi={'GB': 59}), Theta(thLo={'GB': 16}, thHi={'GB': 60}), Theta(thLo={'GB': 16}, thHi={'GB': 61}), Theta(thLo={'GB': 16}, thHi={'GB': 62}), Theta(thLo={'GB': 16}, thHi={'GB': 63}), Theta(thLo={'GB': 16}, thHi={'GB': 64}), Theta(thLo={'GB': 16}, thHi={'GB': 65}), Theta(thLo={'GB': 16}, thHi={'GB': 66}), Theta(thLo={'GB': 16}, thHi={'GB': 67}), Theta(thLo={'GB': 16}, thHi={'GB': 68}), Theta(thLo={'GB': 16}, thHi={'GB': 69}), Theta(thLo={'GB': 16}, thHi={'GB': 70}), Theta(thLo={'GB': 16}, thHi={'GB': 71}), Theta(thLo={'GB': 16}, thHi={'GB': 72}), Theta(thLo={'GB': 16}, thHi={'GB': 73}), Theta(thLo={'GB': 16}, thHi={'GB': 74}), Theta(thLo={'GB': 16}, thHi={'GB': 75}), Theta(thLo={'GB': 16}, thHi={'GB': 76}), Theta(thLo={'GB': 16}, thHi={'GB': 77}), Theta(thLo={'GB': 16}, thHi={'GB': 78}), Theta(thLo={'GB': 16}, thHi={'GB': 79}), Theta(thLo={'GB': 16}, thHi={'GB': 80}), Theta(thLo={'GB': 16}, thHi={'GB': 81}), Theta(thLo={'GB': 16}, thHi={'GB': 82}), Theta(thLo={'GB': 16}, thHi={'GB': 83}), Theta(thLo={'GB': 16}, thHi={'GB': 84}), Theta(thLo={'GB': 16}, thHi={'GB': 85}), Theta(thLo={'GB': 16}, thHi={'GB': 86}), Theta(thLo={'GB': 16}, thHi={'GB': 87}), Theta(thLo={'GB': 16}, thHi={'GB': 88}), Theta(thLo={'GB': 16}, thHi={'GB': 89}), Theta(thLo={'GB': 16}, thHi={'GB': 90}), Theta(thLo={'GB': 16}, thHi={'GB': 91}), Theta(thLo={'GB': 16}, thHi={'GB': 92}), Theta(thLo={'GB': 16}, thHi={'GB': 93}), 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Theta(thLo={'GB': 21}, thHi={'GB': 76}), Theta(thLo={'GB': 21}, thHi={'GB': 77}), Theta(thLo={'GB': 21}, thHi={'GB': 78}), Theta(thLo={'GB': 21}, thHi={'GB': 79}), Theta(thLo={'GB': 21}, thHi={'GB': 80}), Theta(thLo={'GB': 21}, thHi={'GB': 81}), Theta(thLo={'GB': 21}, thHi={'GB': 82}), Theta(thLo={'GB': 21}, thHi={'GB': 83}), Theta(thLo={'GB': 21}, thHi={'GB': 84}), Theta(thLo={'GB': 21}, thHi={'GB': 85}), Theta(thLo={'GB': 21}, thHi={'GB': 86}), Theta(thLo={'GB': 21}, thHi={'GB': 87}), Theta(thLo={'GB': 21}, thHi={'GB': 88}), Theta(thLo={'GB': 21}, thHi={'GB': 89}), Theta(thLo={'GB': 21}, thHi={'GB': 90}), Theta(thLo={'GB': 21}, thHi={'GB': 91}), Theta(thLo={'GB': 21}, thHi={'GB': 92}), Theta(thLo={'GB': 21}, thHi={'GB': 93}), Theta(thLo={'GB': 21}, thHi={'GB': 94}), Theta(thLo={'GB': 21}, thHi={'GB': 95}), Theta(thLo={'GB': 21}, thHi={'GB': 96}), Theta(thLo={'GB': 21}, thHi={'GB': 97}), Theta(thLo={'GB': 21}, thHi={'GB': 98}), Theta(thLo={'GB': 21}, thHi={'GB': 99}), Theta(thLo={'GB': 22}, thHi={'GB': 10}), Theta(thLo={'GB': 22}, thHi={'GB': 11}), Theta(thLo={'GB': 22}, thHi={'GB': 12}), Theta(thLo={'GB': 22}, thHi={'GB': 13}), Theta(thLo={'GB': 22}, thHi={'GB': 14}), Theta(thLo={'GB': 22}, thHi={'GB': 15}), Theta(thLo={'GB': 22}, thHi={'GB': 16}), Theta(thLo={'GB': 22}, thHi={'GB': 17}), Theta(thLo={'GB': 22}, thHi={'GB': 18}), Theta(thLo={'GB': 22}, thHi={'GB': 19}), Theta(thLo={'GB': 22}, thHi={'GB': 20}), Theta(thLo={'GB': 22}, thHi={'GB': 21}), Theta(thLo={'GB': 22}, thHi={'GB': 22}), Theta(thLo={'GB': 22}, thHi={'GB': 23}), Theta(thLo={'GB': 22}, thHi={'GB': 24}), Theta(thLo={'GB': 22}, thHi={'GB': 25}), Theta(thLo={'GB': 22}, thHi={'GB': 26}), Theta(thLo={'GB': 22}, thHi={'GB': 27}), Theta(thLo={'GB': 22}, thHi={'GB': 28}), Theta(thLo={'GB': 22}, thHi={'GB': 29}), Theta(thLo={'GB': 22}, thHi={'GB': 30}), Theta(thLo={'GB': 22}, thHi={'GB': 31}), Theta(thLo={'GB': 22}, thHi={'GB': 32}), Theta(thLo={'GB': 22}, thHi={'GB': 33}), 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Theta(thLo={'GB': 22}, thHi={'GB': 58}), Theta(thLo={'GB': 22}, thHi={'GB': 59}), Theta(thLo={'GB': 22}, thHi={'GB': 60}), Theta(thLo={'GB': 22}, thHi={'GB': 61}), Theta(thLo={'GB': 22}, thHi={'GB': 62}), Theta(thLo={'GB': 22}, thHi={'GB': 63}), Theta(thLo={'GB': 22}, thHi={'GB': 64}), Theta(thLo={'GB': 22}, thHi={'GB': 65}), Theta(thLo={'GB': 22}, thHi={'GB': 66}), Theta(thLo={'GB': 22}, thHi={'GB': 67}), Theta(thLo={'GB': 22}, thHi={'GB': 68}), Theta(thLo={'GB': 22}, thHi={'GB': 69}), Theta(thLo={'GB': 22}, thHi={'GB': 70}), Theta(thLo={'GB': 22}, thHi={'GB': 71}), Theta(thLo={'GB': 22}, thHi={'GB': 72}), Theta(thLo={'GB': 22}, thHi={'GB': 73}), Theta(thLo={'GB': 22}, thHi={'GB': 74}), Theta(thLo={'GB': 22}, thHi={'GB': 75}), Theta(thLo={'GB': 22}, thHi={'GB': 76}), Theta(thLo={'GB': 22}, thHi={'GB': 77}), Theta(thLo={'GB': 22}, thHi={'GB': 78}), Theta(thLo={'GB': 22}, thHi={'GB': 79}), Theta(thLo={'GB': 22}, thHi={'GB': 80}), Theta(thLo={'GB': 22}, thHi={'GB': 81}), 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Theta(thLo={'GB': 29}, thHi={'GB': 28}), Theta(thLo={'GB': 29}, thHi={'GB': 29}), Theta(thLo={'GB': 29}, thHi={'GB': 30}), Theta(thLo={'GB': 29}, thHi={'GB': 31}), Theta(thLo={'GB': 29}, thHi={'GB': 32}), Theta(thLo={'GB': 29}, thHi={'GB': 33}), Theta(thLo={'GB': 29}, thHi={'GB': 34}), Theta(thLo={'GB': 29}, thHi={'GB': 35}), Theta(thLo={'GB': 29}, thHi={'GB': 36}), Theta(thLo={'GB': 29}, thHi={'GB': 37}), Theta(thLo={'GB': 29}, thHi={'GB': 38}), Theta(thLo={'GB': 29}, thHi={'GB': 39}), Theta(thLo={'GB': 29}, thHi={'GB': 40}), Theta(thLo={'GB': 29}, thHi={'GB': 41}), Theta(thLo={'GB': 29}, thHi={'GB': 42}), Theta(thLo={'GB': 29}, thHi={'GB': 43}), Theta(thLo={'GB': 29}, thHi={'GB': 44}), Theta(thLo={'GB': 29}, thHi={'GB': 45}), Theta(thLo={'GB': 29}, thHi={'GB': 46}), Theta(thLo={'GB': 29}, thHi={'GB': 47}), Theta(thLo={'GB': 29}, thHi={'GB': 48}), Theta(thLo={'GB': 29}, thHi={'GB': 49}), Theta(thLo={'GB': 29}, thHi={'GB': 50}), Theta(thLo={'GB': 29}, thHi={'GB': 51}), Theta(thLo={'GB': 29}, thHi={'GB': 52}), Theta(thLo={'GB': 29}, thHi={'GB': 53}), Theta(thLo={'GB': 29}, thHi={'GB': 54}), Theta(thLo={'GB': 29}, thHi={'GB': 55}), Theta(thLo={'GB': 29}, thHi={'GB': 56}), Theta(thLo={'GB': 29}, thHi={'GB': 57}), Theta(thLo={'GB': 29}, thHi={'GB': 58}), Theta(thLo={'GB': 29}, thHi={'GB': 59}), Theta(thLo={'GB': 29}, thHi={'GB': 60}), Theta(thLo={'GB': 29}, thHi={'GB': 61}), Theta(thLo={'GB': 29}, thHi={'GB': 62}), Theta(thLo={'GB': 29}, thHi={'GB': 63}), Theta(thLo={'GB': 29}, thHi={'GB': 64}), Theta(thLo={'GB': 29}, thHi={'GB': 65}), Theta(thLo={'GB': 29}, thHi={'GB': 66}), Theta(thLo={'GB': 29}, thHi={'GB': 67}), Theta(thLo={'GB': 29}, thHi={'GB': 68}), Theta(thLo={'GB': 29}, thHi={'GB': 69}), Theta(thLo={'GB': 29}, thHi={'GB': 70}), Theta(thLo={'GB': 29}, thHi={'GB': 71}), Theta(thLo={'GB': 29}, thHi={'GB': 72}), Theta(thLo={'GB': 29}, thHi={'GB': 73}), Theta(thLo={'GB': 29}, thHi={'GB': 74}), Theta(thLo={'GB': 29}, thHi={'GB': 75}), Theta(thLo={'GB': 29}, thHi={'GB': 76}), Theta(thLo={'GB': 29}, thHi={'GB': 77}), Theta(thLo={'GB': 29}, thHi={'GB': 78}), Theta(thLo={'GB': 29}, thHi={'GB': 79}), Theta(thLo={'GB': 29}, thHi={'GB': 80}), Theta(thLo={'GB': 29}, thHi={'GB': 81}), Theta(thLo={'GB': 29}, thHi={'GB': 82}), Theta(thLo={'GB': 29}, thHi={'GB': 83}), Theta(thLo={'GB': 29}, thHi={'GB': 84}), Theta(thLo={'GB': 29}, thHi={'GB': 85}), Theta(thLo={'GB': 29}, thHi={'GB': 86}), Theta(thLo={'GB': 29}, thHi={'GB': 87}), Theta(thLo={'GB': 29}, thHi={'GB': 88}), Theta(thLo={'GB': 29}, thHi={'GB': 89}), Theta(thLo={'GB': 29}, thHi={'GB': 90}), Theta(thLo={'GB': 29}, thHi={'GB': 91}), Theta(thLo={'GB': 29}, thHi={'GB': 92}), Theta(thLo={'GB': 29}, thHi={'GB': 93}), Theta(thLo={'GB': 29}, thHi={'GB': 94}), Theta(thLo={'GB': 29}, thHi={'GB': 95}), Theta(thLo={'GB': 29}, thHi={'GB': 96}), Theta(thLo={'GB': 29}, thHi={'GB': 97}), Theta(thLo={'GB': 29}, thHi={'GB': 98}), Theta(thLo={'GB': 29}, thHi={'GB': 99}), Theta(thLo={'GB': 30}, thHi={'GB': 10}), Theta(thLo={'GB': 30}, thHi={'GB': 11}), Theta(thLo={'GB': 30}, thHi={'GB': 12}), Theta(thLo={'GB': 30}, thHi={'GB': 13}), Theta(thLo={'GB': 30}, thHi={'GB': 14}), Theta(thLo={'GB': 30}, thHi={'GB': 15}), Theta(thLo={'GB': 30}, thHi={'GB': 16}), Theta(thLo={'GB': 30}, thHi={'GB': 17}), Theta(thLo={'GB': 30}, thHi={'GB': 18}), Theta(thLo={'GB': 30}, thHi={'GB': 19}), Theta(thLo={'GB': 30}, thHi={'GB': 20}), Theta(thLo={'GB': 30}, thHi={'GB': 21}), Theta(thLo={'GB': 30}, thHi={'GB': 22}), Theta(thLo={'GB': 30}, thHi={'GB': 23}), Theta(thLo={'GB': 30}, thHi={'GB': 24}), Theta(thLo={'GB': 30}, thHi={'GB': 25}), Theta(thLo={'GB': 30}, thHi={'GB': 26}), Theta(thLo={'GB': 30}, thHi={'GB': 27}), Theta(thLo={'GB': 30}, thHi={'GB': 28}), Theta(thLo={'GB': 30}, thHi={'GB': 29}), Theta(thLo={'GB': 30}, thHi={'GB': 30}), Theta(thLo={'GB': 30}, thHi={'GB': 31}), Theta(thLo={'GB': 30}, thHi={'GB': 32}), Theta(thLo={'GB': 30}, thHi={'GB': 33}), Theta(thLo={'GB': 30}, thHi={'GB': 34}), Theta(thLo={'GB': 30}, thHi={'GB': 35}), Theta(thLo={'GB': 30}, thHi={'GB': 36}), Theta(thLo={'GB': 30}, thHi={'GB': 37}), Theta(thLo={'GB': 30}, thHi={'GB': 38}), Theta(thLo={'GB': 30}, thHi={'GB': 39}), Theta(thLo={'GB': 30}, thHi={'GB': 40}), Theta(thLo={'GB': 30}, thHi={'GB': 41}), Theta(thLo={'GB': 30}, thHi={'GB': 42}), Theta(thLo={'GB': 30}, thHi={'GB': 43}), Theta(thLo={'GB': 30}, thHi={'GB': 44}), Theta(thLo={'GB': 30}, thHi={'GB': 45}), Theta(thLo={'GB': 30}, thHi={'GB': 46}), Theta(thLo={'GB': 30}, thHi={'GB': 47}), Theta(thLo={'GB': 30}, thHi={'GB': 48}), Theta(thLo={'GB': 30}, thHi={'GB': 49}), Theta(thLo={'GB': 30}, thHi={'GB': 50}), Theta(thLo={'GB': 30}, thHi={'GB': 51}), Theta(thLo={'GB': 30}, thHi={'GB': 52}), Theta(thLo={'GB': 30}, thHi={'GB': 53}), Theta(thLo={'GB': 30}, thHi={'GB': 54}), Theta(thLo={'GB': 30}, thHi={'GB': 55}), Theta(thLo={'GB': 30}, thHi={'GB': 56}), Theta(thLo={'GB': 30}, thHi={'GB': 57}), Theta(thLo={'GB': 30}, thHi={'GB': 58}), Theta(thLo={'GB': 30}, thHi={'GB': 59}), Theta(thLo={'GB': 30}, thHi={'GB': 60}), Theta(thLo={'GB': 30}, thHi={'GB': 61}), Theta(thLo={'GB': 30}, thHi={'GB': 62}), Theta(thLo={'GB': 30}, thHi={'GB': 63}), Theta(thLo={'GB': 30}, thHi={'GB': 64}), Theta(thLo={'GB': 30}, thHi={'GB': 65}), Theta(thLo={'GB': 30}, thHi={'GB': 66}), Theta(thLo={'GB': 30}, thHi={'GB': 67}), Theta(thLo={'GB': 30}, thHi={'GB': 68}), Theta(thLo={'GB': 30}, thHi={'GB': 69}), Theta(thLo={'GB': 30}, thHi={'GB': 70}), Theta(thLo={'GB': 30}, thHi={'GB': 71}), Theta(thLo={'GB': 30}, thHi={'GB': 72}), Theta(thLo={'GB': 30}, thHi={'GB': 73}), Theta(thLo={'GB': 30}, thHi={'GB': 74}), Theta(thLo={'GB': 30}, thHi={'GB': 75}), Theta(thLo={'GB': 30}, thHi={'GB': 76}), Theta(thLo={'GB': 30}, thHi={'GB': 77}), Theta(thLo={'GB': 30}, thHi={'GB': 78}), Theta(thLo={'GB': 30}, thHi={'GB': 79}), Theta(thLo={'GB': 30}, thHi={'GB': 80}), Theta(thLo={'GB': 30}, thHi={'GB': 81}), Theta(thLo={'GB': 30}, thHi={'GB': 82}), Theta(thLo={'GB': 30}, thHi={'GB': 83}), Theta(thLo={'GB': 30}, thHi={'GB': 84}), Theta(thLo={'GB': 30}, thHi={'GB': 85}), Theta(thLo={'GB': 30}, thHi={'GB': 86}), Theta(thLo={'GB': 30}, thHi={'GB': 87}), Theta(thLo={'GB': 30}, thHi={'GB': 88}), Theta(thLo={'GB': 30}, thHi={'GB': 89}), Theta(thLo={'GB': 30}, thHi={'GB': 90}), Theta(thLo={'GB': 30}, thHi={'GB': 91}), Theta(thLo={'GB': 30}, thHi={'GB': 92}), Theta(thLo={'GB': 30}, thHi={'GB': 93}), Theta(thLo={'GB': 30}, thHi={'GB': 94}), Theta(thLo={'GB': 30}, thHi={'GB': 95}), Theta(thLo={'GB': 30}, thHi={'GB': 96}), Theta(thLo={'GB': 30}, thHi={'GB': 97}), Theta(thLo={'GB': 30}, thHi={'GB': 98}), Theta(thLo={'GB': 30}, thHi={'GB': 99}), Theta(thLo={'GB': 31}, thHi={'GB': 10}), Theta(thLo={'GB': 31}, thHi={'GB': 11}), Theta(thLo={'GB': 31}, thHi={'GB': 12}), Theta(thLo={'GB': 31}, thHi={'GB': 13}), Theta(thLo={'GB': 31}, thHi={'GB': 14}), Theta(thLo={'GB': 31}, thHi={'GB': 15}), Theta(thLo={'GB': 31}, thHi={'GB': 16}), Theta(thLo={'GB': 31}, thHi={'GB': 17}), Theta(thLo={'GB': 31}, thHi={'GB': 18}), Theta(thLo={'GB': 31}, thHi={'GB': 19}), Theta(thLo={'GB': 31}, thHi={'GB': 20}), Theta(thLo={'GB': 31}, thHi={'GB': 21}), Theta(thLo={'GB': 31}, thHi={'GB': 22}), Theta(thLo={'GB': 31}, thHi={'GB': 23}), Theta(thLo={'GB': 31}, thHi={'GB': 24}), Theta(thLo={'GB': 31}, thHi={'GB': 25}), Theta(thLo={'GB': 31}, thHi={'GB': 26}), Theta(thLo={'GB': 31}, thHi={'GB': 27}), Theta(thLo={'GB': 31}, thHi={'GB': 28}), Theta(thLo={'GB': 31}, thHi={'GB': 29}), Theta(thLo={'GB': 31}, thHi={'GB': 30}), Theta(thLo={'GB': 31}, thHi={'GB': 31}), Theta(thLo={'GB': 31}, thHi={'GB': 32}), Theta(thLo={'GB': 31}, thHi={'GB': 33}), Theta(thLo={'GB': 31}, thHi={'GB': 34}), Theta(thLo={'GB': 31}, thHi={'GB': 35}), Theta(thLo={'GB': 31}, thHi={'GB': 36}), Theta(thLo={'GB': 31}, thHi={'GB': 37}), Theta(thLo={'GB': 31}, thHi={'GB': 38}), Theta(thLo={'GB': 31}, thHi={'GB': 39}), Theta(thLo={'GB': 31}, thHi={'GB': 40}), Theta(thLo={'GB': 31}, thHi={'GB': 41}), Theta(thLo={'GB': 31}, thHi={'GB': 42}), Theta(thLo={'GB': 31}, thHi={'GB': 43}), Theta(thLo={'GB': 31}, thHi={'GB': 44}), Theta(thLo={'GB': 31}, thHi={'GB': 45}), Theta(thLo={'GB': 31}, thHi={'GB': 46}), Theta(thLo={'GB': 31}, thHi={'GB': 47}), Theta(thLo={'GB': 31}, thHi={'GB': 48}), Theta(thLo={'GB': 31}, thHi={'GB': 49}), Theta(thLo={'GB': 31}, thHi={'GB': 50}), Theta(thLo={'GB': 31}, thHi={'GB': 51}), Theta(thLo={'GB': 31}, thHi={'GB': 52}), Theta(thLo={'GB': 31}, thHi={'GB': 53}), Theta(thLo={'GB': 31}, thHi={'GB': 54}), Theta(thLo={'GB': 31}, thHi={'GB': 55}), Theta(thLo={'GB': 31}, thHi={'GB': 56}), Theta(thLo={'GB': 31}, thHi={'GB': 57}), Theta(thLo={'GB': 31}, thHi={'GB': 58}), Theta(thLo={'GB': 31}, thHi={'GB': 59}), Theta(thLo={'GB': 31}, thHi={'GB': 60}), Theta(thLo={'GB': 31}, thHi={'GB': 61}), Theta(thLo={'GB': 31}, thHi={'GB': 62}), Theta(thLo={'GB': 31}, thHi={'GB': 63}), Theta(thLo={'GB': 31}, thHi={'GB': 64}), Theta(thLo={'GB': 31}, thHi={'GB': 65}), Theta(thLo={'GB': 31}, thHi={'GB': 66}), Theta(thLo={'GB': 31}, thHi={'GB': 67}), Theta(thLo={'GB': 31}, thHi={'GB': 68}), Theta(thLo={'GB': 31}, thHi={'GB': 69}), Theta(thLo={'GB': 31}, thHi={'GB': 70}), Theta(thLo={'GB': 31}, thHi={'GB': 71}), Theta(thLo={'GB': 31}, thHi={'GB': 72}), Theta(thLo={'GB': 31}, thHi={'GB': 73}), Theta(thLo={'GB': 31}, thHi={'GB': 74}), Theta(thLo={'GB': 31}, thHi={'GB': 75}), Theta(thLo={'GB': 31}, thHi={'GB': 76}), Theta(thLo={'GB': 31}, thHi={'GB': 77}), Theta(thLo={'GB': 31}, thHi={'GB': 78}), Theta(thLo={'GB': 31}, thHi={'GB': 79}), Theta(thLo={'GB': 31}, thHi={'GB': 80}), Theta(thLo={'GB': 31}, thHi={'GB': 81}), Theta(thLo={'GB': 31}, thHi={'GB': 82}), Theta(thLo={'GB': 31}, thHi={'GB': 83}), Theta(thLo={'GB': 31}, thHi={'GB': 84}), Theta(thLo={'GB': 31}, thHi={'GB': 85}), Theta(thLo={'GB': 31}, thHi={'GB': 86}), Theta(thLo={'GB': 31}, thHi={'GB': 87}), Theta(thLo={'GB': 31}, thHi={'GB': 88}), Theta(thLo={'GB': 31}, thHi={'GB': 89}), Theta(thLo={'GB': 31}, thHi={'GB': 90}), Theta(thLo={'GB': 31}, thHi={'GB': 91}), Theta(thLo={'GB': 31}, thHi={'GB': 92}), Theta(thLo={'GB': 31}, thHi={'GB': 93}), Theta(thLo={'GB': 31}, thHi={'GB': 94}), Theta(thLo={'GB': 31}, thHi={'GB': 95}), Theta(thLo={'GB': 31}, thHi={'GB': 96}), Theta(thLo={'GB': 31}, thHi={'GB': 97}), Theta(thLo={'GB': 31}, thHi={'GB': 98}), Theta(thLo={'GB': 31}, thHi={'GB': 99}), Theta(thLo={'GB': 32}, thHi={'GB': 10}), Theta(thLo={'GB': 32}, thHi={'GB': 11}), Theta(thLo={'GB': 32}, thHi={'GB': 12}), Theta(thLo={'GB': 32}, thHi={'GB': 13}), Theta(thLo={'GB': 32}, thHi={'GB': 14}), Theta(thLo={'GB': 32}, thHi={'GB': 15}), Theta(thLo={'GB': 32}, thHi={'GB': 16}), Theta(thLo={'GB': 32}, thHi={'GB': 17}), Theta(thLo={'GB': 32}, thHi={'GB': 18}), Theta(thLo={'GB': 32}, thHi={'GB': 19}), Theta(thLo={'GB': 32}, thHi={'GB': 20}), Theta(thLo={'GB': 32}, thHi={'GB': 21}), Theta(thLo={'GB': 32}, thHi={'GB': 22}), Theta(thLo={'GB': 32}, thHi={'GB': 23}), Theta(thLo={'GB': 32}, thHi={'GB': 24}), Theta(thLo={'GB': 32}, thHi={'GB': 25}), Theta(thLo={'GB': 32}, thHi={'GB': 26}), Theta(thLo={'GB': 32}, thHi={'GB': 27}), Theta(thLo={'GB': 32}, thHi={'GB': 28}), Theta(thLo={'GB': 32}, thHi={'GB': 29}), Theta(thLo={'GB': 32}, thHi={'GB': 30}), Theta(thLo={'GB': 32}, thHi={'GB': 31}), Theta(thLo={'GB': 32}, thHi={'GB': 32}), Theta(thLo={'GB': 32}, thHi={'GB': 33}), Theta(thLo={'GB': 32}, thHi={'GB': 34}), Theta(thLo={'GB': 32}, thHi={'GB': 35}), Theta(thLo={'GB': 32}, thHi={'GB': 36}), Theta(thLo={'GB': 32}, thHi={'GB': 37}), Theta(thLo={'GB': 32}, thHi={'GB': 38}), Theta(thLo={'GB': 32}, thHi={'GB': 39}), Theta(thLo={'GB': 32}, thHi={'GB': 40}), Theta(thLo={'GB': 32}, thHi={'GB': 41}), Theta(thLo={'GB': 32}, thHi={'GB': 42}), Theta(thLo={'GB': 32}, thHi={'GB': 43}), Theta(thLo={'GB': 32}, thHi={'GB': 44}), Theta(thLo={'GB': 32}, thHi={'GB': 45}), Theta(thLo={'GB': 32}, thHi={'GB': 46}), Theta(thLo={'GB': 32}, thHi={'GB': 47}), Theta(thLo={'GB': 32}, thHi={'GB': 48}), Theta(thLo={'GB': 32}, thHi={'GB': 49}), Theta(thLo={'GB': 32}, thHi={'GB': 50}), Theta(thLo={'GB': 32}, thHi={'GB': 51}), Theta(thLo={'GB': 32}, thHi={'GB': 52}), Theta(thLo={'GB': 32}, thHi={'GB': 53}), Theta(thLo={'GB': 32}, thHi={'GB': 54}), Theta(thLo={'GB': 32}, thHi={'GB': 55}), Theta(thLo={'GB': 32}, thHi={'GB': 56}), Theta(thLo={'GB': 32}, thHi={'GB': 57}), Theta(thLo={'GB': 32}, thHi={'GB': 58}), Theta(thLo={'GB': 32}, thHi={'GB': 59}), Theta(thLo={'GB': 32}, thHi={'GB': 60}), Theta(thLo={'GB': 32}, thHi={'GB': 61}), Theta(thLo={'GB': 32}, thHi={'GB': 62}), Theta(thLo={'GB': 32}, thHi={'GB': 63}), Theta(thLo={'GB': 32}, thHi={'GB': 64}), Theta(thLo={'GB': 32}, thHi={'GB': 65}), Theta(thLo={'GB': 32}, thHi={'GB': 66}), Theta(thLo={'GB': 32}, thHi={'GB': 67}), Theta(thLo={'GB': 32}, thHi={'GB': 68}), Theta(thLo={'GB': 32}, thHi={'GB': 69}), Theta(thLo={'GB': 32}, thHi={'GB': 70}), Theta(thLo={'GB': 32}, thHi={'GB': 71}), Theta(thLo={'GB': 32}, thHi={'GB': 72}), Theta(thLo={'GB': 32}, thHi={'GB': 73}), Theta(thLo={'GB': 32}, thHi={'GB': 74}), Theta(thLo={'GB': 32}, thHi={'GB': 75}), Theta(thLo={'GB': 32}, thHi={'GB': 76}), Theta(thLo={'GB': 32}, thHi={'GB': 77}), Theta(thLo={'GB': 32}, thHi={'GB': 78}), Theta(thLo={'GB': 32}, thHi={'GB': 79}), Theta(thLo={'GB': 32}, thHi={'GB': 80}), Theta(thLo={'GB': 32}, thHi={'GB': 81}), Theta(thLo={'GB': 32}, thHi={'GB': 82}), Theta(thLo={'GB': 32}, thHi={'GB': 83}), Theta(thLo={'GB': 32}, thHi={'GB': 84}), Theta(thLo={'GB': 32}, thHi={'GB': 85}), Theta(thLo={'GB': 32}, thHi={'GB': 86}), Theta(thLo={'GB': 32}, thHi={'GB': 87}), Theta(thLo={'GB': 32}, thHi={'GB': 88}), Theta(thLo={'GB': 32}, thHi={'GB': 89}), Theta(thLo={'GB': 32}, thHi={'GB': 90}), Theta(thLo={'GB': 32}, thHi={'GB': 91}), Theta(thLo={'GB': 32}, thHi={'GB': 92}), Theta(thLo={'GB': 32}, thHi={'GB': 93}), Theta(thLo={'GB': 32}, thHi={'GB': 94}), Theta(thLo={'GB': 32}, thHi={'GB': 95}), Theta(thLo={'GB': 32}, thHi={'GB': 96}), Theta(thLo={'GB': 32}, thHi={'GB': 97}), Theta(thLo={'GB': 32}, thHi={'GB': 98}), Theta(thLo={'GB': 32}, thHi={'GB': 99}), Theta(thLo={'GB': 33}, thHi={'GB': 10}), Theta(thLo={'GB': 33}, thHi={'GB': 11}), Theta(thLo={'GB': 33}, thHi={'GB': 12}), Theta(thLo={'GB': 33}, thHi={'GB': 13}), Theta(thLo={'GB': 33}, thHi={'GB': 14}), Theta(thLo={'GB': 33}, thHi={'GB': 15}), Theta(thLo={'GB': 33}, thHi={'GB': 16}), Theta(thLo={'GB': 33}, thHi={'GB': 17}), Theta(thLo={'GB': 33}, thHi={'GB': 18}), Theta(thLo={'GB': 33}, thHi={'GB': 19}), Theta(thLo={'GB': 33}, thHi={'GB': 20}), Theta(thLo={'GB': 33}, thHi={'GB': 21}), Theta(thLo={'GB': 33}, thHi={'GB': 22}), Theta(thLo={'GB': 33}, thHi={'GB': 23}), Theta(thLo={'GB': 33}, thHi={'GB': 24}), Theta(thLo={'GB': 33}, thHi={'GB': 25}), Theta(thLo={'GB': 33}, thHi={'GB': 26}), Theta(thLo={'GB': 33}, thHi={'GB': 27}), Theta(thLo={'GB': 33}, thHi={'GB': 28}), Theta(thLo={'GB': 33}, thHi={'GB': 29}), Theta(thLo={'GB': 33}, thHi={'GB': 30}), Theta(thLo={'GB': 33}, thHi={'GB': 31}), Theta(thLo={'GB': 33}, thHi={'GB': 32}), Theta(thLo={'GB': 33}, thHi={'GB': 33}), Theta(thLo={'GB': 33}, thHi={'GB': 34}), Theta(thLo={'GB': 33}, thHi={'GB': 35}), Theta(thLo={'GB': 33}, thHi={'GB': 36}), Theta(thLo={'GB': 33}, thHi={'GB': 37}), Theta(thLo={'GB': 33}, thHi={'GB': 38}), Theta(thLo={'GB': 33}, thHi={'GB': 39}), Theta(thLo={'GB': 33}, thHi={'GB': 40}), Theta(thLo={'GB': 33}, thHi={'GB': 41}), Theta(thLo={'GB': 33}, thHi={'GB': 42}), Theta(thLo={'GB': 33}, thHi={'GB': 43}), Theta(thLo={'GB': 33}, thHi={'GB': 44}), Theta(thLo={'GB': 33}, thHi={'GB': 45}), Theta(thLo={'GB': 33}, thHi={'GB': 46}), Theta(thLo={'GB': 33}, thHi={'GB': 47}), Theta(thLo={'GB': 33}, thHi={'GB': 48}), Theta(thLo={'GB': 33}, thHi={'GB': 49}), Theta(thLo={'GB': 33}, thHi={'GB': 50}), Theta(thLo={'GB': 33}, thHi={'GB': 51}), Theta(thLo={'GB': 33}, thHi={'GB': 52}), Theta(thLo={'GB': 33}, thHi={'GB': 53}), Theta(thLo={'GB': 33}, thHi={'GB': 54}), Theta(thLo={'GB': 33}, thHi={'GB': 55}), Theta(thLo={'GB': 33}, thHi={'GB': 56}), Theta(thLo={'GB': 33}, thHi={'GB': 57}), Theta(thLo={'GB': 33}, thHi={'GB': 58}), Theta(thLo={'GB': 33}, thHi={'GB': 59}), Theta(thLo={'GB': 33}, thHi={'GB': 60}), Theta(thLo={'GB': 33}, thHi={'GB': 61}), Theta(thLo={'GB': 33}, thHi={'GB': 62}), Theta(thLo={'GB': 33}, thHi={'GB': 63}), Theta(thLo={'GB': 33}, thHi={'GB': 64}), Theta(thLo={'GB': 33}, thHi={'GB': 65}), Theta(thLo={'GB': 33}, thHi={'GB': 66}), Theta(thLo={'GB': 33}, thHi={'GB': 67}), Theta(thLo={'GB': 33}, thHi={'GB': 68}), Theta(thLo={'GB': 33}, thHi={'GB': 69}), Theta(thLo={'GB': 33}, thHi={'GB': 70}), Theta(thLo={'GB': 33}, thHi={'GB': 71}), Theta(thLo={'GB': 33}, thHi={'GB': 72}), Theta(thLo={'GB': 33}, thHi={'GB': 73}), Theta(thLo={'GB': 33}, thHi={'GB': 74}), Theta(thLo={'GB': 33}, thHi={'GB': 75}), Theta(thLo={'GB': 33}, thHi={'GB': 76}), Theta(thLo={'GB': 33}, thHi={'GB': 77}), Theta(thLo={'GB': 33}, thHi={'GB': 78}), Theta(thLo={'GB': 33}, thHi={'GB': 79}), Theta(thLo={'GB': 33}, thHi={'GB': 80}), Theta(thLo={'GB': 33}, thHi={'GB': 81}), Theta(thLo={'GB': 33}, thHi={'GB': 82}), Theta(thLo={'GB': 33}, thHi={'GB': 83}), Theta(thLo={'GB': 33}, thHi={'GB': 84}), Theta(thLo={'GB': 33}, thHi={'GB': 85}), Theta(thLo={'GB': 33}, thHi={'GB': 86}), Theta(thLo={'GB': 33}, thHi={'GB': 87}), Theta(thLo={'GB': 33}, thHi={'GB': 88}), Theta(thLo={'GB': 33}, thHi={'GB': 89}), Theta(thLo={'GB': 33}, thHi={'GB': 90}), Theta(thLo={'GB': 33}, thHi={'GB': 91}), Theta(thLo={'GB': 33}, thHi={'GB': 92}), Theta(thLo={'GB': 33}, thHi={'GB': 93}), Theta(thLo={'GB': 33}, thHi={'GB': 94}), Theta(thLo={'GB': 33}, thHi={'GB': 95}), Theta(thLo={'GB': 33}, thHi={'GB': 96}), Theta(thLo={'GB': 33}, thHi={'GB': 97}), Theta(thLo={'GB': 33}, thHi={'GB': 98}), Theta(thLo={'GB': 33}, thHi={'GB': 99}), Theta(thLo={'GB': 34}, thHi={'GB': 10}), Theta(thLo={'GB': 34}, thHi={'GB': 11}), Theta(thLo={'GB': 34}, thHi={'GB': 12}), Theta(thLo={'GB': 34}, thHi={'GB': 13}), Theta(thLo={'GB': 34}, thHi={'GB': 14}), Theta(thLo={'GB': 34}, thHi={'GB': 15}), Theta(thLo={'GB': 34}, thHi={'GB': 16}), Theta(thLo={'GB': 34}, thHi={'GB': 17}), Theta(thLo={'GB': 34}, thHi={'GB': 18}), Theta(thLo={'GB': 34}, thHi={'GB': 19}), Theta(thLo={'GB': 34}, thHi={'GB': 20}), Theta(thLo={'GB': 34}, thHi={'GB': 21}), Theta(thLo={'GB': 34}, thHi={'GB': 22}), Theta(thLo={'GB': 34}, thHi={'GB': 23}), Theta(thLo={'GB': 34}, thHi={'GB': 24}), Theta(thLo={'GB': 34}, thHi={'GB': 25}), Theta(thLo={'GB': 34}, thHi={'GB': 26}), Theta(thLo={'GB': 34}, thHi={'GB': 27}), Theta(thLo={'GB': 34}, thHi={'GB': 28}), Theta(thLo={'GB': 34}, thHi={'GB': 29}), Theta(thLo={'GB': 34}, thHi={'GB': 30}), Theta(thLo={'GB': 34}, thHi={'GB': 31}), Theta(thLo={'GB': 34}, thHi={'GB': 32}), Theta(thLo={'GB': 34}, thHi={'GB': 33}), Theta(thLo={'GB': 34}, thHi={'GB': 34}), Theta(thLo={'GB': 34}, thHi={'GB': 35}), Theta(thLo={'GB': 34}, thHi={'GB': 36}), Theta(thLo={'GB': 34}, thHi={'GB': 37}), Theta(thLo={'GB': 34}, thHi={'GB': 38}), Theta(thLo={'GB': 34}, thHi={'GB': 39}), Theta(thLo={'GB': 34}, thHi={'GB': 40}), Theta(thLo={'GB': 34}, thHi={'GB': 41}), Theta(thLo={'GB': 34}, thHi={'GB': 42}), Theta(thLo={'GB': 34}, thHi={'GB': 43}), Theta(thLo={'GB': 34}, thHi={'GB': 44}), Theta(thLo={'GB': 34}, thHi={'GB': 45}), Theta(thLo={'GB': 34}, thHi={'GB': 46}), Theta(thLo={'GB': 34}, thHi={'GB': 47}), Theta(thLo={'GB': 34}, thHi={'GB': 48}), Theta(thLo={'GB': 34}, thHi={'GB': 49}), Theta(thLo={'GB': 34}, thHi={'GB': 50}), Theta(thLo={'GB': 34}, thHi={'GB': 51}), Theta(thLo={'GB': 34}, thHi={'GB': 52}), Theta(thLo={'GB': 34}, thHi={'GB': 53}), Theta(thLo={'GB': 34}, thHi={'GB': 54}), Theta(thLo={'GB': 34}, thHi={'GB': 55}), Theta(thLo={'GB': 34}, thHi={'GB': 56}), Theta(thLo={'GB': 34}, thHi={'GB': 57}), Theta(thLo={'GB': 34}, thHi={'GB': 58}), Theta(thLo={'GB': 34}, thHi={'GB': 59}), Theta(thLo={'GB': 34}, thHi={'GB': 60}), Theta(thLo={'GB': 34}, thHi={'GB': 61}), Theta(thLo={'GB': 34}, thHi={'GB': 62}), Theta(thLo={'GB': 34}, thHi={'GB': 63}), Theta(thLo={'GB': 34}, thHi={'GB': 64}), Theta(thLo={'GB': 34}, thHi={'GB': 65}), Theta(thLo={'GB': 34}, thHi={'GB': 66}), Theta(thLo={'GB': 34}, thHi={'GB': 67}), Theta(thLo={'GB': 34}, thHi={'GB': 68}), Theta(thLo={'GB': 34}, thHi={'GB': 69}), Theta(thLo={'GB': 34}, thHi={'GB': 70}), Theta(thLo={'GB': 34}, thHi={'GB': 71}), Theta(thLo={'GB': 34}, thHi={'GB': 72}), Theta(thLo={'GB': 34}, thHi={'GB': 73}), Theta(thLo={'GB': 34}, thHi={'GB': 74}), Theta(thLo={'GB': 34}, thHi={'GB': 75}), Theta(thLo={'GB': 34}, thHi={'GB': 76}), Theta(thLo={'GB': 34}, thHi={'GB': 77}), Theta(thLo={'GB': 34}, thHi={'GB': 78}), Theta(thLo={'GB': 34}, thHi={'GB': 79}), Theta(thLo={'GB': 34}, thHi={'GB': 80}), Theta(thLo={'GB': 34}, thHi={'GB': 81}), Theta(thLo={'GB': 34}, thHi={'GB': 82}), Theta(thLo={'GB': 34}, thHi={'GB': 83}), Theta(thLo={'GB': 34}, thHi={'GB': 84}), Theta(thLo={'GB': 34}, thHi={'GB': 85}), Theta(thLo={'GB': 34}, thHi={'GB': 86}), Theta(thLo={'GB': 34}, thHi={'GB': 87}), Theta(thLo={'GB': 34}, thHi={'GB': 88}), Theta(thLo={'GB': 34}, thHi={'GB': 89}), Theta(thLo={'GB': 34}, thHi={'GB': 90}), Theta(thLo={'GB': 34}, thHi={'GB': 91}), Theta(thLo={'GB': 34}, thHi={'GB': 92}), Theta(thLo={'GB': 34}, thHi={'GB': 93}), Theta(thLo={'GB': 34}, thHi={'GB': 94}), Theta(thLo={'GB': 34}, thHi={'GB': 95}), Theta(thLo={'GB': 34}, thHi={'GB': 96}), Theta(thLo={'GB': 34}, thHi={'GB': 97}), Theta(thLo={'GB': 34}, thHi={'GB': 98}), Theta(thLo={'GB': 34}, thHi={'GB': 99}), Theta(thLo={'GB': 35}, thHi={'GB': 10}), Theta(thLo={'GB': 35}, thHi={'GB': 11}), Theta(thLo={'GB': 35}, thHi={'GB': 12}), Theta(thLo={'GB': 35}, thHi={'GB': 13}), Theta(thLo={'GB': 35}, thHi={'GB': 14}), Theta(thLo={'GB': 35}, thHi={'GB': 15}), Theta(thLo={'GB': 35}, thHi={'GB': 16}), Theta(thLo={'GB': 35}, thHi={'GB': 17}), Theta(thLo={'GB': 35}, thHi={'GB': 18}), Theta(thLo={'GB': 35}, thHi={'GB': 19}), Theta(thLo={'GB': 35}, thHi={'GB': 20}), Theta(thLo={'GB': 35}, thHi={'GB': 21}), Theta(thLo={'GB': 35}, thHi={'GB': 22}), Theta(thLo={'GB': 35}, thHi={'GB': 23}), Theta(thLo={'GB': 35}, thHi={'GB': 24}), Theta(thLo={'GB': 35}, thHi={'GB': 25}), Theta(thLo={'GB': 35}, thHi={'GB': 26}), Theta(thLo={'GB': 35}, thHi={'GB': 27}), Theta(thLo={'GB': 35}, thHi={'GB': 28}), Theta(thLo={'GB': 35}, thHi={'GB': 29}), Theta(thLo={'GB': 35}, thHi={'GB': 30}), Theta(thLo={'GB': 35}, thHi={'GB': 31}), Theta(thLo={'GB': 35}, thHi={'GB': 32}), Theta(thLo={'GB': 35}, thHi={'GB': 33}), Theta(thLo={'GB': 35}, thHi={'GB': 34}), Theta(thLo={'GB': 35}, thHi={'GB': 35}), Theta(thLo={'GB': 35}, thHi={'GB': 36}), Theta(thLo={'GB': 35}, thHi={'GB': 37}), Theta(thLo={'GB': 35}, thHi={'GB': 38}), Theta(thLo={'GB': 35}, thHi={'GB': 39}), Theta(thLo={'GB': 35}, thHi={'GB': 40}), Theta(thLo={'GB': 35}, thHi={'GB': 41}), Theta(thLo={'GB': 35}, thHi={'GB': 42}), Theta(thLo={'GB': 35}, thHi={'GB': 43}), Theta(thLo={'GB': 35}, thHi={'GB': 44}), Theta(thLo={'GB': 35}, thHi={'GB': 45}), Theta(thLo={'GB': 35}, thHi={'GB': 46}), Theta(thLo={'GB': 35}, thHi={'GB': 47}), Theta(thLo={'GB': 35}, thHi={'GB': 48}), Theta(thLo={'GB': 35}, thHi={'GB': 49}), Theta(thLo={'GB': 35}, thHi={'GB': 50}), Theta(thLo={'GB': 35}, thHi={'GB': 51}), Theta(thLo={'GB': 35}, thHi={'GB': 52}), Theta(thLo={'GB': 35}, thHi={'GB': 53}), Theta(thLo={'GB': 35}, thHi={'GB': 54}), Theta(thLo={'GB': 35}, thHi={'GB': 55}), Theta(thLo={'GB': 35}, thHi={'GB': 56}), Theta(thLo={'GB': 35}, thHi={'GB': 57}), Theta(thLo={'GB': 35}, thHi={'GB': 58}), Theta(thLo={'GB': 35}, thHi={'GB': 59}), Theta(thLo={'GB': 35}, thHi={'GB': 60}), Theta(thLo={'GB': 35}, thHi={'GB': 61}), Theta(thLo={'GB': 35}, thHi={'GB': 62}), Theta(thLo={'GB': 35}, thHi={'GB': 63}), Theta(thLo={'GB': 35}, thHi={'GB': 64}), Theta(thLo={'GB': 35}, thHi={'GB': 65}), Theta(thLo={'GB': 35}, thHi={'GB': 66}), Theta(thLo={'GB': 35}, thHi={'GB': 67}), Theta(thLo={'GB': 35}, thHi={'GB': 68}), Theta(thLo={'GB': 35}, thHi={'GB': 69}), Theta(thLo={'GB': 35}, thHi={'GB': 70}), Theta(thLo={'GB': 35}, thHi={'GB': 71}), Theta(thLo={'GB': 35}, thHi={'GB': 72}), Theta(thLo={'GB': 35}, thHi={'GB': 73}), Theta(thLo={'GB': 35}, thHi={'GB': 74}), Theta(thLo={'GB': 35}, thHi={'GB': 75}), Theta(thLo={'GB': 35}, thHi={'GB': 76}), Theta(thLo={'GB': 35}, thHi={'GB': 77}), Theta(thLo={'GB': 35}, thHi={'GB': 78}), Theta(thLo={'GB': 35}, thHi={'GB': 79}), Theta(thLo={'GB': 35}, thHi={'GB': 80}), Theta(thLo={'GB': 35}, thHi={'GB': 81}), Theta(thLo={'GB': 35}, thHi={'GB': 82}), Theta(thLo={'GB': 35}, thHi={'GB': 83}), Theta(thLo={'GB': 35}, thHi={'GB': 84}), Theta(thLo={'GB': 35}, thHi={'GB': 85}), Theta(thLo={'GB': 35}, thHi={'GB': 86}), Theta(thLo={'GB': 35}, thHi={'GB': 87}), Theta(thLo={'GB': 35}, thHi={'GB': 88}), Theta(thLo={'GB': 35}, thHi={'GB': 89}), Theta(thLo={'GB': 35}, thHi={'GB': 90}), Theta(thLo={'GB': 35}, thHi={'GB': 91}), Theta(thLo={'GB': 35}, thHi={'GB': 92}), Theta(thLo={'GB': 35}, thHi={'GB': 93}), Theta(thLo={'GB': 35}, thHi={'GB': 94}), Theta(thLo={'GB': 35}, thHi={'GB': 95}), Theta(thLo={'GB': 35}, thHi={'GB': 96}), Theta(thLo={'GB': 35}, thHi={'GB': 97}), Theta(thLo={'GB': 35}, thHi={'GB': 98}), Theta(thLo={'GB': 35}, thHi={'GB': 99}), Theta(thLo={'GB': 36}, thHi={'GB': 10}), Theta(thLo={'GB': 36}, thHi={'GB': 11}), Theta(thLo={'GB': 36}, thHi={'GB': 12}), Theta(thLo={'GB': 36}, thHi={'GB': 13}), Theta(thLo={'GB': 36}, thHi={'GB': 14}), Theta(thLo={'GB': 36}, thHi={'GB': 15}), Theta(thLo={'GB': 36}, thHi={'GB': 16}), Theta(thLo={'GB': 36}, thHi={'GB': 17}), Theta(thLo={'GB': 36}, thHi={'GB': 18}), Theta(thLo={'GB': 36}, thHi={'GB': 19}), Theta(thLo={'GB': 36}, thHi={'GB': 20}), Theta(thLo={'GB': 36}, thHi={'GB': 21}), Theta(thLo={'GB': 36}, thHi={'GB': 22}), Theta(thLo={'GB': 36}, thHi={'GB': 23}), Theta(thLo={'GB': 36}, thHi={'GB': 24}), Theta(thLo={'GB': 36}, thHi={'GB': 25}), Theta(thLo={'GB': 36}, thHi={'GB': 26}), Theta(thLo={'GB': 36}, thHi={'GB': 27}), Theta(thLo={'GB': 36}, thHi={'GB': 28}), Theta(thLo={'GB': 36}, thHi={'GB': 29}), Theta(thLo={'GB': 36}, thHi={'GB': 30}), Theta(thLo={'GB': 36}, thHi={'GB': 31}), Theta(thLo={'GB': 36}, thHi={'GB': 32}), Theta(thLo={'GB': 36}, thHi={'GB': 33}), Theta(thLo={'GB': 36}, thHi={'GB': 34}), Theta(thLo={'GB': 36}, thHi={'GB': 35}), Theta(thLo={'GB': 36}, thHi={'GB': 36}), Theta(thLo={'GB': 36}, thHi={'GB': 37}), Theta(thLo={'GB': 36}, thHi={'GB': 38}), Theta(thLo={'GB': 36}, thHi={'GB': 39}), Theta(thLo={'GB': 36}, thHi={'GB': 40}), Theta(thLo={'GB': 36}, thHi={'GB': 41}), Theta(thLo={'GB': 36}, thHi={'GB': 42}), Theta(thLo={'GB': 36}, thHi={'GB': 43}), Theta(thLo={'GB': 36}, thHi={'GB': 44}), Theta(thLo={'GB': 36}, thHi={'GB': 45}), Theta(thLo={'GB': 36}, thHi={'GB': 46}), Theta(thLo={'GB': 36}, thHi={'GB': 47}), Theta(thLo={'GB': 36}, thHi={'GB': 48}), Theta(thLo={'GB': 36}, thHi={'GB': 49}), Theta(thLo={'GB': 36}, thHi={'GB': 50}), Theta(thLo={'GB': 36}, thHi={'GB': 51}), Theta(thLo={'GB': 36}, thHi={'GB': 52}), Theta(thLo={'GB': 36}, thHi={'GB': 53}), Theta(thLo={'GB': 36}, thHi={'GB': 54}), Theta(thLo={'GB': 36}, thHi={'GB': 55}), Theta(thLo={'GB': 36}, thHi={'GB': 56}), Theta(thLo={'GB': 36}, thHi={'GB': 57}), Theta(thLo={'GB': 36}, thHi={'GB': 58}), Theta(thLo={'GB': 36}, thHi={'GB': 59}), Theta(thLo={'GB': 36}, thHi={'GB': 60}), Theta(thLo={'GB': 36}, thHi={'GB': 61}), Theta(thLo={'GB': 36}, thHi={'GB': 62}), Theta(thLo={'GB': 36}, thHi={'GB': 63}), Theta(thLo={'GB': 36}, thHi={'GB': 64}), Theta(thLo={'GB': 36}, thHi={'GB': 65}), Theta(thLo={'GB': 36}, thHi={'GB': 66}), Theta(thLo={'GB': 36}, thHi={'GB': 67}), Theta(thLo={'GB': 36}, thHi={'GB': 68}), Theta(thLo={'GB': 36}, thHi={'GB': 69}), Theta(thLo={'GB': 36}, thHi={'GB': 70}), Theta(thLo={'GB': 36}, thHi={'GB': 71}), Theta(thLo={'GB': 36}, thHi={'GB': 72}), Theta(thLo={'GB': 36}, thHi={'GB': 73}), Theta(thLo={'GB': 36}, thHi={'GB': 74}), Theta(thLo={'GB': 36}, thHi={'GB': 75}), Theta(thLo={'GB': 36}, thHi={'GB': 76}), Theta(thLo={'GB': 36}, thHi={'GB': 77}), Theta(thLo={'GB': 36}, thHi={'GB': 78}), Theta(thLo={'GB': 36}, thHi={'GB': 79}), Theta(thLo={'GB': 36}, thHi={'GB': 80}), Theta(thLo={'GB': 36}, thHi={'GB': 81}), Theta(thLo={'GB': 36}, thHi={'GB': 82}), Theta(thLo={'GB': 36}, thHi={'GB': 83}), Theta(thLo={'GB': 36}, thHi={'GB': 84}), Theta(thLo={'GB': 36}, thHi={'GB': 85}), Theta(thLo={'GB': 36}, thHi={'GB': 86}), Theta(thLo={'GB': 36}, thHi={'GB': 87}), Theta(thLo={'GB': 36}, thHi={'GB': 88}), Theta(thLo={'GB': 36}, thHi={'GB': 89}), Theta(thLo={'GB': 36}, thHi={'GB': 90}), Theta(thLo={'GB': 36}, thHi={'GB': 91}), Theta(thLo={'GB': 36}, thHi={'GB': 92}), Theta(thLo={'GB': 36}, thHi={'GB': 93}), Theta(thLo={'GB': 36}, thHi={'GB': 94}), Theta(thLo={'GB': 36}, thHi={'GB': 95}), Theta(thLo={'GB': 36}, thHi={'GB': 96}), Theta(thLo={'GB': 36}, thHi={'GB': 97}), Theta(thLo={'GB': 36}, thHi={'GB': 98}), Theta(thLo={'GB': 36}, thHi={'GB': 99}), Theta(thLo={'GB': 37}, thHi={'GB': 10}), Theta(thLo={'GB': 37}, thHi={'GB': 11}), Theta(thLo={'GB': 37}, thHi={'GB': 12}), Theta(thLo={'GB': 37}, thHi={'GB': 13}), Theta(thLo={'GB': 37}, thHi={'GB': 14}), Theta(thLo={'GB': 37}, thHi={'GB': 15}), Theta(thLo={'GB': 37}, thHi={'GB': 16}), Theta(thLo={'GB': 37}, thHi={'GB': 17}), Theta(thLo={'GB': 37}, thHi={'GB': 18}), Theta(thLo={'GB': 37}, thHi={'GB': 19}), Theta(thLo={'GB': 37}, thHi={'GB': 20}), Theta(thLo={'GB': 37}, thHi={'GB': 21}), Theta(thLo={'GB': 37}, thHi={'GB': 22}), Theta(thLo={'GB': 37}, thHi={'GB': 23}), Theta(thLo={'GB': 37}, thHi={'GB': 24}), Theta(thLo={'GB': 37}, thHi={'GB': 25}), Theta(thLo={'GB': 37}, thHi={'GB': 26}), Theta(thLo={'GB': 37}, thHi={'GB': 27}), Theta(thLo={'GB': 37}, thHi={'GB': 28}), Theta(thLo={'GB': 37}, thHi={'GB': 29}), Theta(thLo={'GB': 37}, thHi={'GB': 30}), Theta(thLo={'GB': 37}, thHi={'GB': 31}), Theta(thLo={'GB': 37}, thHi={'GB': 32}), Theta(thLo={'GB': 37}, thHi={'GB': 33}), Theta(thLo={'GB': 37}, thHi={'GB': 34}), Theta(thLo={'GB': 37}, thHi={'GB': 35}), Theta(thLo={'GB': 37}, thHi={'GB': 36}), Theta(thLo={'GB': 37}, thHi={'GB': 37}), Theta(thLo={'GB': 37}, thHi={'GB': 38}), Theta(thLo={'GB': 37}, thHi={'GB': 39}), Theta(thLo={'GB': 37}, thHi={'GB': 40}), Theta(thLo={'GB': 37}, thHi={'GB': 41}), Theta(thLo={'GB': 37}, thHi={'GB': 42}), Theta(thLo={'GB': 37}, thHi={'GB': 43}), Theta(thLo={'GB': 37}, thHi={'GB': 44}), Theta(thLo={'GB': 37}, thHi={'GB': 45}), Theta(thLo={'GB': 37}, thHi={'GB': 46}), Theta(thLo={'GB': 37}, thHi={'GB': 47}), Theta(thLo={'GB': 37}, thHi={'GB': 48}), Theta(thLo={'GB': 37}, thHi={'GB': 49}), Theta(thLo={'GB': 37}, thHi={'GB': 50}), Theta(thLo={'GB': 37}, thHi={'GB': 51}), Theta(thLo={'GB': 37}, thHi={'GB': 52}), Theta(thLo={'GB': 37}, thHi={'GB': 53}), Theta(thLo={'GB': 37}, thHi={'GB': 54}), Theta(thLo={'GB': 37}, thHi={'GB': 55}), Theta(thLo={'GB': 37}, thHi={'GB': 56}), Theta(thLo={'GB': 37}, thHi={'GB': 57}), Theta(thLo={'GB': 37}, thHi={'GB': 58}), Theta(thLo={'GB': 37}, thHi={'GB': 59}), Theta(thLo={'GB': 37}, thHi={'GB': 60}), Theta(thLo={'GB': 37}, thHi={'GB': 61}), Theta(thLo={'GB': 37}, thHi={'GB': 62}), Theta(thLo={'GB': 37}, thHi={'GB': 63}), Theta(thLo={'GB': 37}, thHi={'GB': 64}), Theta(thLo={'GB': 37}, thHi={'GB': 65}), Theta(thLo={'GB': 37}, thHi={'GB': 66}), Theta(thLo={'GB': 37}, thHi={'GB': 67}), Theta(thLo={'GB': 37}, thHi={'GB': 68}), Theta(thLo={'GB': 37}, thHi={'GB': 69}), Theta(thLo={'GB': 37}, thHi={'GB': 70}), Theta(thLo={'GB': 37}, thHi={'GB': 71}), Theta(thLo={'GB': 37}, thHi={'GB': 72}), Theta(thLo={'GB': 37}, thHi={'GB': 73}), Theta(thLo={'GB': 37}, thHi={'GB': 74}), Theta(thLo={'GB': 37}, thHi={'GB': 75}), Theta(thLo={'GB': 37}, thHi={'GB': 76}), Theta(thLo={'GB': 37}, thHi={'GB': 77}), Theta(thLo={'GB': 37}, thHi={'GB': 78}), Theta(thLo={'GB': 37}, thHi={'GB': 79}), Theta(thLo={'GB': 37}, thHi={'GB': 80}), Theta(thLo={'GB': 37}, thHi={'GB': 81}), Theta(thLo={'GB': 37}, thHi={'GB': 82}), Theta(thLo={'GB': 37}, thHi={'GB': 83}), Theta(thLo={'GB': 37}, thHi={'GB': 84}), Theta(thLo={'GB': 37}, thHi={'GB': 85}), Theta(thLo={'GB': 37}, thHi={'GB': 86}), Theta(thLo={'GB': 37}, thHi={'GB': 87}), Theta(thLo={'GB': 37}, thHi={'GB': 88}), Theta(thLo={'GB': 37}, thHi={'GB': 89}), Theta(thLo={'GB': 37}, thHi={'GB': 90}), Theta(thLo={'GB': 37}, thHi={'GB': 91}), Theta(thLo={'GB': 37}, thHi={'GB': 92}), Theta(thLo={'GB': 37}, thHi={'GB': 93}), Theta(thLo={'GB': 37}, thHi={'GB': 94}), Theta(thLo={'GB': 37}, thHi={'GB': 95}), Theta(thLo={'GB': 37}, thHi={'GB': 96}), Theta(thLo={'GB': 37}, thHi={'GB': 97}), Theta(thLo={'GB': 37}, thHi={'GB': 98}), Theta(thLo={'GB': 37}, thHi={'GB': 99}), Theta(thLo={'GB': 38}, thHi={'GB': 10}), Theta(thLo={'GB': 38}, thHi={'GB': 11}), Theta(thLo={'GB': 38}, thHi={'GB': 12}), Theta(thLo={'GB': 38}, thHi={'GB': 13}), Theta(thLo={'GB': 38}, thHi={'GB': 14}), Theta(thLo={'GB': 38}, thHi={'GB': 15}), Theta(thLo={'GB': 38}, thHi={'GB': 16}), Theta(thLo={'GB': 38}, thHi={'GB': 17}), Theta(thLo={'GB': 38}, thHi={'GB': 18}), Theta(thLo={'GB': 38}, thHi={'GB': 19}), Theta(thLo={'GB': 38}, thHi={'GB': 20}), Theta(thLo={'GB': 38}, thHi={'GB': 21}), Theta(thLo={'GB': 38}, thHi={'GB': 22}), Theta(thLo={'GB': 38}, thHi={'GB': 23}), Theta(thLo={'GB': 38}, thHi={'GB': 24}), Theta(thLo={'GB': 38}, thHi={'GB': 25}), Theta(thLo={'GB': 38}, thHi={'GB': 26}), Theta(thLo={'GB': 38}, thHi={'GB': 27}), Theta(thLo={'GB': 38}, thHi={'GB': 28}), Theta(thLo={'GB': 38}, thHi={'GB': 29}), Theta(thLo={'GB': 38}, thHi={'GB': 30}), Theta(thLo={'GB': 38}, thHi={'GB': 31}), Theta(thLo={'GB': 38}, thHi={'GB': 32}), Theta(thLo={'GB': 38}, thHi={'GB': 33}), Theta(thLo={'GB': 38}, thHi={'GB': 34}), Theta(thLo={'GB': 38}, thHi={'GB': 35}), Theta(thLo={'GB': 38}, thHi={'GB': 36}), Theta(thLo={'GB': 38}, thHi={'GB': 37}), Theta(thLo={'GB': 38}, thHi={'GB': 38}), Theta(thLo={'GB': 38}, thHi={'GB': 39}), Theta(thLo={'GB': 38}, thHi={'GB': 40}), Theta(thLo={'GB': 38}, thHi={'GB': 41}), Theta(thLo={'GB': 38}, thHi={'GB': 42}), Theta(thLo={'GB': 38}, thHi={'GB': 43}), Theta(thLo={'GB': 38}, thHi={'GB': 44}), Theta(thLo={'GB': 38}, thHi={'GB': 45}), Theta(thLo={'GB': 38}, thHi={'GB': 46}), Theta(thLo={'GB': 38}, thHi={'GB': 47}), Theta(thLo={'GB': 38}, thHi={'GB': 48}), Theta(thLo={'GB': 38}, thHi={'GB': 49}), Theta(thLo={'GB': 38}, thHi={'GB': 50}), Theta(thLo={'GB': 38}, thHi={'GB': 51}), Theta(thLo={'GB': 38}, thHi={'GB': 52}), Theta(thLo={'GB': 38}, thHi={'GB': 53}), Theta(thLo={'GB': 38}, thHi={'GB': 54}), Theta(thLo={'GB': 38}, thHi={'GB': 55}), Theta(thLo={'GB': 38}, thHi={'GB': 56}), Theta(thLo={'GB': 38}, thHi={'GB': 57}), Theta(thLo={'GB': 38}, thHi={'GB': 58}), Theta(thLo={'GB': 38}, thHi={'GB': 59}), Theta(thLo={'GB': 38}, thHi={'GB': 60}), Theta(thLo={'GB': 38}, thHi={'GB': 61}), Theta(thLo={'GB': 38}, thHi={'GB': 62}), Theta(thLo={'GB': 38}, thHi={'GB': 63}), Theta(thLo={'GB': 38}, thHi={'GB': 64}), Theta(thLo={'GB': 38}, thHi={'GB': 65}), Theta(thLo={'GB': 38}, thHi={'GB': 66}), Theta(thLo={'GB': 38}, thHi={'GB': 67}), Theta(thLo={'GB': 38}, thHi={'GB': 68}), Theta(thLo={'GB': 38}, thHi={'GB': 69}), Theta(thLo={'GB': 38}, thHi={'GB': 70}), Theta(thLo={'GB': 38}, thHi={'GB': 71}), Theta(thLo={'GB': 38}, thHi={'GB': 72}), Theta(thLo={'GB': 38}, thHi={'GB': 73}), Theta(thLo={'GB': 38}, thHi={'GB': 74}), Theta(thLo={'GB': 38}, thHi={'GB': 75}), Theta(thLo={'GB': 38}, thHi={'GB': 76}), Theta(thLo={'GB': 38}, thHi={'GB': 77}), Theta(thLo={'GB': 38}, thHi={'GB': 78}), Theta(thLo={'GB': 38}, thHi={'GB': 79}), Theta(thLo={'GB': 38}, thHi={'GB': 80}), Theta(thLo={'GB': 38}, thHi={'GB': 81}), Theta(thLo={'GB': 38}, thHi={'GB': 82}), Theta(thLo={'GB': 38}, thHi={'GB': 83}), Theta(thLo={'GB': 38}, thHi={'GB': 84}), Theta(thLo={'GB': 38}, thHi={'GB': 85}), Theta(thLo={'GB': 38}, thHi={'GB': 86}), Theta(thLo={'GB': 38}, thHi={'GB': 87}), Theta(thLo={'GB': 38}, thHi={'GB': 88}), Theta(thLo={'GB': 38}, thHi={'GB': 89}), Theta(thLo={'GB': 38}, thHi={'GB': 90}), Theta(thLo={'GB': 38}, thHi={'GB': 91}), Theta(thLo={'GB': 38}, thHi={'GB': 92}), Theta(thLo={'GB': 38}, thHi={'GB': 93}), Theta(thLo={'GB': 38}, thHi={'GB': 94}), Theta(thLo={'GB': 38}, thHi={'GB': 95}), Theta(thLo={'GB': 38}, thHi={'GB': 96}), Theta(thLo={'GB': 38}, thHi={'GB': 97}), Theta(thLo={'GB': 38}, thHi={'GB': 98}), Theta(thLo={'GB': 38}, thHi={'GB': 99}), Theta(thLo={'GB': 39}, thHi={'GB': 10}), Theta(thLo={'GB': 39}, thHi={'GB': 11}), Theta(thLo={'GB': 39}, thHi={'GB': 12}), Theta(thLo={'GB': 39}, thHi={'GB': 13}), Theta(thLo={'GB': 39}, thHi={'GB': 14}), Theta(thLo={'GB': 39}, thHi={'GB': 15}), Theta(thLo={'GB': 39}, thHi={'GB': 16}), Theta(thLo={'GB': 39}, thHi={'GB': 17}), Theta(thLo={'GB': 39}, thHi={'GB': 18}), Theta(thLo={'GB': 39}, thHi={'GB': 19}), Theta(thLo={'GB': 39}, thHi={'GB': 20}), Theta(thLo={'GB': 39}, thHi={'GB': 21}), Theta(thLo={'GB': 39}, thHi={'GB': 22}), Theta(thLo={'GB': 39}, thHi={'GB': 23}), Theta(thLo={'GB': 39}, thHi={'GB': 24}), Theta(thLo={'GB': 39}, thHi={'GB': 25}), Theta(thLo={'GB': 39}, thHi={'GB': 26}), Theta(thLo={'GB': 39}, thHi={'GB': 27}), Theta(thLo={'GB': 39}, thHi={'GB': 28}), Theta(thLo={'GB': 39}, thHi={'GB': 29}), Theta(thLo={'GB': 39}, thHi={'GB': 30}), Theta(thLo={'GB': 39}, thHi={'GB': 31}), Theta(thLo={'GB': 39}, thHi={'GB': 32}), Theta(thLo={'GB': 39}, thHi={'GB': 33}), Theta(thLo={'GB': 39}, thHi={'GB': 34}), Theta(thLo={'GB': 39}, thHi={'GB': 35}), Theta(thLo={'GB': 39}, thHi={'GB': 36}), Theta(thLo={'GB': 39}, thHi={'GB': 37}), Theta(thLo={'GB': 39}, thHi={'GB': 38}), Theta(thLo={'GB': 39}, thHi={'GB': 39}), Theta(thLo={'GB': 39}, thHi={'GB': 40}), Theta(thLo={'GB': 39}, thHi={'GB': 41}), Theta(thLo={'GB': 39}, thHi={'GB': 42}), Theta(thLo={'GB': 39}, thHi={'GB': 43}), Theta(thLo={'GB': 39}, thHi={'GB': 44}), Theta(thLo={'GB': 39}, thHi={'GB': 45}), Theta(thLo={'GB': 39}, thHi={'GB': 46}), Theta(thLo={'GB': 39}, thHi={'GB': 47}), Theta(thLo={'GB': 39}, thHi={'GB': 48}), Theta(thLo={'GB': 39}, thHi={'GB': 49}), Theta(thLo={'GB': 39}, thHi={'GB': 50}), Theta(thLo={'GB': 39}, thHi={'GB': 51}), Theta(thLo={'GB': 39}, thHi={'GB': 52}), Theta(thLo={'GB': 39}, thHi={'GB': 53}), Theta(thLo={'GB': 39}, thHi={'GB': 54}), Theta(thLo={'GB': 39}, thHi={'GB': 55}), Theta(thLo={'GB': 39}, thHi={'GB': 56}), Theta(thLo={'GB': 39}, thHi={'GB': 57}), Theta(thLo={'GB': 39}, thHi={'GB': 58}), Theta(thLo={'GB': 39}, thHi={'GB': 59}), Theta(thLo={'GB': 39}, thHi={'GB': 60}), Theta(thLo={'GB': 39}, thHi={'GB': 61}), Theta(thLo={'GB': 39}, thHi={'GB': 62}), Theta(thLo={'GB': 39}, thHi={'GB': 63}), Theta(thLo={'GB': 39}, thHi={'GB': 64}), Theta(thLo={'GB': 39}, thHi={'GB': 65}), Theta(thLo={'GB': 39}, thHi={'GB': 66}), Theta(thLo={'GB': 39}, thHi={'GB': 67}), Theta(thLo={'GB': 39}, thHi={'GB': 68}), Theta(thLo={'GB': 39}, thHi={'GB': 69}), Theta(thLo={'GB': 39}, thHi={'GB': 70}), Theta(thLo={'GB': 39}, thHi={'GB': 71}), Theta(thLo={'GB': 39}, thHi={'GB': 72}), Theta(thLo={'GB': 39}, thHi={'GB': 73}), Theta(thLo={'GB': 39}, thHi={'GB': 74}), Theta(thLo={'GB': 39}, thHi={'GB': 75}), Theta(thLo={'GB': 39}, thHi={'GB': 76}), Theta(thLo={'GB': 39}, thHi={'GB': 77}), Theta(thLo={'GB': 39}, thHi={'GB': 78}), Theta(thLo={'GB': 39}, thHi={'GB': 79}), Theta(thLo={'GB': 39}, thHi={'GB': 80}), Theta(thLo={'GB': 39}, thHi={'GB': 81}), Theta(thLo={'GB': 39}, thHi={'GB': 82}), Theta(thLo={'GB': 39}, thHi={'GB': 83}), Theta(thLo={'GB': 39}, thHi={'GB': 84}), Theta(thLo={'GB': 39}, thHi={'GB': 85}), Theta(thLo={'GB': 39}, thHi={'GB': 86}), Theta(thLo={'GB': 39}, thHi={'GB': 87}), Theta(thLo={'GB': 39}, thHi={'GB': 88}), Theta(thLo={'GB': 39}, thHi={'GB': 89}), Theta(thLo={'GB': 39}, thHi={'GB': 90}), Theta(thLo={'GB': 39}, thHi={'GB': 91}), Theta(thLo={'GB': 39}, thHi={'GB': 92}), Theta(thLo={'GB': 39}, thHi={'GB': 93}), Theta(thLo={'GB': 39}, thHi={'GB': 94}), Theta(thLo={'GB': 39}, thHi={'GB': 95}), Theta(thLo={'GB': 39}, thHi={'GB': 96}), Theta(thLo={'GB': 39}, thHi={'GB': 97}), Theta(thLo={'GB': 39}, thHi={'GB': 98}), Theta(thLo={'GB': 39}, thHi={'GB': 99}), Theta(thLo={'GB': 40}, thHi={'GB': 10}), Theta(thLo={'GB': 40}, thHi={'GB': 11}), Theta(thLo={'GB': 40}, thHi={'GB': 12}), Theta(thLo={'GB': 40}, thHi={'GB': 13}), Theta(thLo={'GB': 40}, thHi={'GB': 14}), Theta(thLo={'GB': 40}, thHi={'GB': 15}), Theta(thLo={'GB': 40}, thHi={'GB': 16}), Theta(thLo={'GB': 40}, thHi={'GB': 17}), Theta(thLo={'GB': 40}, thHi={'GB': 18}), Theta(thLo={'GB': 40}, thHi={'GB': 19}), Theta(thLo={'GB': 40}, thHi={'GB': 20}), Theta(thLo={'GB': 40}, thHi={'GB': 21}), Theta(thLo={'GB': 40}, thHi={'GB': 22}), Theta(thLo={'GB': 40}, thHi={'GB': 23}), Theta(thLo={'GB': 40}, thHi={'GB': 24}), Theta(thLo={'GB': 40}, thHi={'GB': 25}), Theta(thLo={'GB': 40}, thHi={'GB': 26}), Theta(thLo={'GB': 40}, thHi={'GB': 27}), Theta(thLo={'GB': 40}, thHi={'GB': 28}), Theta(thLo={'GB': 40}, thHi={'GB': 29}), Theta(thLo={'GB': 40}, thHi={'GB': 30}), Theta(thLo={'GB': 40}, thHi={'GB': 31}), Theta(thLo={'GB': 40}, thHi={'GB': 32}), Theta(thLo={'GB': 40}, thHi={'GB': 33}), Theta(thLo={'GB': 40}, thHi={'GB': 34}), Theta(thLo={'GB': 40}, thHi={'GB': 35}), Theta(thLo={'GB': 40}, thHi={'GB': 36}), Theta(thLo={'GB': 40}, thHi={'GB': 37}), Theta(thLo={'GB': 40}, thHi={'GB': 38}), Theta(thLo={'GB': 40}, thHi={'GB': 39}), Theta(thLo={'GB': 40}, thHi={'GB': 40}), Theta(thLo={'GB': 40}, thHi={'GB': 41}), Theta(thLo={'GB': 40}, thHi={'GB': 42}), Theta(thLo={'GB': 40}, thHi={'GB': 43}), Theta(thLo={'GB': 40}, thHi={'GB': 44}), Theta(thLo={'GB': 40}, thHi={'GB': 45}), Theta(thLo={'GB': 40}, thHi={'GB': 46}), Theta(thLo={'GB': 40}, thHi={'GB': 47}), Theta(thLo={'GB': 40}, thHi={'GB': 48}), Theta(thLo={'GB': 40}, thHi={'GB': 49}), Theta(thLo={'GB': 40}, thHi={'GB': 50}), Theta(thLo={'GB': 40}, thHi={'GB': 51}), Theta(thLo={'GB': 40}, thHi={'GB': 52}), Theta(thLo={'GB': 40}, thHi={'GB': 53}), Theta(thLo={'GB': 40}, thHi={'GB': 54}), Theta(thLo={'GB': 40}, thHi={'GB': 55}), Theta(thLo={'GB': 40}, thHi={'GB': 56}), Theta(thLo={'GB': 40}, thHi={'GB': 57}), Theta(thLo={'GB': 40}, thHi={'GB': 58}), Theta(thLo={'GB': 40}, thHi={'GB': 59}), Theta(thLo={'GB': 40}, thHi={'GB': 60}), Theta(thLo={'GB': 40}, thHi={'GB': 61}), Theta(thLo={'GB': 40}, thHi={'GB': 62}), Theta(thLo={'GB': 40}, thHi={'GB': 63}), Theta(thLo={'GB': 40}, thHi={'GB': 64}), Theta(thLo={'GB': 40}, thHi={'GB': 65}), Theta(thLo={'GB': 40}, thHi={'GB': 66}), Theta(thLo={'GB': 40}, thHi={'GB': 67}), Theta(thLo={'GB': 40}, thHi={'GB': 68}), Theta(thLo={'GB': 40}, thHi={'GB': 69}), Theta(thLo={'GB': 40}, thHi={'GB': 70}), Theta(thLo={'GB': 40}, thHi={'GB': 71}), Theta(thLo={'GB': 40}, thHi={'GB': 72}), Theta(thLo={'GB': 40}, thHi={'GB': 73}), Theta(thLo={'GB': 40}, thHi={'GB': 74}), Theta(thLo={'GB': 40}, thHi={'GB': 75}), Theta(thLo={'GB': 40}, thHi={'GB': 76}), Theta(thLo={'GB': 40}, thHi={'GB': 77}), Theta(thLo={'GB': 40}, thHi={'GB': 78}), Theta(thLo={'GB': 40}, thHi={'GB': 79}), Theta(thLo={'GB': 40}, thHi={'GB': 80}), Theta(thLo={'GB': 40}, thHi={'GB': 81}), Theta(thLo={'GB': 40}, thHi={'GB': 82}), Theta(thLo={'GB': 40}, thHi={'GB': 83}), Theta(thLo={'GB': 40}, thHi={'GB': 84}), Theta(thLo={'GB': 40}, thHi={'GB': 85}), Theta(thLo={'GB': 40}, thHi={'GB': 86}), Theta(thLo={'GB': 40}, thHi={'GB': 87}), Theta(thLo={'GB': 40}, thHi={'GB': 88}), Theta(thLo={'GB': 40}, thHi={'GB': 89}), Theta(thLo={'GB': 40}, thHi={'GB': 90}), Theta(thLo={'GB': 40}, thHi={'GB': 91}), Theta(thLo={'GB': 40}, thHi={'GB': 92}), Theta(thLo={'GB': 40}, thHi={'GB': 93}), 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Theta(thLo={'GB': 41}, thHi={'GB': 28}), Theta(thLo={'GB': 41}, thHi={'GB': 29}), Theta(thLo={'GB': 41}, thHi={'GB': 30}), Theta(thLo={'GB': 41}, thHi={'GB': 31}), Theta(thLo={'GB': 41}, thHi={'GB': 32}), Theta(thLo={'GB': 41}, thHi={'GB': 33}), Theta(thLo={'GB': 41}, thHi={'GB': 34}), Theta(thLo={'GB': 41}, thHi={'GB': 35}), Theta(thLo={'GB': 41}, thHi={'GB': 36}), Theta(thLo={'GB': 41}, thHi={'GB': 37}), Theta(thLo={'GB': 41}, thHi={'GB': 38}), Theta(thLo={'GB': 41}, thHi={'GB': 39}), Theta(thLo={'GB': 41}, thHi={'GB': 40}), Theta(thLo={'GB': 41}, thHi={'GB': 41}), Theta(thLo={'GB': 41}, thHi={'GB': 42}), Theta(thLo={'GB': 41}, thHi={'GB': 43}), Theta(thLo={'GB': 41}, thHi={'GB': 44}), Theta(thLo={'GB': 41}, thHi={'GB': 45}), Theta(thLo={'GB': 41}, thHi={'GB': 46}), Theta(thLo={'GB': 41}, thHi={'GB': 47}), Theta(thLo={'GB': 41}, thHi={'GB': 48}), Theta(thLo={'GB': 41}, thHi={'GB': 49}), Theta(thLo={'GB': 41}, thHi={'GB': 50}), Theta(thLo={'GB': 41}, thHi={'GB': 51}), Theta(thLo={'GB': 41}, thHi={'GB': 52}), Theta(thLo={'GB': 41}, thHi={'GB': 53}), Theta(thLo={'GB': 41}, thHi={'GB': 54}), Theta(thLo={'GB': 41}, thHi={'GB': 55}), Theta(thLo={'GB': 41}, thHi={'GB': 56}), Theta(thLo={'GB': 41}, thHi={'GB': 57}), Theta(thLo={'GB': 41}, thHi={'GB': 58}), Theta(thLo={'GB': 41}, thHi={'GB': 59}), Theta(thLo={'GB': 41}, thHi={'GB': 60}), Theta(thLo={'GB': 41}, thHi={'GB': 61}), Theta(thLo={'GB': 41}, thHi={'GB': 62}), Theta(thLo={'GB': 41}, thHi={'GB': 63}), Theta(thLo={'GB': 41}, thHi={'GB': 64}), Theta(thLo={'GB': 41}, thHi={'GB': 65}), Theta(thLo={'GB': 41}, thHi={'GB': 66}), Theta(thLo={'GB': 41}, thHi={'GB': 67}), Theta(thLo={'GB': 41}, thHi={'GB': 68}), Theta(thLo={'GB': 41}, thHi={'GB': 69}), Theta(thLo={'GB': 41}, thHi={'GB': 70}), Theta(thLo={'GB': 41}, thHi={'GB': 71}), Theta(thLo={'GB': 41}, thHi={'GB': 72}), Theta(thLo={'GB': 41}, thHi={'GB': 73}), Theta(thLo={'GB': 41}, thHi={'GB': 74}), Theta(thLo={'GB': 41}, thHi={'GB': 75}), Theta(thLo={'GB': 41}, thHi={'GB': 76}), Theta(thLo={'GB': 41}, thHi={'GB': 77}), Theta(thLo={'GB': 41}, thHi={'GB': 78}), Theta(thLo={'GB': 41}, thHi={'GB': 79}), Theta(thLo={'GB': 41}, thHi={'GB': 80}), Theta(thLo={'GB': 41}, thHi={'GB': 81}), Theta(thLo={'GB': 41}, thHi={'GB': 82}), Theta(thLo={'GB': 41}, thHi={'GB': 83}), Theta(thLo={'GB': 41}, thHi={'GB': 84}), Theta(thLo={'GB': 41}, thHi={'GB': 85}), Theta(thLo={'GB': 41}, thHi={'GB': 86}), Theta(thLo={'GB': 41}, thHi={'GB': 87}), Theta(thLo={'GB': 41}, thHi={'GB': 88}), Theta(thLo={'GB': 41}, thHi={'GB': 89}), Theta(thLo={'GB': 41}, thHi={'GB': 90}), Theta(thLo={'GB': 41}, thHi={'GB': 91}), Theta(thLo={'GB': 41}, thHi={'GB': 92}), Theta(thLo={'GB': 41}, thHi={'GB': 93}), Theta(thLo={'GB': 41}, thHi={'GB': 94}), Theta(thLo={'GB': 41}, thHi={'GB': 95}), Theta(thLo={'GB': 41}, thHi={'GB': 96}), Theta(thLo={'GB': 41}, thHi={'GB': 97}), Theta(thLo={'GB': 41}, thHi={'GB': 98}), Theta(thLo={'GB': 41}, thHi={'GB': 99}), Theta(thLo={'GB': 42}, thHi={'GB': 10}), Theta(thLo={'GB': 42}, thHi={'GB': 11}), Theta(thLo={'GB': 42}, thHi={'GB': 12}), Theta(thLo={'GB': 42}, thHi={'GB': 13}), Theta(thLo={'GB': 42}, thHi={'GB': 14}), Theta(thLo={'GB': 42}, thHi={'GB': 15}), Theta(thLo={'GB': 42}, thHi={'GB': 16}), Theta(thLo={'GB': 42}, thHi={'GB': 17}), Theta(thLo={'GB': 42}, thHi={'GB': 18}), Theta(thLo={'GB': 42}, thHi={'GB': 19}), Theta(thLo={'GB': 42}, thHi={'GB': 20}), Theta(thLo={'GB': 42}, thHi={'GB': 21}), Theta(thLo={'GB': 42}, thHi={'GB': 22}), Theta(thLo={'GB': 42}, thHi={'GB': 23}), Theta(thLo={'GB': 42}, thHi={'GB': 24}), Theta(thLo={'GB': 42}, thHi={'GB': 25}), Theta(thLo={'GB': 42}, thHi={'GB': 26}), Theta(thLo={'GB': 42}, thHi={'GB': 27}), Theta(thLo={'GB': 42}, thHi={'GB': 28}), Theta(thLo={'GB': 42}, thHi={'GB': 29}), Theta(thLo={'GB': 42}, thHi={'GB': 30}), Theta(thLo={'GB': 42}, thHi={'GB': 31}), Theta(thLo={'GB': 42}, thHi={'GB': 32}), Theta(thLo={'GB': 42}, thHi={'GB': 33}), Theta(thLo={'GB': 42}, thHi={'GB': 34}), Theta(thLo={'GB': 42}, thHi={'GB': 35}), Theta(thLo={'GB': 42}, thHi={'GB': 36}), Theta(thLo={'GB': 42}, thHi={'GB': 37}), Theta(thLo={'GB': 42}, thHi={'GB': 38}), Theta(thLo={'GB': 42}, thHi={'GB': 39}), Theta(thLo={'GB': 42}, thHi={'GB': 40}), Theta(thLo={'GB': 42}, thHi={'GB': 41}), Theta(thLo={'GB': 42}, thHi={'GB': 42}), Theta(thLo={'GB': 42}, thHi={'GB': 43}), Theta(thLo={'GB': 42}, thHi={'GB': 44}), Theta(thLo={'GB': 42}, thHi={'GB': 45}), Theta(thLo={'GB': 42}, thHi={'GB': 46}), Theta(thLo={'GB': 42}, thHi={'GB': 47}), Theta(thLo={'GB': 42}, thHi={'GB': 48}), Theta(thLo={'GB': 42}, thHi={'GB': 49}), Theta(thLo={'GB': 42}, thHi={'GB': 50}), Theta(thLo={'GB': 42}, thHi={'GB': 51}), Theta(thLo={'GB': 42}, thHi={'GB': 52}), Theta(thLo={'GB': 42}, thHi={'GB': 53}), Theta(thLo={'GB': 42}, thHi={'GB': 54}), Theta(thLo={'GB': 42}, thHi={'GB': 55}), Theta(thLo={'GB': 42}, thHi={'GB': 56}), Theta(thLo={'GB': 42}, thHi={'GB': 57}), Theta(thLo={'GB': 42}, thHi={'GB': 58}), Theta(thLo={'GB': 42}, thHi={'GB': 59}), Theta(thLo={'GB': 42}, thHi={'GB': 60}), Theta(thLo={'GB': 42}, thHi={'GB': 61}), Theta(thLo={'GB': 42}, thHi={'GB': 62}), Theta(thLo={'GB': 42}, thHi={'GB': 63}), Theta(thLo={'GB': 42}, thHi={'GB': 64}), Theta(thLo={'GB': 42}, thHi={'GB': 65}), Theta(thLo={'GB': 42}, thHi={'GB': 66}), Theta(thLo={'GB': 42}, thHi={'GB': 67}), Theta(thLo={'GB': 42}, thHi={'GB': 68}), Theta(thLo={'GB': 42}, thHi={'GB': 69}), Theta(thLo={'GB': 42}, thHi={'GB': 70}), Theta(thLo={'GB': 42}, thHi={'GB': 71}), Theta(thLo={'GB': 42}, thHi={'GB': 72}), Theta(thLo={'GB': 42}, thHi={'GB': 73}), Theta(thLo={'GB': 42}, thHi={'GB': 74}), Theta(thLo={'GB': 42}, thHi={'GB': 75}), Theta(thLo={'GB': 42}, thHi={'GB': 76}), Theta(thLo={'GB': 42}, thHi={'GB': 77}), Theta(thLo={'GB': 42}, thHi={'GB': 78}), Theta(thLo={'GB': 42}, thHi={'GB': 79}), Theta(thLo={'GB': 42}, thHi={'GB': 80}), Theta(thLo={'GB': 42}, thHi={'GB': 81}), Theta(thLo={'GB': 42}, thHi={'GB': 82}), Theta(thLo={'GB': 42}, thHi={'GB': 83}), Theta(thLo={'GB': 42}, thHi={'GB': 84}), Theta(thLo={'GB': 42}, thHi={'GB': 85}), Theta(thLo={'GB': 42}, thHi={'GB': 86}), Theta(thLo={'GB': 42}, thHi={'GB': 87}), Theta(thLo={'GB': 42}, thHi={'GB': 88}), Theta(thLo={'GB': 42}, thHi={'GB': 89}), Theta(thLo={'GB': 42}, thHi={'GB': 90}), Theta(thLo={'GB': 42}, thHi={'GB': 91}), Theta(thLo={'GB': 42}, thHi={'GB': 92}), Theta(thLo={'GB': 42}, thHi={'GB': 93}), Theta(thLo={'GB': 42}, thHi={'GB': 94}), Theta(thLo={'GB': 42}, thHi={'GB': 95}), Theta(thLo={'GB': 42}, thHi={'GB': 96}), Theta(thLo={'GB': 42}, thHi={'GB': 97}), Theta(thLo={'GB': 42}, thHi={'GB': 98}), Theta(thLo={'GB': 42}, thHi={'GB': 99}), Theta(thLo={'GB': 43}, thHi={'GB': 10}), Theta(thLo={'GB': 43}, thHi={'GB': 11}), Theta(thLo={'GB': 43}, thHi={'GB': 12}), Theta(thLo={'GB': 43}, thHi={'GB': 13}), Theta(thLo={'GB': 43}, thHi={'GB': 14}), Theta(thLo={'GB': 43}, thHi={'GB': 15}), Theta(thLo={'GB': 43}, thHi={'GB': 16}), Theta(thLo={'GB': 43}, thHi={'GB': 17}), Theta(thLo={'GB': 43}, thHi={'GB': 18}), Theta(thLo={'GB': 43}, thHi={'GB': 19}), Theta(thLo={'GB': 43}, thHi={'GB': 20}), Theta(thLo={'GB': 43}, thHi={'GB': 21}), Theta(thLo={'GB': 43}, thHi={'GB': 22}), Theta(thLo={'GB': 43}, thHi={'GB': 23}), Theta(thLo={'GB': 43}, thHi={'GB': 24}), Theta(thLo={'GB': 43}, thHi={'GB': 25}), Theta(thLo={'GB': 43}, thHi={'GB': 26}), Theta(thLo={'GB': 43}, thHi={'GB': 27}), Theta(thLo={'GB': 43}, thHi={'GB': 28}), Theta(thLo={'GB': 43}, thHi={'GB': 29}), Theta(thLo={'GB': 43}, thHi={'GB': 30}), Theta(thLo={'GB': 43}, thHi={'GB': 31}), Theta(thLo={'GB': 43}, thHi={'GB': 32}), Theta(thLo={'GB': 43}, thHi={'GB': 33}), Theta(thLo={'GB': 43}, thHi={'GB': 34}), Theta(thLo={'GB': 43}, thHi={'GB': 35}), Theta(thLo={'GB': 43}, thHi={'GB': 36}), Theta(thLo={'GB': 43}, thHi={'GB': 37}), Theta(thLo={'GB': 43}, thHi={'GB': 38}), Theta(thLo={'GB': 43}, thHi={'GB': 39}), Theta(thLo={'GB': 43}, thHi={'GB': 40}), Theta(thLo={'GB': 43}, thHi={'GB': 41}), Theta(thLo={'GB': 43}, thHi={'GB': 42}), Theta(thLo={'GB': 43}, thHi={'GB': 43}), Theta(thLo={'GB': 43}, thHi={'GB': 44}), Theta(thLo={'GB': 43}, thHi={'GB': 45}), Theta(thLo={'GB': 43}, thHi={'GB': 46}), Theta(thLo={'GB': 43}, thHi={'GB': 47}), Theta(thLo={'GB': 43}, thHi={'GB': 48}), Theta(thLo={'GB': 43}, thHi={'GB': 49}), Theta(thLo={'GB': 43}, thHi={'GB': 50}), Theta(thLo={'GB': 43}, thHi={'GB': 51}), Theta(thLo={'GB': 43}, thHi={'GB': 52}), Theta(thLo={'GB': 43}, thHi={'GB': 53}), Theta(thLo={'GB': 43}, thHi={'GB': 54}), Theta(thLo={'GB': 43}, thHi={'GB': 55}), Theta(thLo={'GB': 43}, thHi={'GB': 56}), Theta(thLo={'GB': 43}, thHi={'GB': 57}), Theta(thLo={'GB': 43}, thHi={'GB': 58}), Theta(thLo={'GB': 43}, thHi={'GB': 59}), Theta(thLo={'GB': 43}, thHi={'GB': 60}), Theta(thLo={'GB': 43}, thHi={'GB': 61}), Theta(thLo={'GB': 43}, thHi={'GB': 62}), Theta(thLo={'GB': 43}, thHi={'GB': 63}), 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Theta(thLo={'GB': 45}, thHi={'GB': 76}), Theta(thLo={'GB': 45}, thHi={'GB': 77}), Theta(thLo={'GB': 45}, thHi={'GB': 78}), Theta(thLo={'GB': 45}, thHi={'GB': 79}), Theta(thLo={'GB': 45}, thHi={'GB': 80}), Theta(thLo={'GB': 45}, thHi={'GB': 81}), Theta(thLo={'GB': 45}, thHi={'GB': 82}), Theta(thLo={'GB': 45}, thHi={'GB': 83}), Theta(thLo={'GB': 45}, thHi={'GB': 84}), Theta(thLo={'GB': 45}, thHi={'GB': 85}), Theta(thLo={'GB': 45}, thHi={'GB': 86}), Theta(thLo={'GB': 45}, thHi={'GB': 87}), Theta(thLo={'GB': 45}, thHi={'GB': 88}), Theta(thLo={'GB': 45}, thHi={'GB': 89}), Theta(thLo={'GB': 45}, thHi={'GB': 90}), Theta(thLo={'GB': 45}, thHi={'GB': 91}), Theta(thLo={'GB': 45}, thHi={'GB': 92}), Theta(thLo={'GB': 45}, thHi={'GB': 93}), Theta(thLo={'GB': 45}, thHi={'GB': 94}), Theta(thLo={'GB': 45}, thHi={'GB': 95}), Theta(thLo={'GB': 45}, thHi={'GB': 96}), Theta(thLo={'GB': 45}, thHi={'GB': 97}), Theta(thLo={'GB': 45}, thHi={'GB': 98}), Theta(thLo={'GB': 45}, thHi={'GB': 99}), 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Theta(thLo={'GB': 49}, thHi={'GB': 52}), Theta(thLo={'GB': 49}, thHi={'GB': 53}), Theta(thLo={'GB': 49}, thHi={'GB': 54}), Theta(thLo={'GB': 49}, thHi={'GB': 55}), Theta(thLo={'GB': 49}, thHi={'GB': 56}), Theta(thLo={'GB': 49}, thHi={'GB': 57}), Theta(thLo={'GB': 49}, thHi={'GB': 58}), Theta(thLo={'GB': 49}, thHi={'GB': 59}), Theta(thLo={'GB': 49}, thHi={'GB': 60}), Theta(thLo={'GB': 49}, thHi={'GB': 61}), Theta(thLo={'GB': 49}, thHi={'GB': 62}), Theta(thLo={'GB': 49}, thHi={'GB': 63}), Theta(thLo={'GB': 49}, thHi={'GB': 64}), Theta(thLo={'GB': 49}, thHi={'GB': 65}), Theta(thLo={'GB': 49}, thHi={'GB': 66}), Theta(thLo={'GB': 49}, thHi={'GB': 67}), Theta(thLo={'GB': 49}, thHi={'GB': 68}), Theta(thLo={'GB': 49}, thHi={'GB': 69}), Theta(thLo={'GB': 49}, thHi={'GB': 70}), Theta(thLo={'GB': 49}, thHi={'GB': 71}), Theta(thLo={'GB': 49}, thHi={'GB': 72}), Theta(thLo={'GB': 49}, thHi={'GB': 73}), Theta(thLo={'GB': 49}, thHi={'GB': 74}), Theta(thLo={'GB': 49}, thHi={'GB': 75}), Theta(thLo={'GB': 49}, thHi={'GB': 76}), Theta(thLo={'GB': 49}, thHi={'GB': 77}), Theta(thLo={'GB': 49}, thHi={'GB': 78}), Theta(thLo={'GB': 49}, thHi={'GB': 79}), Theta(thLo={'GB': 49}, thHi={'GB': 80}), Theta(thLo={'GB': 49}, thHi={'GB': 81}), Theta(thLo={'GB': 49}, thHi={'GB': 82}), Theta(thLo={'GB': 49}, thHi={'GB': 83}), Theta(thLo={'GB': 49}, thHi={'GB': 84}), Theta(thLo={'GB': 49}, thHi={'GB': 85}), Theta(thLo={'GB': 49}, thHi={'GB': 86}), Theta(thLo={'GB': 49}, thHi={'GB': 87}), Theta(thLo={'GB': 49}, thHi={'GB': 88}), Theta(thLo={'GB': 49}, thHi={'GB': 89}), Theta(thLo={'GB': 49}, thHi={'GB': 90}), Theta(thLo={'GB': 49}, thHi={'GB': 91}), Theta(thLo={'GB': 49}, thHi={'GB': 92}), Theta(thLo={'GB': 49}, thHi={'GB': 93}), Theta(thLo={'GB': 49}, thHi={'GB': 94}), Theta(thLo={'GB': 49}, thHi={'GB': 95}), Theta(thLo={'GB': 49}, thHi={'GB': 96}), Theta(thLo={'GB': 49}, thHi={'GB': 97}), Theta(thLo={'GB': 49}, thHi={'GB': 98}), Theta(thLo={'GB': 49}, thHi={'GB': 99}), Theta(thLo={'GB': 50}, thHi={'GB': 10}), Theta(thLo={'GB': 50}, thHi={'GB': 11}), Theta(thLo={'GB': 50}, thHi={'GB': 12}), Theta(thLo={'GB': 50}, thHi={'GB': 13}), Theta(thLo={'GB': 50}, thHi={'GB': 14}), Theta(thLo={'GB': 50}, thHi={'GB': 15}), Theta(thLo={'GB': 50}, thHi={'GB': 16}), Theta(thLo={'GB': 50}, thHi={'GB': 17}), Theta(thLo={'GB': 50}, thHi={'GB': 18}), Theta(thLo={'GB': 50}, thHi={'GB': 19}), Theta(thLo={'GB': 50}, thHi={'GB': 20}), Theta(thLo={'GB': 50}, thHi={'GB': 21}), Theta(thLo={'GB': 50}, thHi={'GB': 22}), Theta(thLo={'GB': 50}, thHi={'GB': 23}), Theta(thLo={'GB': 50}, thHi={'GB': 24}), Theta(thLo={'GB': 50}, thHi={'GB': 25}), Theta(thLo={'GB': 50}, thHi={'GB': 26}), Theta(thLo={'GB': 50}, thHi={'GB': 27}), Theta(thLo={'GB': 50}, thHi={'GB': 28}), Theta(thLo={'GB': 50}, thHi={'GB': 29}), Theta(thLo={'GB': 50}, thHi={'GB': 30}), Theta(thLo={'GB': 50}, thHi={'GB': 31}), Theta(thLo={'GB': 50}, thHi={'GB': 32}), Theta(thLo={'GB': 50}, thHi={'GB': 33}), Theta(thLo={'GB': 50}, thHi={'GB': 34}), Theta(thLo={'GB': 50}, thHi={'GB': 35}), Theta(thLo={'GB': 50}, thHi={'GB': 36}), Theta(thLo={'GB': 50}, thHi={'GB': 37}), Theta(thLo={'GB': 50}, thHi={'GB': 38}), Theta(thLo={'GB': 50}, thHi={'GB': 39}), Theta(thLo={'GB': 50}, thHi={'GB': 40}), Theta(thLo={'GB': 50}, thHi={'GB': 41}), Theta(thLo={'GB': 50}, thHi={'GB': 42}), Theta(thLo={'GB': 50}, thHi={'GB': 43}), Theta(thLo={'GB': 50}, thHi={'GB': 44}), Theta(thLo={'GB': 50}, thHi={'GB': 45}), Theta(thLo={'GB': 50}, thHi={'GB': 46}), Theta(thLo={'GB': 50}, thHi={'GB': 47}), Theta(thLo={'GB': 50}, thHi={'GB': 48}), Theta(thLo={'GB': 50}, thHi={'GB': 49}), Theta(thLo={'GB': 50}, thHi={'GB': 50}), Theta(thLo={'GB': 50}, thHi={'GB': 51}), Theta(thLo={'GB': 50}, thHi={'GB': 52}), Theta(thLo={'GB': 50}, thHi={'GB': 53}), Theta(thLo={'GB': 50}, thHi={'GB': 54}), Theta(thLo={'GB': 50}, thHi={'GB': 55}), Theta(thLo={'GB': 50}, thHi={'GB': 56}), Theta(thLo={'GB': 50}, thHi={'GB': 57}), Theta(thLo={'GB': 50}, thHi={'GB': 58}), Theta(thLo={'GB': 50}, thHi={'GB': 59}), Theta(thLo={'GB': 50}, thHi={'GB': 60}), Theta(thLo={'GB': 50}, thHi={'GB': 61}), Theta(thLo={'GB': 50}, thHi={'GB': 62}), Theta(thLo={'GB': 50}, thHi={'GB': 63}), Theta(thLo={'GB': 50}, thHi={'GB': 64}), Theta(thLo={'GB': 50}, thHi={'GB': 65}), Theta(thLo={'GB': 50}, thHi={'GB': 66}), Theta(thLo={'GB': 50}, thHi={'GB': 67}), Theta(thLo={'GB': 50}, thHi={'GB': 68}), Theta(thLo={'GB': 50}, thHi={'GB': 69}), Theta(thLo={'GB': 50}, thHi={'GB': 70}), Theta(thLo={'GB': 50}, thHi={'GB': 71}), Theta(thLo={'GB': 50}, thHi={'GB': 72}), Theta(thLo={'GB': 50}, thHi={'GB': 73}), Theta(thLo={'GB': 50}, thHi={'GB': 74}), Theta(thLo={'GB': 50}, thHi={'GB': 75}), Theta(thLo={'GB': 50}, thHi={'GB': 76}), Theta(thLo={'GB': 50}, thHi={'GB': 77}), Theta(thLo={'GB': 50}, thHi={'GB': 78}), Theta(thLo={'GB': 50}, thHi={'GB': 79}), Theta(thLo={'GB': 50}, thHi={'GB': 80}), Theta(thLo={'GB': 50}, thHi={'GB': 81}), Theta(thLo={'GB': 50}, thHi={'GB': 82}), Theta(thLo={'GB': 50}, thHi={'GB': 83}), Theta(thLo={'GB': 50}, thHi={'GB': 84}), Theta(thLo={'GB': 50}, thHi={'GB': 85}), Theta(thLo={'GB': 50}, thHi={'GB': 86}), Theta(thLo={'GB': 50}, thHi={'GB': 87}), Theta(thLo={'GB': 50}, thHi={'GB': 88}), Theta(thLo={'GB': 50}, thHi={'GB': 89}), Theta(thLo={'GB': 50}, thHi={'GB': 90}), Theta(thLo={'GB': 50}, thHi={'GB': 91}), Theta(thLo={'GB': 50}, thHi={'GB': 92}), Theta(thLo={'GB': 50}, thHi={'GB': 93}), Theta(thLo={'GB': 50}, thHi={'GB': 94}), Theta(thLo={'GB': 50}, thHi={'GB': 95}), Theta(thLo={'GB': 50}, thHi={'GB': 96}), Theta(thLo={'GB': 50}, thHi={'GB': 97}), Theta(thLo={'GB': 50}, thHi={'GB': 98}), Theta(thLo={'GB': 50}, thHi={'GB': 99}), Theta(thLo={'GB': 51}, thHi={'GB': 10}), Theta(thLo={'GB': 51}, thHi={'GB': 11}), Theta(thLo={'GB': 51}, thHi={'GB': 12}), Theta(thLo={'GB': 51}, thHi={'GB': 13}), Theta(thLo={'GB': 51}, thHi={'GB': 14}), Theta(thLo={'GB': 51}, thHi={'GB': 15}), Theta(thLo={'GB': 51}, thHi={'GB': 16}), Theta(thLo={'GB': 51}, thHi={'GB': 17}), Theta(thLo={'GB': 51}, thHi={'GB': 18}), Theta(thLo={'GB': 51}, thHi={'GB': 19}), Theta(thLo={'GB': 51}, thHi={'GB': 20}), Theta(thLo={'GB': 51}, thHi={'GB': 21}), Theta(thLo={'GB': 51}, thHi={'GB': 22}), Theta(thLo={'GB': 51}, thHi={'GB': 23}), Theta(thLo={'GB': 51}, thHi={'GB': 24}), Theta(thLo={'GB': 51}, thHi={'GB': 25}), Theta(thLo={'GB': 51}, thHi={'GB': 26}), Theta(thLo={'GB': 51}, thHi={'GB': 27}), Theta(thLo={'GB': 51}, thHi={'GB': 28}), Theta(thLo={'GB': 51}, thHi={'GB': 29}), Theta(thLo={'GB': 51}, thHi={'GB': 30}), Theta(thLo={'GB': 51}, thHi={'GB': 31}), Theta(thLo={'GB': 51}, thHi={'GB': 32}), Theta(thLo={'GB': 51}, thHi={'GB': 33}), Theta(thLo={'GB': 51}, thHi={'GB': 34}), Theta(thLo={'GB': 51}, thHi={'GB': 35}), Theta(thLo={'GB': 51}, thHi={'GB': 36}), Theta(thLo={'GB': 51}, thHi={'GB': 37}), Theta(thLo={'GB': 51}, thHi={'GB': 38}), Theta(thLo={'GB': 51}, thHi={'GB': 39}), Theta(thLo={'GB': 51}, thHi={'GB': 40}), Theta(thLo={'GB': 51}, thHi={'GB': 41}), Theta(thLo={'GB': 51}, thHi={'GB': 42}), Theta(thLo={'GB': 51}, thHi={'GB': 43}), Theta(thLo={'GB': 51}, thHi={'GB': 44}), Theta(thLo={'GB': 51}, thHi={'GB': 45}), Theta(thLo={'GB': 51}, thHi={'GB': 46}), Theta(thLo={'GB': 51}, thHi={'GB': 47}), Theta(thLo={'GB': 51}, thHi={'GB': 48}), Theta(thLo={'GB': 51}, thHi={'GB': 49}), Theta(thLo={'GB': 51}, thHi={'GB': 50}), Theta(thLo={'GB': 51}, thHi={'GB': 51}), Theta(thLo={'GB': 51}, thHi={'GB': 52}), Theta(thLo={'GB': 51}, thHi={'GB': 53}), Theta(thLo={'GB': 51}, thHi={'GB': 54}), Theta(thLo={'GB': 51}, thHi={'GB': 55}), Theta(thLo={'GB': 51}, thHi={'GB': 56}), Theta(thLo={'GB': 51}, thHi={'GB': 57}), Theta(thLo={'GB': 51}, thHi={'GB': 58}), Theta(thLo={'GB': 51}, thHi={'GB': 59}), Theta(thLo={'GB': 51}, thHi={'GB': 60}), Theta(thLo={'GB': 51}, thHi={'GB': 61}), Theta(thLo={'GB': 51}, thHi={'GB': 62}), Theta(thLo={'GB': 51}, thHi={'GB': 63}), Theta(thLo={'GB': 51}, thHi={'GB': 64}), Theta(thLo={'GB': 51}, thHi={'GB': 65}), Theta(thLo={'GB': 51}, thHi={'GB': 66}), Theta(thLo={'GB': 51}, thHi={'GB': 67}), Theta(thLo={'GB': 51}, thHi={'GB': 68}), Theta(thLo={'GB': 51}, thHi={'GB': 69}), Theta(thLo={'GB': 51}, thHi={'GB': 70}), Theta(thLo={'GB': 51}, thHi={'GB': 71}), Theta(thLo={'GB': 51}, thHi={'GB': 72}), Theta(thLo={'GB': 51}, thHi={'GB': 73}), Theta(thLo={'GB': 51}, thHi={'GB': 74}), Theta(thLo={'GB': 51}, thHi={'GB': 75}), Theta(thLo={'GB': 51}, thHi={'GB': 76}), Theta(thLo={'GB': 51}, thHi={'GB': 77}), Theta(thLo={'GB': 51}, thHi={'GB': 78}), Theta(thLo={'GB': 51}, thHi={'GB': 79}), Theta(thLo={'GB': 51}, thHi={'GB': 80}), Theta(thLo={'GB': 51}, thHi={'GB': 81}), Theta(thLo={'GB': 51}, thHi={'GB': 82}), Theta(thLo={'GB': 51}, thHi={'GB': 83}), Theta(thLo={'GB': 51}, thHi={'GB': 84}), Theta(thLo={'GB': 51}, thHi={'GB': 85}), Theta(thLo={'GB': 51}, thHi={'GB': 86}), Theta(thLo={'GB': 51}, thHi={'GB': 87}), Theta(thLo={'GB': 51}, thHi={'GB': 88}), Theta(thLo={'GB': 51}, thHi={'GB': 89}), Theta(thLo={'GB': 51}, thHi={'GB': 90}), Theta(thLo={'GB': 51}, thHi={'GB': 91}), Theta(thLo={'GB': 51}, thHi={'GB': 92}), Theta(thLo={'GB': 51}, thHi={'GB': 93}), Theta(thLo={'GB': 51}, thHi={'GB': 94}), Theta(thLo={'GB': 51}, thHi={'GB': 95}), Theta(thLo={'GB': 51}, thHi={'GB': 96}), Theta(thLo={'GB': 51}, thHi={'GB': 97}), Theta(thLo={'GB': 51}, thHi={'GB': 98}), Theta(thLo={'GB': 51}, thHi={'GB': 99}), Theta(thLo={'GB': 52}, thHi={'GB': 10}), Theta(thLo={'GB': 52}, thHi={'GB': 11}), Theta(thLo={'GB': 52}, thHi={'GB': 12}), Theta(thLo={'GB': 52}, thHi={'GB': 13}), Theta(thLo={'GB': 52}, thHi={'GB': 14}), Theta(thLo={'GB': 52}, thHi={'GB': 15}), Theta(thLo={'GB': 52}, thHi={'GB': 16}), Theta(thLo={'GB': 52}, thHi={'GB': 17}), Theta(thLo={'GB': 52}, thHi={'GB': 18}), Theta(thLo={'GB': 52}, thHi={'GB': 19}), Theta(thLo={'GB': 52}, thHi={'GB': 20}), Theta(thLo={'GB': 52}, thHi={'GB': 21}), Theta(thLo={'GB': 52}, thHi={'GB': 22}), Theta(thLo={'GB': 52}, thHi={'GB': 23}), Theta(thLo={'GB': 52}, thHi={'GB': 24}), Theta(thLo={'GB': 52}, thHi={'GB': 25}), Theta(thLo={'GB': 52}, thHi={'GB': 26}), Theta(thLo={'GB': 52}, thHi={'GB': 27}), Theta(thLo={'GB': 52}, thHi={'GB': 28}), Theta(thLo={'GB': 52}, thHi={'GB': 29}), Theta(thLo={'GB': 52}, thHi={'GB': 30}), Theta(thLo={'GB': 52}, thHi={'GB': 31}), Theta(thLo={'GB': 52}, thHi={'GB': 32}), Theta(thLo={'GB': 52}, thHi={'GB': 33}), Theta(thLo={'GB': 52}, thHi={'GB': 34}), Theta(thLo={'GB': 52}, thHi={'GB': 35}), Theta(thLo={'GB': 52}, thHi={'GB': 36}), Theta(thLo={'GB': 52}, thHi={'GB': 37}), Theta(thLo={'GB': 52}, thHi={'GB': 38}), Theta(thLo={'GB': 52}, thHi={'GB': 39}), Theta(thLo={'GB': 52}, thHi={'GB': 40}), Theta(thLo={'GB': 52}, thHi={'GB': 41}), Theta(thLo={'GB': 52}, thHi={'GB': 42}), Theta(thLo={'GB': 52}, thHi={'GB': 43}), Theta(thLo={'GB': 52}, thHi={'GB': 44}), Theta(thLo={'GB': 52}, thHi={'GB': 45}), Theta(thLo={'GB': 52}, thHi={'GB': 46}), Theta(thLo={'GB': 52}, thHi={'GB': 47}), Theta(thLo={'GB': 52}, thHi={'GB': 48}), Theta(thLo={'GB': 52}, thHi={'GB': 49}), Theta(thLo={'GB': 52}, thHi={'GB': 50}), Theta(thLo={'GB': 52}, thHi={'GB': 51}), Theta(thLo={'GB': 52}, thHi={'GB': 52}), Theta(thLo={'GB': 52}, thHi={'GB': 53}), Theta(thLo={'GB': 52}, thHi={'GB': 54}), Theta(thLo={'GB': 52}, thHi={'GB': 55}), Theta(thLo={'GB': 52}, thHi={'GB': 56}), Theta(thLo={'GB': 52}, thHi={'GB': 57}), Theta(thLo={'GB': 52}, thHi={'GB': 58}), Theta(thLo={'GB': 52}, thHi={'GB': 59}), Theta(thLo={'GB': 52}, thHi={'GB': 60}), Theta(thLo={'GB': 52}, thHi={'GB': 61}), Theta(thLo={'GB': 52}, thHi={'GB': 62}), Theta(thLo={'GB': 52}, thHi={'GB': 63}), Theta(thLo={'GB': 52}, thHi={'GB': 64}), Theta(thLo={'GB': 52}, thHi={'GB': 65}), Theta(thLo={'GB': 52}, thHi={'GB': 66}), Theta(thLo={'GB': 52}, thHi={'GB': 67}), Theta(thLo={'GB': 52}, thHi={'GB': 68}), Theta(thLo={'GB': 52}, thHi={'GB': 69}), Theta(thLo={'GB': 52}, thHi={'GB': 70}), Theta(thLo={'GB': 52}, thHi={'GB': 71}), Theta(thLo={'GB': 52}, thHi={'GB': 72}), Theta(thLo={'GB': 52}, thHi={'GB': 73}), Theta(thLo={'GB': 52}, thHi={'GB': 74}), Theta(thLo={'GB': 52}, thHi={'GB': 75}), Theta(thLo={'GB': 52}, thHi={'GB': 76}), Theta(thLo={'GB': 52}, thHi={'GB': 77}), Theta(thLo={'GB': 52}, thHi={'GB': 78}), Theta(thLo={'GB': 52}, thHi={'GB': 79}), Theta(thLo={'GB': 52}, thHi={'GB': 80}), Theta(thLo={'GB': 52}, thHi={'GB': 81}), Theta(thLo={'GB': 52}, thHi={'GB': 82}), Theta(thLo={'GB': 52}, thHi={'GB': 83}), Theta(thLo={'GB': 52}, thHi={'GB': 84}), Theta(thLo={'GB': 52}, thHi={'GB': 85}), Theta(thLo={'GB': 52}, thHi={'GB': 86}), Theta(thLo={'GB': 52}, thHi={'GB': 87}), Theta(thLo={'GB': 52}, thHi={'GB': 88}), Theta(thLo={'GB': 52}, thHi={'GB': 89}), Theta(thLo={'GB': 52}, thHi={'GB': 90}), Theta(thLo={'GB': 52}, thHi={'GB': 91}), Theta(thLo={'GB': 52}, thHi={'GB': 92}), Theta(thLo={'GB': 52}, thHi={'GB': 93}), 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Theta(thLo={'GB': 57}, thHi={'GB': 28}), Theta(thLo={'GB': 57}, thHi={'GB': 29}), Theta(thLo={'GB': 57}, thHi={'GB': 30}), Theta(thLo={'GB': 57}, thHi={'GB': 31}), Theta(thLo={'GB': 57}, thHi={'GB': 32}), Theta(thLo={'GB': 57}, thHi={'GB': 33}), Theta(thLo={'GB': 57}, thHi={'GB': 34}), Theta(thLo={'GB': 57}, thHi={'GB': 35}), Theta(thLo={'GB': 57}, thHi={'GB': 36}), Theta(thLo={'GB': 57}, thHi={'GB': 37}), Theta(thLo={'GB': 57}, thHi={'GB': 38}), Theta(thLo={'GB': 57}, thHi={'GB': 39}), Theta(thLo={'GB': 57}, thHi={'GB': 40}), Theta(thLo={'GB': 57}, thHi={'GB': 41}), Theta(thLo={'GB': 57}, thHi={'GB': 42}), Theta(thLo={'GB': 57}, thHi={'GB': 43}), Theta(thLo={'GB': 57}, thHi={'GB': 44}), Theta(thLo={'GB': 57}, thHi={'GB': 45}), Theta(thLo={'GB': 57}, thHi={'GB': 46}), Theta(thLo={'GB': 57}, thHi={'GB': 47}), Theta(thLo={'GB': 57}, thHi={'GB': 48}), Theta(thLo={'GB': 57}, thHi={'GB': 49}), Theta(thLo={'GB': 57}, thHi={'GB': 50}), Theta(thLo={'GB': 57}, thHi={'GB': 51}), Theta(thLo={'GB': 57}, thHi={'GB': 52}), Theta(thLo={'GB': 57}, thHi={'GB': 53}), Theta(thLo={'GB': 57}, thHi={'GB': 54}), Theta(thLo={'GB': 57}, thHi={'GB': 55}), Theta(thLo={'GB': 57}, thHi={'GB': 56}), Theta(thLo={'GB': 57}, thHi={'GB': 57}), Theta(thLo={'GB': 57}, thHi={'GB': 58}), Theta(thLo={'GB': 57}, thHi={'GB': 59}), Theta(thLo={'GB': 57}, thHi={'GB': 60}), Theta(thLo={'GB': 57}, thHi={'GB': 61}), Theta(thLo={'GB': 57}, thHi={'GB': 62}), Theta(thLo={'GB': 57}, thHi={'GB': 63}), Theta(thLo={'GB': 57}, thHi={'GB': 64}), Theta(thLo={'GB': 57}, thHi={'GB': 65}), Theta(thLo={'GB': 57}, thHi={'GB': 66}), Theta(thLo={'GB': 57}, thHi={'GB': 67}), Theta(thLo={'GB': 57}, thHi={'GB': 68}), Theta(thLo={'GB': 57}, thHi={'GB': 69}), Theta(thLo={'GB': 57}, thHi={'GB': 70}), Theta(thLo={'GB': 57}, thHi={'GB': 71}), Theta(thLo={'GB': 57}, thHi={'GB': 72}), Theta(thLo={'GB': 57}, thHi={'GB': 73}), Theta(thLo={'GB': 57}, thHi={'GB': 74}), Theta(thLo={'GB': 57}, thHi={'GB': 75}), Theta(thLo={'GB': 57}, thHi={'GB': 76}), Theta(thLo={'GB': 57}, thHi={'GB': 77}), Theta(thLo={'GB': 57}, thHi={'GB': 78}), Theta(thLo={'GB': 57}, thHi={'GB': 79}), Theta(thLo={'GB': 57}, thHi={'GB': 80}), Theta(thLo={'GB': 57}, thHi={'GB': 81}), Theta(thLo={'GB': 57}, thHi={'GB': 82}), Theta(thLo={'GB': 57}, thHi={'GB': 83}), Theta(thLo={'GB': 57}, thHi={'GB': 84}), Theta(thLo={'GB': 57}, thHi={'GB': 85}), Theta(thLo={'GB': 57}, thHi={'GB': 86}), Theta(thLo={'GB': 57}, thHi={'GB': 87}), Theta(thLo={'GB': 57}, thHi={'GB': 88}), Theta(thLo={'GB': 57}, thHi={'GB': 89}), Theta(thLo={'GB': 57}, thHi={'GB': 90}), Theta(thLo={'GB': 57}, thHi={'GB': 91}), Theta(thLo={'GB': 57}, thHi={'GB': 92}), Theta(thLo={'GB': 57}, thHi={'GB': 93}), Theta(thLo={'GB': 57}, thHi={'GB': 94}), Theta(thLo={'GB': 57}, thHi={'GB': 95}), Theta(thLo={'GB': 57}, thHi={'GB': 96}), Theta(thLo={'GB': 57}, thHi={'GB': 97}), Theta(thLo={'GB': 57}, thHi={'GB': 98}), Theta(thLo={'GB': 57}, thHi={'GB': 99}), Theta(thLo={'GB': 58}, thHi={'GB': 10}), Theta(thLo={'GB': 58}, thHi={'GB': 11}), Theta(thLo={'GB': 58}, thHi={'GB': 12}), Theta(thLo={'GB': 58}, thHi={'GB': 13}), Theta(thLo={'GB': 58}, thHi={'GB': 14}), Theta(thLo={'GB': 58}, thHi={'GB': 15}), Theta(thLo={'GB': 58}, thHi={'GB': 16}), Theta(thLo={'GB': 58}, thHi={'GB': 17}), Theta(thLo={'GB': 58}, thHi={'GB': 18}), Theta(thLo={'GB': 58}, thHi={'GB': 19}), Theta(thLo={'GB': 58}, thHi={'GB': 20}), Theta(thLo={'GB': 58}, thHi={'GB': 21}), Theta(thLo={'GB': 58}, thHi={'GB': 22}), Theta(thLo={'GB': 58}, thHi={'GB': 23}), Theta(thLo={'GB': 58}, thHi={'GB': 24}), Theta(thLo={'GB': 58}, thHi={'GB': 25}), Theta(thLo={'GB': 58}, thHi={'GB': 26}), Theta(thLo={'GB': 58}, thHi={'GB': 27}), Theta(thLo={'GB': 58}, thHi={'GB': 28}), Theta(thLo={'GB': 58}, thHi={'GB': 29}), Theta(thLo={'GB': 58}, thHi={'GB': 30}), Theta(thLo={'GB': 58}, thHi={'GB': 31}), Theta(thLo={'GB': 58}, thHi={'GB': 32}), Theta(thLo={'GB': 58}, thHi={'GB': 33}), Theta(thLo={'GB': 58}, thHi={'GB': 34}), Theta(thLo={'GB': 58}, thHi={'GB': 35}), Theta(thLo={'GB': 58}, thHi={'GB': 36}), Theta(thLo={'GB': 58}, thHi={'GB': 37}), Theta(thLo={'GB': 58}, thHi={'GB': 38}), Theta(thLo={'GB': 58}, thHi={'GB': 39}), Theta(thLo={'GB': 58}, thHi={'GB': 40}), Theta(thLo={'GB': 58}, thHi={'GB': 41}), Theta(thLo={'GB': 58}, thHi={'GB': 42}), Theta(thLo={'GB': 58}, thHi={'GB': 43}), Theta(thLo={'GB': 58}, thHi={'GB': 44}), Theta(thLo={'GB': 58}, thHi={'GB': 45}), Theta(thLo={'GB': 58}, thHi={'GB': 46}), Theta(thLo={'GB': 58}, thHi={'GB': 47}), Theta(thLo={'GB': 58}, thHi={'GB': 48}), Theta(thLo={'GB': 58}, thHi={'GB': 49}), Theta(thLo={'GB': 58}, thHi={'GB': 50}), Theta(thLo={'GB': 58}, thHi={'GB': 51}), Theta(thLo={'GB': 58}, thHi={'GB': 52}), Theta(thLo={'GB': 58}, thHi={'GB': 53}), Theta(thLo={'GB': 58}, thHi={'GB': 54}), Theta(thLo={'GB': 58}, thHi={'GB': 55}), Theta(thLo={'GB': 58}, thHi={'GB': 56}), Theta(thLo={'GB': 58}, thHi={'GB': 57}), Theta(thLo={'GB': 58}, thHi={'GB': 58}), Theta(thLo={'GB': 58}, thHi={'GB': 59}), Theta(thLo={'GB': 58}, thHi={'GB': 60}), Theta(thLo={'GB': 58}, thHi={'GB': 61}), Theta(thLo={'GB': 58}, thHi={'GB': 62}), Theta(thLo={'GB': 58}, thHi={'GB': 63}), Theta(thLo={'GB': 58}, thHi={'GB': 64}), Theta(thLo={'GB': 58}, thHi={'GB': 65}), Theta(thLo={'GB': 58}, thHi={'GB': 66}), Theta(thLo={'GB': 58}, thHi={'GB': 67}), Theta(thLo={'GB': 58}, thHi={'GB': 68}), Theta(thLo={'GB': 58}, thHi={'GB': 69}), Theta(thLo={'GB': 58}, thHi={'GB': 70}), Theta(thLo={'GB': 58}, thHi={'GB': 71}), Theta(thLo={'GB': 58}, thHi={'GB': 72}), Theta(thLo={'GB': 58}, thHi={'GB': 73}), Theta(thLo={'GB': 58}, thHi={'GB': 74}), Theta(thLo={'GB': 58}, thHi={'GB': 75}), Theta(thLo={'GB': 58}, thHi={'GB': 76}), Theta(thLo={'GB': 58}, thHi={'GB': 77}), Theta(thLo={'GB': 58}, thHi={'GB': 78}), Theta(thLo={'GB': 58}, thHi={'GB': 79}), Theta(thLo={'GB': 58}, thHi={'GB': 80}), Theta(thLo={'GB': 58}, thHi={'GB': 81}), Theta(thLo={'GB': 58}, thHi={'GB': 82}), Theta(thLo={'GB': 58}, thHi={'GB': 83}), Theta(thLo={'GB': 58}, thHi={'GB': 84}), Theta(thLo={'GB': 58}, thHi={'GB': 85}), Theta(thLo={'GB': 58}, thHi={'GB': 86}), Theta(thLo={'GB': 58}, thHi={'GB': 87}), Theta(thLo={'GB': 58}, thHi={'GB': 88}), Theta(thLo={'GB': 58}, thHi={'GB': 89}), Theta(thLo={'GB': 58}, thHi={'GB': 90}), Theta(thLo={'GB': 58}, thHi={'GB': 91}), Theta(thLo={'GB': 58}, thHi={'GB': 92}), Theta(thLo={'GB': 58}, thHi={'GB': 93}), Theta(thLo={'GB': 58}, thHi={'GB': 94}), Theta(thLo={'GB': 58}, thHi={'GB': 95}), Theta(thLo={'GB': 58}, thHi={'GB': 96}), Theta(thLo={'GB': 58}, thHi={'GB': 97}), Theta(thLo={'GB': 58}, thHi={'GB': 98}), Theta(thLo={'GB': 58}, thHi={'GB': 99}), Theta(thLo={'GB': 59}, thHi={'GB': 10}), Theta(thLo={'GB': 59}, thHi={'GB': 11}), Theta(thLo={'GB': 59}, thHi={'GB': 12}), Theta(thLo={'GB': 59}, thHi={'GB': 13}), Theta(thLo={'GB': 59}, thHi={'GB': 14}), Theta(thLo={'GB': 59}, thHi={'GB': 15}), Theta(thLo={'GB': 59}, thHi={'GB': 16}), Theta(thLo={'GB': 59}, thHi={'GB': 17}), Theta(thLo={'GB': 59}, thHi={'GB': 18}), Theta(thLo={'GB': 59}, thHi={'GB': 19}), Theta(thLo={'GB': 59}, thHi={'GB': 20}), Theta(thLo={'GB': 59}, thHi={'GB': 21}), Theta(thLo={'GB': 59}, thHi={'GB': 22}), Theta(thLo={'GB': 59}, thHi={'GB': 23}), Theta(thLo={'GB': 59}, thHi={'GB': 24}), Theta(thLo={'GB': 59}, thHi={'GB': 25}), Theta(thLo={'GB': 59}, thHi={'GB': 26}), Theta(thLo={'GB': 59}, thHi={'GB': 27}), Theta(thLo={'GB': 59}, thHi={'GB': 28}), Theta(thLo={'GB': 59}, thHi={'GB': 29}), Theta(thLo={'GB': 59}, thHi={'GB': 30}), Theta(thLo={'GB': 59}, thHi={'GB': 31}), Theta(thLo={'GB': 59}, thHi={'GB': 32}), Theta(thLo={'GB': 59}, thHi={'GB': 33}), Theta(thLo={'GB': 59}, thHi={'GB': 34}), Theta(thLo={'GB': 59}, thHi={'GB': 35}), Theta(thLo={'GB': 59}, thHi={'GB': 36}), Theta(thLo={'GB': 59}, thHi={'GB': 37}), Theta(thLo={'GB': 59}, thHi={'GB': 38}), Theta(thLo={'GB': 59}, thHi={'GB': 39}), Theta(thLo={'GB': 59}, thHi={'GB': 40}), Theta(thLo={'GB': 59}, thHi={'GB': 41}), Theta(thLo={'GB': 59}, thHi={'GB': 42}), Theta(thLo={'GB': 59}, thHi={'GB': 43}), Theta(thLo={'GB': 59}, thHi={'GB': 44}), Theta(thLo={'GB': 59}, thHi={'GB': 45}), Theta(thLo={'GB': 59}, thHi={'GB': 46}), Theta(thLo={'GB': 59}, thHi={'GB': 47}), Theta(thLo={'GB': 59}, thHi={'GB': 48}), Theta(thLo={'GB': 59}, thHi={'GB': 49}), Theta(thLo={'GB': 59}, thHi={'GB': 50}), Theta(thLo={'GB': 59}, thHi={'GB': 51}), Theta(thLo={'GB': 59}, thHi={'GB': 52}), Theta(thLo={'GB': 59}, thHi={'GB': 53}), Theta(thLo={'GB': 59}, thHi={'GB': 54}), Theta(thLo={'GB': 59}, thHi={'GB': 55}), Theta(thLo={'GB': 59}, thHi={'GB': 56}), Theta(thLo={'GB': 59}, thHi={'GB': 57}), Theta(thLo={'GB': 59}, thHi={'GB': 58}), Theta(thLo={'GB': 59}, thHi={'GB': 59}), Theta(thLo={'GB': 59}, thHi={'GB': 60}), Theta(thLo={'GB': 59}, thHi={'GB': 61}), Theta(thLo={'GB': 59}, thHi={'GB': 62}), Theta(thLo={'GB': 59}, thHi={'GB': 63}), Theta(thLo={'GB': 59}, thHi={'GB': 64}), Theta(thLo={'GB': 59}, thHi={'GB': 65}), Theta(thLo={'GB': 59}, thHi={'GB': 66}), Theta(thLo={'GB': 59}, thHi={'GB': 67}), Theta(thLo={'GB': 59}, thHi={'GB': 68}), Theta(thLo={'GB': 59}, thHi={'GB': 69}), Theta(thLo={'GB': 59}, thHi={'GB': 70}), Theta(thLo={'GB': 59}, thHi={'GB': 71}), Theta(thLo={'GB': 59}, thHi={'GB': 72}), Theta(thLo={'GB': 59}, thHi={'GB': 73}), Theta(thLo={'GB': 59}, thHi={'GB': 74}), Theta(thLo={'GB': 59}, thHi={'GB': 75}), Theta(thLo={'GB': 59}, thHi={'GB': 76}), Theta(thLo={'GB': 59}, thHi={'GB': 77}), Theta(thLo={'GB': 59}, thHi={'GB': 78}), Theta(thLo={'GB': 59}, thHi={'GB': 79}), Theta(thLo={'GB': 59}, thHi={'GB': 80}), Theta(thLo={'GB': 59}, thHi={'GB': 81}), Theta(thLo={'GB': 59}, thHi={'GB': 82}), Theta(thLo={'GB': 59}, thHi={'GB': 83}), Theta(thLo={'GB': 59}, thHi={'GB': 84}), Theta(thLo={'GB': 59}, thHi={'GB': 85}), Theta(thLo={'GB': 59}, thHi={'GB': 86}), Theta(thLo={'GB': 59}, thHi={'GB': 87}), Theta(thLo={'GB': 59}, thHi={'GB': 88}), Theta(thLo={'GB': 59}, thHi={'GB': 89}), Theta(thLo={'GB': 59}, thHi={'GB': 90}), Theta(thLo={'GB': 59}, thHi={'GB': 91}), Theta(thLo={'GB': 59}, thHi={'GB': 92}), Theta(thLo={'GB': 59}, thHi={'GB': 93}), Theta(thLo={'GB': 59}, thHi={'GB': 94}), Theta(thLo={'GB': 59}, thHi={'GB': 95}), Theta(thLo={'GB': 59}, thHi={'GB': 96}), Theta(thLo={'GB': 59}, thHi={'GB': 97}), Theta(thLo={'GB': 59}, thHi={'GB': 98}), Theta(thLo={'GB': 59}, thHi={'GB': 99}), Theta(thLo={'GB': 60}, thHi={'GB': 10}), Theta(thLo={'GB': 60}, thHi={'GB': 11}), Theta(thLo={'GB': 60}, thHi={'GB': 12}), Theta(thLo={'GB': 60}, thHi={'GB': 13}), Theta(thLo={'GB': 60}, thHi={'GB': 14}), Theta(thLo={'GB': 60}, thHi={'GB': 15}), Theta(thLo={'GB': 60}, thHi={'GB': 16}), Theta(thLo={'GB': 60}, thHi={'GB': 17}), Theta(thLo={'GB': 60}, thHi={'GB': 18}), Theta(thLo={'GB': 60}, thHi={'GB': 19}), Theta(thLo={'GB': 60}, thHi={'GB': 20}), Theta(thLo={'GB': 60}, thHi={'GB': 21}), Theta(thLo={'GB': 60}, thHi={'GB': 22}), Theta(thLo={'GB': 60}, thHi={'GB': 23}), Theta(thLo={'GB': 60}, thHi={'GB': 24}), Theta(thLo={'GB': 60}, thHi={'GB': 25}), Theta(thLo={'GB': 60}, thHi={'GB': 26}), Theta(thLo={'GB': 60}, thHi={'GB': 27}), Theta(thLo={'GB': 60}, thHi={'GB': 28}), Theta(thLo={'GB': 60}, thHi={'GB': 29}), Theta(thLo={'GB': 60}, thHi={'GB': 30}), Theta(thLo={'GB': 60}, thHi={'GB': 31}), Theta(thLo={'GB': 60}, thHi={'GB': 32}), Theta(thLo={'GB': 60}, thHi={'GB': 33}), Theta(thLo={'GB': 60}, thHi={'GB': 34}), Theta(thLo={'GB': 60}, thHi={'GB': 35}), Theta(thLo={'GB': 60}, thHi={'GB': 36}), Theta(thLo={'GB': 60}, thHi={'GB': 37}), Theta(thLo={'GB': 60}, thHi={'GB': 38}), Theta(thLo={'GB': 60}, thHi={'GB': 39}), Theta(thLo={'GB': 60}, thHi={'GB': 40}), Theta(thLo={'GB': 60}, thHi={'GB': 41}), Theta(thLo={'GB': 60}, thHi={'GB': 42}), Theta(thLo={'GB': 60}, thHi={'GB': 43}), Theta(thLo={'GB': 60}, thHi={'GB': 44}), Theta(thLo={'GB': 60}, thHi={'GB': 45}), Theta(thLo={'GB': 60}, thHi={'GB': 46}), Theta(thLo={'GB': 60}, thHi={'GB': 47}), Theta(thLo={'GB': 60}, thHi={'GB': 48}), Theta(thLo={'GB': 60}, thHi={'GB': 49}), Theta(thLo={'GB': 60}, thHi={'GB': 50}), Theta(thLo={'GB': 60}, thHi={'GB': 51}), Theta(thLo={'GB': 60}, thHi={'GB': 52}), Theta(thLo={'GB': 60}, thHi={'GB': 53}), Theta(thLo={'GB': 60}, thHi={'GB': 54}), Theta(thLo={'GB': 60}, thHi={'GB': 55}), Theta(thLo={'GB': 60}, thHi={'GB': 56}), Theta(thLo={'GB': 60}, thHi={'GB': 57}), Theta(thLo={'GB': 60}, thHi={'GB': 58}), Theta(thLo={'GB': 60}, thHi={'GB': 59}), Theta(thLo={'GB': 60}, thHi={'GB': 60}), Theta(thLo={'GB': 60}, thHi={'GB': 61}), Theta(thLo={'GB': 60}, thHi={'GB': 62}), Theta(thLo={'GB': 60}, thHi={'GB': 63}), Theta(thLo={'GB': 60}, thHi={'GB': 64}), Theta(thLo={'GB': 60}, thHi={'GB': 65}), Theta(thLo={'GB': 60}, thHi={'GB': 66}), Theta(thLo={'GB': 60}, thHi={'GB': 67}), Theta(thLo={'GB': 60}, thHi={'GB': 68}), Theta(thLo={'GB': 60}, thHi={'GB': 69}), Theta(thLo={'GB': 60}, thHi={'GB': 70}), Theta(thLo={'GB': 60}, thHi={'GB': 71}), Theta(thLo={'GB': 60}, thHi={'GB': 72}), Theta(thLo={'GB': 60}, thHi={'GB': 73}), Theta(thLo={'GB': 60}, thHi={'GB': 74}), Theta(thLo={'GB': 60}, thHi={'GB': 75}), Theta(thLo={'GB': 60}, thHi={'GB': 76}), Theta(thLo={'GB': 60}, thHi={'GB': 77}), Theta(thLo={'GB': 60}, thHi={'GB': 78}), Theta(thLo={'GB': 60}, thHi={'GB': 79}), Theta(thLo={'GB': 60}, thHi={'GB': 80}), Theta(thLo={'GB': 60}, thHi={'GB': 81}), Theta(thLo={'GB': 60}, thHi={'GB': 82}), Theta(thLo={'GB': 60}, thHi={'GB': 83}), Theta(thLo={'GB': 60}, thHi={'GB': 84}), Theta(thLo={'GB': 60}, thHi={'GB': 85}), Theta(thLo={'GB': 60}, thHi={'GB': 86}), Theta(thLo={'GB': 60}, thHi={'GB': 87}), Theta(thLo={'GB': 60}, thHi={'GB': 88}), Theta(thLo={'GB': 60}, thHi={'GB': 89}), Theta(thLo={'GB': 60}, thHi={'GB': 90}), Theta(thLo={'GB': 60}, thHi={'GB': 91}), Theta(thLo={'GB': 60}, thHi={'GB': 92}), Theta(thLo={'GB': 60}, thHi={'GB': 93}), Theta(thLo={'GB': 60}, thHi={'GB': 94}), Theta(thLo={'GB': 60}, thHi={'GB': 95}), Theta(thLo={'GB': 60}, thHi={'GB': 96}), Theta(thLo={'GB': 60}, thHi={'GB': 97}), Theta(thLo={'GB': 60}, thHi={'GB': 98}), Theta(thLo={'GB': 60}, thHi={'GB': 99}), Theta(thLo={'GB': 61}, thHi={'GB': 10}), Theta(thLo={'GB': 61}, thHi={'GB': 11}), Theta(thLo={'GB': 61}, thHi={'GB': 12}), Theta(thLo={'GB': 61}, thHi={'GB': 13}), Theta(thLo={'GB': 61}, thHi={'GB': 14}), Theta(thLo={'GB': 61}, thHi={'GB': 15}), Theta(thLo={'GB': 61}, thHi={'GB': 16}), Theta(thLo={'GB': 61}, thHi={'GB': 17}), Theta(thLo={'GB': 61}, thHi={'GB': 18}), Theta(thLo={'GB': 61}, thHi={'GB': 19}), Theta(thLo={'GB': 61}, thHi={'GB': 20}), Theta(thLo={'GB': 61}, thHi={'GB': 21}), Theta(thLo={'GB': 61}, thHi={'GB': 22}), Theta(thLo={'GB': 61}, thHi={'GB': 23}), Theta(thLo={'GB': 61}, thHi={'GB': 24}), Theta(thLo={'GB': 61}, thHi={'GB': 25}), Theta(thLo={'GB': 61}, thHi={'GB': 26}), Theta(thLo={'GB': 61}, thHi={'GB': 27}), Theta(thLo={'GB': 61}, thHi={'GB': 28}), Theta(thLo={'GB': 61}, thHi={'GB': 29}), Theta(thLo={'GB': 61}, thHi={'GB': 30}), Theta(thLo={'GB': 61}, thHi={'GB': 31}), Theta(thLo={'GB': 61}, thHi={'GB': 32}), Theta(thLo={'GB': 61}, thHi={'GB': 33}), Theta(thLo={'GB': 61}, thHi={'GB': 34}), Theta(thLo={'GB': 61}, thHi={'GB': 35}), Theta(thLo={'GB': 61}, thHi={'GB': 36}), Theta(thLo={'GB': 61}, thHi={'GB': 37}), Theta(thLo={'GB': 61}, thHi={'GB': 38}), Theta(thLo={'GB': 61}, thHi={'GB': 39}), Theta(thLo={'GB': 61}, thHi={'GB': 40}), Theta(thLo={'GB': 61}, thHi={'GB': 41}), Theta(thLo={'GB': 61}, thHi={'GB': 42}), Theta(thLo={'GB': 61}, thHi={'GB': 43}), Theta(thLo={'GB': 61}, thHi={'GB': 44}), Theta(thLo={'GB': 61}, thHi={'GB': 45}), Theta(thLo={'GB': 61}, thHi={'GB': 46}), Theta(thLo={'GB': 61}, thHi={'GB': 47}), Theta(thLo={'GB': 61}, thHi={'GB': 48}), Theta(thLo={'GB': 61}, thHi={'GB': 49}), Theta(thLo={'GB': 61}, thHi={'GB': 50}), Theta(thLo={'GB': 61}, thHi={'GB': 51}), Theta(thLo={'GB': 61}, thHi={'GB': 52}), Theta(thLo={'GB': 61}, thHi={'GB': 53}), Theta(thLo={'GB': 61}, thHi={'GB': 54}), Theta(thLo={'GB': 61}, thHi={'GB': 55}), Theta(thLo={'GB': 61}, thHi={'GB': 56}), Theta(thLo={'GB': 61}, thHi={'GB': 57}), Theta(thLo={'GB': 61}, thHi={'GB': 58}), Theta(thLo={'GB': 61}, thHi={'GB': 59}), Theta(thLo={'GB': 61}, thHi={'GB': 60}), Theta(thLo={'GB': 61}, thHi={'GB': 61}), Theta(thLo={'GB': 61}, thHi={'GB': 62}), Theta(thLo={'GB': 61}, thHi={'GB': 63}), Theta(thLo={'GB': 61}, thHi={'GB': 64}), Theta(thLo={'GB': 61}, thHi={'GB': 65}), Theta(thLo={'GB': 61}, thHi={'GB': 66}), Theta(thLo={'GB': 61}, thHi={'GB': 67}), Theta(thLo={'GB': 61}, thHi={'GB': 68}), Theta(thLo={'GB': 61}, thHi={'GB': 69}), Theta(thLo={'GB': 61}, thHi={'GB': 70}), Theta(thLo={'GB': 61}, thHi={'GB': 71}), Theta(thLo={'GB': 61}, thHi={'GB': 72}), Theta(thLo={'GB': 61}, thHi={'GB': 73}), Theta(thLo={'GB': 61}, thHi={'GB': 74}), Theta(thLo={'GB': 61}, thHi={'GB': 75}), Theta(thLo={'GB': 61}, thHi={'GB': 76}), Theta(thLo={'GB': 61}, thHi={'GB': 77}), Theta(thLo={'GB': 61}, thHi={'GB': 78}), Theta(thLo={'GB': 61}, thHi={'GB': 79}), Theta(thLo={'GB': 61}, thHi={'GB': 80}), Theta(thLo={'GB': 61}, thHi={'GB': 81}), Theta(thLo={'GB': 61}, thHi={'GB': 82}), Theta(thLo={'GB': 61}, thHi={'GB': 83}), Theta(thLo={'GB': 61}, thHi={'GB': 84}), Theta(thLo={'GB': 61}, thHi={'GB': 85}), Theta(thLo={'GB': 61}, thHi={'GB': 86}), Theta(thLo={'GB': 61}, thHi={'GB': 87}), Theta(thLo={'GB': 61}, thHi={'GB': 88}), Theta(thLo={'GB': 61}, thHi={'GB': 89}), Theta(thLo={'GB': 61}, thHi={'GB': 90}), Theta(thLo={'GB': 61}, thHi={'GB': 91}), Theta(thLo={'GB': 61}, thHi={'GB': 92}), Theta(thLo={'GB': 61}, thHi={'GB': 93}), Theta(thLo={'GB': 61}, thHi={'GB': 94}), Theta(thLo={'GB': 61}, thHi={'GB': 95}), Theta(thLo={'GB': 61}, thHi={'GB': 96}), Theta(thLo={'GB': 61}, thHi={'GB': 97}), Theta(thLo={'GB': 61}, thHi={'GB': 98}), Theta(thLo={'GB': 61}, thHi={'GB': 99}), Theta(thLo={'GB': 62}, thHi={'GB': 10}), Theta(thLo={'GB': 62}, thHi={'GB': 11}), Theta(thLo={'GB': 62}, thHi={'GB': 12}), Theta(thLo={'GB': 62}, thHi={'GB': 13}), Theta(thLo={'GB': 62}, thHi={'GB': 14}), Theta(thLo={'GB': 62}, thHi={'GB': 15}), Theta(thLo={'GB': 62}, thHi={'GB': 16}), Theta(thLo={'GB': 62}, thHi={'GB': 17}), Theta(thLo={'GB': 62}, thHi={'GB': 18}), Theta(thLo={'GB': 62}, thHi={'GB': 19}), Theta(thLo={'GB': 62}, thHi={'GB': 20}), Theta(thLo={'GB': 62}, thHi={'GB': 21}), Theta(thLo={'GB': 62}, thHi={'GB': 22}), Theta(thLo={'GB': 62}, thHi={'GB': 23}), Theta(thLo={'GB': 62}, thHi={'GB': 24}), Theta(thLo={'GB': 62}, thHi={'GB': 25}), Theta(thLo={'GB': 62}, thHi={'GB': 26}), Theta(thLo={'GB': 62}, thHi={'GB': 27}), Theta(thLo={'GB': 62}, thHi={'GB': 28}), Theta(thLo={'GB': 62}, thHi={'GB': 29}), Theta(thLo={'GB': 62}, thHi={'GB': 30}), Theta(thLo={'GB': 62}, thHi={'GB': 31}), Theta(thLo={'GB': 62}, thHi={'GB': 32}), Theta(thLo={'GB': 62}, thHi={'GB': 33}), Theta(thLo={'GB': 62}, thHi={'GB': 34}), Theta(thLo={'GB': 62}, thHi={'GB': 35}), Theta(thLo={'GB': 62}, thHi={'GB': 36}), Theta(thLo={'GB': 62}, thHi={'GB': 37}), Theta(thLo={'GB': 62}, thHi={'GB': 38}), Theta(thLo={'GB': 62}, thHi={'GB': 39}), Theta(thLo={'GB': 62}, thHi={'GB': 40}), Theta(thLo={'GB': 62}, thHi={'GB': 41}), Theta(thLo={'GB': 62}, thHi={'GB': 42}), Theta(thLo={'GB': 62}, thHi={'GB': 43}), Theta(thLo={'GB': 62}, thHi={'GB': 44}), Theta(thLo={'GB': 62}, thHi={'GB': 45}), Theta(thLo={'GB': 62}, thHi={'GB': 46}), Theta(thLo={'GB': 62}, thHi={'GB': 47}), Theta(thLo={'GB': 62}, thHi={'GB': 48}), Theta(thLo={'GB': 62}, thHi={'GB': 49}), Theta(thLo={'GB': 62}, thHi={'GB': 50}), Theta(thLo={'GB': 62}, thHi={'GB': 51}), Theta(thLo={'GB': 62}, thHi={'GB': 52}), Theta(thLo={'GB': 62}, thHi={'GB': 53}), Theta(thLo={'GB': 62}, thHi={'GB': 54}), Theta(thLo={'GB': 62}, thHi={'GB': 55}), Theta(thLo={'GB': 62}, thHi={'GB': 56}), Theta(thLo={'GB': 62}, thHi={'GB': 57}), Theta(thLo={'GB': 62}, thHi={'GB': 58}), Theta(thLo={'GB': 62}, thHi={'GB': 59}), Theta(thLo={'GB': 62}, thHi={'GB': 60}), Theta(thLo={'GB': 62}, thHi={'GB': 61}), Theta(thLo={'GB': 62}, thHi={'GB': 62}), Theta(thLo={'GB': 62}, thHi={'GB': 63}), Theta(thLo={'GB': 62}, thHi={'GB': 64}), Theta(thLo={'GB': 62}, thHi={'GB': 65}), Theta(thLo={'GB': 62}, thHi={'GB': 66}), Theta(thLo={'GB': 62}, thHi={'GB': 67}), Theta(thLo={'GB': 62}, thHi={'GB': 68}), Theta(thLo={'GB': 62}, thHi={'GB': 69}), Theta(thLo={'GB': 62}, thHi={'GB': 70}), Theta(thLo={'GB': 62}, thHi={'GB': 71}), Theta(thLo={'GB': 62}, thHi={'GB': 72}), Theta(thLo={'GB': 62}, thHi={'GB': 73}), Theta(thLo={'GB': 62}, thHi={'GB': 74}), Theta(thLo={'GB': 62}, thHi={'GB': 75}), Theta(thLo={'GB': 62}, thHi={'GB': 76}), Theta(thLo={'GB': 62}, thHi={'GB': 77}), Theta(thLo={'GB': 62}, thHi={'GB': 78}), Theta(thLo={'GB': 62}, thHi={'GB': 79}), Theta(thLo={'GB': 62}, thHi={'GB': 80}), Theta(thLo={'GB': 62}, thHi={'GB': 81}), Theta(thLo={'GB': 62}, thHi={'GB': 82}), Theta(thLo={'GB': 62}, thHi={'GB': 83}), Theta(thLo={'GB': 62}, thHi={'GB': 84}), Theta(thLo={'GB': 62}, thHi={'GB': 85}), Theta(thLo={'GB': 62}, thHi={'GB': 86}), Theta(thLo={'GB': 62}, thHi={'GB': 87}), Theta(thLo={'GB': 62}, thHi={'GB': 88}), Theta(thLo={'GB': 62}, thHi={'GB': 89}), Theta(thLo={'GB': 62}, thHi={'GB': 90}), Theta(thLo={'GB': 62}, thHi={'GB': 91}), Theta(thLo={'GB': 62}, thHi={'GB': 92}), Theta(thLo={'GB': 62}, thHi={'GB': 93}), Theta(thLo={'GB': 62}, thHi={'GB': 94}), Theta(thLo={'GB': 62}, thHi={'GB': 95}), Theta(thLo={'GB': 62}, thHi={'GB': 96}), Theta(thLo={'GB': 62}, thHi={'GB': 97}), Theta(thLo={'GB': 62}, thHi={'GB': 98}), Theta(thLo={'GB': 62}, thHi={'GB': 99}), Theta(thLo={'GB': 63}, thHi={'GB': 10}), Theta(thLo={'GB': 63}, thHi={'GB': 11}), Theta(thLo={'GB': 63}, thHi={'GB': 12}), Theta(thLo={'GB': 63}, thHi={'GB': 13}), Theta(thLo={'GB': 63}, thHi={'GB': 14}), Theta(thLo={'GB': 63}, thHi={'GB': 15}), Theta(thLo={'GB': 63}, thHi={'GB': 16}), Theta(thLo={'GB': 63}, thHi={'GB': 17}), Theta(thLo={'GB': 63}, thHi={'GB': 18}), Theta(thLo={'GB': 63}, thHi={'GB': 19}), Theta(thLo={'GB': 63}, thHi={'GB': 20}), Theta(thLo={'GB': 63}, thHi={'GB': 21}), Theta(thLo={'GB': 63}, thHi={'GB': 22}), Theta(thLo={'GB': 63}, thHi={'GB': 23}), Theta(thLo={'GB': 63}, thHi={'GB': 24}), Theta(thLo={'GB': 63}, thHi={'GB': 25}), Theta(thLo={'GB': 63}, thHi={'GB': 26}), Theta(thLo={'GB': 63}, thHi={'GB': 27}), Theta(thLo={'GB': 63}, thHi={'GB': 28}), Theta(thLo={'GB': 63}, thHi={'GB': 29}), Theta(thLo={'GB': 63}, thHi={'GB': 30}), Theta(thLo={'GB': 63}, thHi={'GB': 31}), Theta(thLo={'GB': 63}, thHi={'GB': 32}), Theta(thLo={'GB': 63}, thHi={'GB': 33}), Theta(thLo={'GB': 63}, thHi={'GB': 34}), Theta(thLo={'GB': 63}, thHi={'GB': 35}), Theta(thLo={'GB': 63}, thHi={'GB': 36}), Theta(thLo={'GB': 63}, thHi={'GB': 37}), Theta(thLo={'GB': 63}, thHi={'GB': 38}), Theta(thLo={'GB': 63}, thHi={'GB': 39}), Theta(thLo={'GB': 63}, thHi={'GB': 40}), Theta(thLo={'GB': 63}, thHi={'GB': 41}), Theta(thLo={'GB': 63}, thHi={'GB': 42}), Theta(thLo={'GB': 63}, thHi={'GB': 43}), Theta(thLo={'GB': 63}, thHi={'GB': 44}), Theta(thLo={'GB': 63}, thHi={'GB': 45}), Theta(thLo={'GB': 63}, thHi={'GB': 46}), Theta(thLo={'GB': 63}, thHi={'GB': 47}), Theta(thLo={'GB': 63}, thHi={'GB': 48}), Theta(thLo={'GB': 63}, thHi={'GB': 49}), Theta(thLo={'GB': 63}, thHi={'GB': 50}), Theta(thLo={'GB': 63}, thHi={'GB': 51}), Theta(thLo={'GB': 63}, thHi={'GB': 52}), Theta(thLo={'GB': 63}, thHi={'GB': 53}), Theta(thLo={'GB': 63}, thHi={'GB': 54}), Theta(thLo={'GB': 63}, thHi={'GB': 55}), Theta(thLo={'GB': 63}, thHi={'GB': 56}), Theta(thLo={'GB': 63}, thHi={'GB': 57}), Theta(thLo={'GB': 63}, thHi={'GB': 58}), Theta(thLo={'GB': 63}, thHi={'GB': 59}), Theta(thLo={'GB': 63}, thHi={'GB': 60}), Theta(thLo={'GB': 63}, thHi={'GB': 61}), Theta(thLo={'GB': 63}, thHi={'GB': 62}), Theta(thLo={'GB': 63}, thHi={'GB': 63}), Theta(thLo={'GB': 63}, thHi={'GB': 64}), Theta(thLo={'GB': 63}, thHi={'GB': 65}), Theta(thLo={'GB': 63}, thHi={'GB': 66}), Theta(thLo={'GB': 63}, thHi={'GB': 67}), Theta(thLo={'GB': 63}, thHi={'GB': 68}), Theta(thLo={'GB': 63}, thHi={'GB': 69}), Theta(thLo={'GB': 63}, thHi={'GB': 70}), Theta(thLo={'GB': 63}, thHi={'GB': 71}), Theta(thLo={'GB': 63}, thHi={'GB': 72}), Theta(thLo={'GB': 63}, thHi={'GB': 73}), Theta(thLo={'GB': 63}, thHi={'GB': 74}), Theta(thLo={'GB': 63}, thHi={'GB': 75}), Theta(thLo={'GB': 63}, thHi={'GB': 76}), Theta(thLo={'GB': 63}, thHi={'GB': 77}), Theta(thLo={'GB': 63}, thHi={'GB': 78}), Theta(thLo={'GB': 63}, thHi={'GB': 79}), Theta(thLo={'GB': 63}, thHi={'GB': 80}), Theta(thLo={'GB': 63}, thHi={'GB': 81}), Theta(thLo={'GB': 63}, thHi={'GB': 82}), Theta(thLo={'GB': 63}, thHi={'GB': 83}), Theta(thLo={'GB': 63}, thHi={'GB': 84}), Theta(thLo={'GB': 63}, thHi={'GB': 85}), Theta(thLo={'GB': 63}, thHi={'GB': 86}), Theta(thLo={'GB': 63}, thHi={'GB': 87}), Theta(thLo={'GB': 63}, thHi={'GB': 88}), Theta(thLo={'GB': 63}, thHi={'GB': 89}), Theta(thLo={'GB': 63}, thHi={'GB': 90}), Theta(thLo={'GB': 63}, thHi={'GB': 91}), Theta(thLo={'GB': 63}, thHi={'GB': 92}), Theta(thLo={'GB': 63}, thHi={'GB': 93}), Theta(thLo={'GB': 63}, thHi={'GB': 94}), Theta(thLo={'GB': 63}, thHi={'GB': 95}), Theta(thLo={'GB': 63}, thHi={'GB': 96}), Theta(thLo={'GB': 63}, thHi={'GB': 97}), Theta(thLo={'GB': 63}, thHi={'GB': 98}), Theta(thLo={'GB': 63}, thHi={'GB': 99}), Theta(thLo={'GB': 64}, thHi={'GB': 10}), Theta(thLo={'GB': 64}, thHi={'GB': 11}), Theta(thLo={'GB': 64}, thHi={'GB': 12}), Theta(thLo={'GB': 64}, thHi={'GB': 13}), Theta(thLo={'GB': 64}, thHi={'GB': 14}), Theta(thLo={'GB': 64}, thHi={'GB': 15}), Theta(thLo={'GB': 64}, thHi={'GB': 16}), Theta(thLo={'GB': 64}, thHi={'GB': 17}), Theta(thLo={'GB': 64}, thHi={'GB': 18}), Theta(thLo={'GB': 64}, thHi={'GB': 19}), Theta(thLo={'GB': 64}, thHi={'GB': 20}), Theta(thLo={'GB': 64}, thHi={'GB': 21}), Theta(thLo={'GB': 64}, thHi={'GB': 22}), Theta(thLo={'GB': 64}, thHi={'GB': 23}), Theta(thLo={'GB': 64}, thHi={'GB': 24}), Theta(thLo={'GB': 64}, thHi={'GB': 25}), Theta(thLo={'GB': 64}, thHi={'GB': 26}), Theta(thLo={'GB': 64}, thHi={'GB': 27}), Theta(thLo={'GB': 64}, thHi={'GB': 28}), Theta(thLo={'GB': 64}, thHi={'GB': 29}), Theta(thLo={'GB': 64}, thHi={'GB': 30}), Theta(thLo={'GB': 64}, thHi={'GB': 31}), Theta(thLo={'GB': 64}, thHi={'GB': 32}), Theta(thLo={'GB': 64}, thHi={'GB': 33}), Theta(thLo={'GB': 64}, thHi={'GB': 34}), Theta(thLo={'GB': 64}, thHi={'GB': 35}), Theta(thLo={'GB': 64}, thHi={'GB': 36}), Theta(thLo={'GB': 64}, thHi={'GB': 37}), Theta(thLo={'GB': 64}, thHi={'GB': 38}), Theta(thLo={'GB': 64}, thHi={'GB': 39}), Theta(thLo={'GB': 64}, thHi={'GB': 40}), Theta(thLo={'GB': 64}, thHi={'GB': 41}), Theta(thLo={'GB': 64}, thHi={'GB': 42}), Theta(thLo={'GB': 64}, thHi={'GB': 43}), Theta(thLo={'GB': 64}, thHi={'GB': 44}), Theta(thLo={'GB': 64}, thHi={'GB': 45}), Theta(thLo={'GB': 64}, thHi={'GB': 46}), Theta(thLo={'GB': 64}, thHi={'GB': 47}), Theta(thLo={'GB': 64}, thHi={'GB': 48}), Theta(thLo={'GB': 64}, thHi={'GB': 49}), Theta(thLo={'GB': 64}, thHi={'GB': 50}), Theta(thLo={'GB': 64}, thHi={'GB': 51}), Theta(thLo={'GB': 64}, thHi={'GB': 52}), Theta(thLo={'GB': 64}, thHi={'GB': 53}), Theta(thLo={'GB': 64}, thHi={'GB': 54}), Theta(thLo={'GB': 64}, thHi={'GB': 55}), Theta(thLo={'GB': 64}, thHi={'GB': 56}), Theta(thLo={'GB': 64}, thHi={'GB': 57}), Theta(thLo={'GB': 64}, thHi={'GB': 58}), Theta(thLo={'GB': 64}, thHi={'GB': 59}), Theta(thLo={'GB': 64}, thHi={'GB': 60}), Theta(thLo={'GB': 64}, thHi={'GB': 61}), Theta(thLo={'GB': 64}, thHi={'GB': 62}), Theta(thLo={'GB': 64}, thHi={'GB': 63}), Theta(thLo={'GB': 64}, thHi={'GB': 64}), Theta(thLo={'GB': 64}, thHi={'GB': 65}), Theta(thLo={'GB': 64}, thHi={'GB': 66}), Theta(thLo={'GB': 64}, thHi={'GB': 67}), Theta(thLo={'GB': 64}, thHi={'GB': 68}), Theta(thLo={'GB': 64}, thHi={'GB': 69}), Theta(thLo={'GB': 64}, thHi={'GB': 70}), Theta(thLo={'GB': 64}, thHi={'GB': 71}), Theta(thLo={'GB': 64}, thHi={'GB': 72}), Theta(thLo={'GB': 64}, thHi={'GB': 73}), Theta(thLo={'GB': 64}, thHi={'GB': 74}), Theta(thLo={'GB': 64}, thHi={'GB': 75}), Theta(thLo={'GB': 64}, thHi={'GB': 76}), Theta(thLo={'GB': 64}, thHi={'GB': 77}), Theta(thLo={'GB': 64}, thHi={'GB': 78}), Theta(thLo={'GB': 64}, thHi={'GB': 79}), Theta(thLo={'GB': 64}, thHi={'GB': 80}), Theta(thLo={'GB': 64}, thHi={'GB': 81}), Theta(thLo={'GB': 64}, thHi={'GB': 82}), Theta(thLo={'GB': 64}, thHi={'GB': 83}), Theta(thLo={'GB': 64}, thHi={'GB': 84}), Theta(thLo={'GB': 64}, thHi={'GB': 85}), Theta(thLo={'GB': 64}, thHi={'GB': 86}), Theta(thLo={'GB': 64}, thHi={'GB': 87}), Theta(thLo={'GB': 64}, thHi={'GB': 88}), Theta(thLo={'GB': 64}, thHi={'GB': 89}), Theta(thLo={'GB': 64}, thHi={'GB': 90}), Theta(thLo={'GB': 64}, thHi={'GB': 91}), Theta(thLo={'GB': 64}, thHi={'GB': 92}), Theta(thLo={'GB': 64}, thHi={'GB': 93}), Theta(thLo={'GB': 64}, thHi={'GB': 94}), Theta(thLo={'GB': 64}, thHi={'GB': 95}), Theta(thLo={'GB': 64}, thHi={'GB': 96}), Theta(thLo={'GB': 64}, thHi={'GB': 97}), Theta(thLo={'GB': 64}, thHi={'GB': 98}), Theta(thLo={'GB': 64}, thHi={'GB': 99}), Theta(thLo={'GB': 65}, thHi={'GB': 10}), Theta(thLo={'GB': 65}, thHi={'GB': 11}), Theta(thLo={'GB': 65}, thHi={'GB': 12}), Theta(thLo={'GB': 65}, thHi={'GB': 13}), Theta(thLo={'GB': 65}, thHi={'GB': 14}), Theta(thLo={'GB': 65}, thHi={'GB': 15}), Theta(thLo={'GB': 65}, thHi={'GB': 16}), Theta(thLo={'GB': 65}, thHi={'GB': 17}), Theta(thLo={'GB': 65}, thHi={'GB': 18}), Theta(thLo={'GB': 65}, thHi={'GB': 19}), Theta(thLo={'GB': 65}, thHi={'GB': 20}), Theta(thLo={'GB': 65}, thHi={'GB': 21}), Theta(thLo={'GB': 65}, thHi={'GB': 22}), Theta(thLo={'GB': 65}, thHi={'GB': 23}), Theta(thLo={'GB': 65}, thHi={'GB': 24}), Theta(thLo={'GB': 65}, thHi={'GB': 25}), Theta(thLo={'GB': 65}, thHi={'GB': 26}), Theta(thLo={'GB': 65}, thHi={'GB': 27}), Theta(thLo={'GB': 65}, thHi={'GB': 28}), Theta(thLo={'GB': 65}, thHi={'GB': 29}), Theta(thLo={'GB': 65}, thHi={'GB': 30}), Theta(thLo={'GB': 65}, thHi={'GB': 31}), Theta(thLo={'GB': 65}, thHi={'GB': 32}), Theta(thLo={'GB': 65}, thHi={'GB': 33}), Theta(thLo={'GB': 65}, thHi={'GB': 34}), Theta(thLo={'GB': 65}, thHi={'GB': 35}), Theta(thLo={'GB': 65}, thHi={'GB': 36}), Theta(thLo={'GB': 65}, thHi={'GB': 37}), Theta(thLo={'GB': 65}, thHi={'GB': 38}), Theta(thLo={'GB': 65}, thHi={'GB': 39}), Theta(thLo={'GB': 65}, thHi={'GB': 40}), Theta(thLo={'GB': 65}, thHi={'GB': 41}), Theta(thLo={'GB': 65}, thHi={'GB': 42}), Theta(thLo={'GB': 65}, thHi={'GB': 43}), Theta(thLo={'GB': 65}, thHi={'GB': 44}), Theta(thLo={'GB': 65}, thHi={'GB': 45}), Theta(thLo={'GB': 65}, thHi={'GB': 46}), Theta(thLo={'GB': 65}, thHi={'GB': 47}), Theta(thLo={'GB': 65}, thHi={'GB': 48}), Theta(thLo={'GB': 65}, thHi={'GB': 49}), Theta(thLo={'GB': 65}, thHi={'GB': 50}), Theta(thLo={'GB': 65}, thHi={'GB': 51}), Theta(thLo={'GB': 65}, thHi={'GB': 52}), Theta(thLo={'GB': 65}, thHi={'GB': 53}), Theta(thLo={'GB': 65}, thHi={'GB': 54}), Theta(thLo={'GB': 65}, thHi={'GB': 55}), Theta(thLo={'GB': 65}, thHi={'GB': 56}), Theta(thLo={'GB': 65}, thHi={'GB': 57}), Theta(thLo={'GB': 65}, thHi={'GB': 58}), Theta(thLo={'GB': 65}, thHi={'GB': 59}), Theta(thLo={'GB': 65}, thHi={'GB': 60}), Theta(thLo={'GB': 65}, thHi={'GB': 61}), Theta(thLo={'GB': 65}, thHi={'GB': 62}), Theta(thLo={'GB': 65}, thHi={'GB': 63}), Theta(thLo={'GB': 65}, thHi={'GB': 64}), Theta(thLo={'GB': 65}, thHi={'GB': 65}), Theta(thLo={'GB': 65}, thHi={'GB': 66}), Theta(thLo={'GB': 65}, thHi={'GB': 67}), Theta(thLo={'GB': 65}, thHi={'GB': 68}), Theta(thLo={'GB': 65}, thHi={'GB': 69}), Theta(thLo={'GB': 65}, thHi={'GB': 70}), Theta(thLo={'GB': 65}, thHi={'GB': 71}), Theta(thLo={'GB': 65}, thHi={'GB': 72}), Theta(thLo={'GB': 65}, thHi={'GB': 73}), Theta(thLo={'GB': 65}, thHi={'GB': 74}), Theta(thLo={'GB': 65}, thHi={'GB': 75}), Theta(thLo={'GB': 65}, thHi={'GB': 76}), Theta(thLo={'GB': 65}, thHi={'GB': 77}), Theta(thLo={'GB': 65}, thHi={'GB': 78}), Theta(thLo={'GB': 65}, thHi={'GB': 79}), Theta(thLo={'GB': 65}, thHi={'GB': 80}), Theta(thLo={'GB': 65}, thHi={'GB': 81}), Theta(thLo={'GB': 65}, thHi={'GB': 82}), Theta(thLo={'GB': 65}, thHi={'GB': 83}), Theta(thLo={'GB': 65}, thHi={'GB': 84}), Theta(thLo={'GB': 65}, thHi={'GB': 85}), Theta(thLo={'GB': 65}, thHi={'GB': 86}), Theta(thLo={'GB': 65}, thHi={'GB': 87}), Theta(thLo={'GB': 65}, thHi={'GB': 88}), Theta(thLo={'GB': 65}, thHi={'GB': 89}), Theta(thLo={'GB': 65}, thHi={'GB': 90}), Theta(thLo={'GB': 65}, thHi={'GB': 91}), Theta(thLo={'GB': 65}, thHi={'GB': 92}), Theta(thLo={'GB': 65}, thHi={'GB': 93}), Theta(thLo={'GB': 65}, thHi={'GB': 94}), Theta(thLo={'GB': 65}, thHi={'GB': 95}), Theta(thLo={'GB': 65}, thHi={'GB': 96}), Theta(thLo={'GB': 65}, thHi={'GB': 97}), Theta(thLo={'GB': 65}, thHi={'GB': 98}), Theta(thLo={'GB': 65}, thHi={'GB': 99}), Theta(thLo={'GB': 66}, thHi={'GB': 10}), Theta(thLo={'GB': 66}, thHi={'GB': 11}), Theta(thLo={'GB': 66}, thHi={'GB': 12}), Theta(thLo={'GB': 66}, thHi={'GB': 13}), Theta(thLo={'GB': 66}, thHi={'GB': 14}), Theta(thLo={'GB': 66}, thHi={'GB': 15}), Theta(thLo={'GB': 66}, thHi={'GB': 16}), Theta(thLo={'GB': 66}, thHi={'GB': 17}), Theta(thLo={'GB': 66}, thHi={'GB': 18}), Theta(thLo={'GB': 66}, thHi={'GB': 19}), Theta(thLo={'GB': 66}, thHi={'GB': 20}), Theta(thLo={'GB': 66}, thHi={'GB': 21}), Theta(thLo={'GB': 66}, thHi={'GB': 22}), Theta(thLo={'GB': 66}, thHi={'GB': 23}), Theta(thLo={'GB': 66}, thHi={'GB': 24}), Theta(thLo={'GB': 66}, thHi={'GB': 25}), Theta(thLo={'GB': 66}, thHi={'GB': 26}), Theta(thLo={'GB': 66}, thHi={'GB': 27}), Theta(thLo={'GB': 66}, thHi={'GB': 28}), Theta(thLo={'GB': 66}, thHi={'GB': 29}), Theta(thLo={'GB': 66}, thHi={'GB': 30}), Theta(thLo={'GB': 66}, thHi={'GB': 31}), Theta(thLo={'GB': 66}, thHi={'GB': 32}), Theta(thLo={'GB': 66}, thHi={'GB': 33}), Theta(thLo={'GB': 66}, thHi={'GB': 34}), Theta(thLo={'GB': 66}, thHi={'GB': 35}), Theta(thLo={'GB': 66}, thHi={'GB': 36}), Theta(thLo={'GB': 66}, thHi={'GB': 37}), Theta(thLo={'GB': 66}, thHi={'GB': 38}), Theta(thLo={'GB': 66}, thHi={'GB': 39}), Theta(thLo={'GB': 66}, thHi={'GB': 40}), Theta(thLo={'GB': 66}, thHi={'GB': 41}), Theta(thLo={'GB': 66}, thHi={'GB': 42}), Theta(thLo={'GB': 66}, thHi={'GB': 43}), Theta(thLo={'GB': 66}, thHi={'GB': 44}), Theta(thLo={'GB': 66}, thHi={'GB': 45}), Theta(thLo={'GB': 66}, thHi={'GB': 46}), Theta(thLo={'GB': 66}, thHi={'GB': 47}), Theta(thLo={'GB': 66}, thHi={'GB': 48}), Theta(thLo={'GB': 66}, thHi={'GB': 49}), Theta(thLo={'GB': 66}, thHi={'GB': 50}), Theta(thLo={'GB': 66}, thHi={'GB': 51}), Theta(thLo={'GB': 66}, thHi={'GB': 52}), Theta(thLo={'GB': 66}, thHi={'GB': 53}), Theta(thLo={'GB': 66}, thHi={'GB': 54}), Theta(thLo={'GB': 66}, thHi={'GB': 55}), Theta(thLo={'GB': 66}, thHi={'GB': 56}), Theta(thLo={'GB': 66}, thHi={'GB': 57}), Theta(thLo={'GB': 66}, thHi={'GB': 58}), Theta(thLo={'GB': 66}, thHi={'GB': 59}), Theta(thLo={'GB': 66}, thHi={'GB': 60}), Theta(thLo={'GB': 66}, thHi={'GB': 61}), Theta(thLo={'GB': 66}, thHi={'GB': 62}), Theta(thLo={'GB': 66}, thHi={'GB': 63}), Theta(thLo={'GB': 66}, thHi={'GB': 64}), Theta(thLo={'GB': 66}, thHi={'GB': 65}), Theta(thLo={'GB': 66}, thHi={'GB': 66}), Theta(thLo={'GB': 66}, thHi={'GB': 67}), Theta(thLo={'GB': 66}, thHi={'GB': 68}), Theta(thLo={'GB': 66}, thHi={'GB': 69}), Theta(thLo={'GB': 66}, thHi={'GB': 70}), Theta(thLo={'GB': 66}, thHi={'GB': 71}), Theta(thLo={'GB': 66}, thHi={'GB': 72}), Theta(thLo={'GB': 66}, thHi={'GB': 73}), Theta(thLo={'GB': 66}, thHi={'GB': 74}), Theta(thLo={'GB': 66}, thHi={'GB': 75}), Theta(thLo={'GB': 66}, thHi={'GB': 76}), Theta(thLo={'GB': 66}, thHi={'GB': 77}), Theta(thLo={'GB': 66}, thHi={'GB': 78}), Theta(thLo={'GB': 66}, thHi={'GB': 79}), Theta(thLo={'GB': 66}, thHi={'GB': 80}), Theta(thLo={'GB': 66}, thHi={'GB': 81}), Theta(thLo={'GB': 66}, thHi={'GB': 82}), Theta(thLo={'GB': 66}, thHi={'GB': 83}), Theta(thLo={'GB': 66}, thHi={'GB': 84}), Theta(thLo={'GB': 66}, thHi={'GB': 85}), Theta(thLo={'GB': 66}, thHi={'GB': 86}), Theta(thLo={'GB': 66}, thHi={'GB': 87}), Theta(thLo={'GB': 66}, thHi={'GB': 88}), Theta(thLo={'GB': 66}, thHi={'GB': 89}), Theta(thLo={'GB': 66}, thHi={'GB': 90}), Theta(thLo={'GB': 66}, thHi={'GB': 91}), Theta(thLo={'GB': 66}, thHi={'GB': 92}), Theta(thLo={'GB': 66}, thHi={'GB': 93}), Theta(thLo={'GB': 66}, thHi={'GB': 94}), Theta(thLo={'GB': 66}, thHi={'GB': 95}), Theta(thLo={'GB': 66}, thHi={'GB': 96}), Theta(thLo={'GB': 66}, thHi={'GB': 97}), Theta(thLo={'GB': 66}, thHi={'GB': 98}), Theta(thLo={'GB': 66}, thHi={'GB': 99}), Theta(thLo={'GB': 67}, thHi={'GB': 10}), Theta(thLo={'GB': 67}, thHi={'GB': 11}), Theta(thLo={'GB': 67}, thHi={'GB': 12}), Theta(thLo={'GB': 67}, thHi={'GB': 13}), Theta(thLo={'GB': 67}, thHi={'GB': 14}), Theta(thLo={'GB': 67}, thHi={'GB': 15}), Theta(thLo={'GB': 67}, thHi={'GB': 16}), Theta(thLo={'GB': 67}, thHi={'GB': 17}), Theta(thLo={'GB': 67}, thHi={'GB': 18}), Theta(thLo={'GB': 67}, thHi={'GB': 19}), Theta(thLo={'GB': 67}, thHi={'GB': 20}), Theta(thLo={'GB': 67}, thHi={'GB': 21}), Theta(thLo={'GB': 67}, thHi={'GB': 22}), Theta(thLo={'GB': 67}, thHi={'GB': 23}), Theta(thLo={'GB': 67}, thHi={'GB': 24}), Theta(thLo={'GB': 67}, thHi={'GB': 25}), Theta(thLo={'GB': 67}, thHi={'GB': 26}), Theta(thLo={'GB': 67}, thHi={'GB': 27}), Theta(thLo={'GB': 67}, thHi={'GB': 28}), Theta(thLo={'GB': 67}, thHi={'GB': 29}), Theta(thLo={'GB': 67}, thHi={'GB': 30}), Theta(thLo={'GB': 67}, thHi={'GB': 31}), Theta(thLo={'GB': 67}, thHi={'GB': 32}), Theta(thLo={'GB': 67}, thHi={'GB': 33}), Theta(thLo={'GB': 67}, thHi={'GB': 34}), Theta(thLo={'GB': 67}, thHi={'GB': 35}), Theta(thLo={'GB': 67}, thHi={'GB': 36}), Theta(thLo={'GB': 67}, thHi={'GB': 37}), Theta(thLo={'GB': 67}, thHi={'GB': 38}), Theta(thLo={'GB': 67}, thHi={'GB': 39}), Theta(thLo={'GB': 67}, thHi={'GB': 40}), Theta(thLo={'GB': 67}, thHi={'GB': 41}), Theta(thLo={'GB': 67}, thHi={'GB': 42}), Theta(thLo={'GB': 67}, thHi={'GB': 43}), Theta(thLo={'GB': 67}, thHi={'GB': 44}), Theta(thLo={'GB': 67}, thHi={'GB': 45}), Theta(thLo={'GB': 67}, thHi={'GB': 46}), Theta(thLo={'GB': 67}, thHi={'GB': 47}), Theta(thLo={'GB': 67}, thHi={'GB': 48}), Theta(thLo={'GB': 67}, thHi={'GB': 49}), Theta(thLo={'GB': 67}, thHi={'GB': 50}), Theta(thLo={'GB': 67}, thHi={'GB': 51}), Theta(thLo={'GB': 67}, thHi={'GB': 52}), Theta(thLo={'GB': 67}, thHi={'GB': 53}), Theta(thLo={'GB': 67}, thHi={'GB': 54}), Theta(thLo={'GB': 67}, thHi={'GB': 55}), Theta(thLo={'GB': 67}, thHi={'GB': 56}), Theta(thLo={'GB': 67}, thHi={'GB': 57}), Theta(thLo={'GB': 67}, thHi={'GB': 58}), Theta(thLo={'GB': 67}, thHi={'GB': 59}), Theta(thLo={'GB': 67}, thHi={'GB': 60}), Theta(thLo={'GB': 67}, thHi={'GB': 61}), Theta(thLo={'GB': 67}, thHi={'GB': 62}), Theta(thLo={'GB': 67}, thHi={'GB': 63}), Theta(thLo={'GB': 67}, thHi={'GB': 64}), Theta(thLo={'GB': 67}, thHi={'GB': 65}), Theta(thLo={'GB': 67}, thHi={'GB': 66}), Theta(thLo={'GB': 67}, thHi={'GB': 67}), Theta(thLo={'GB': 67}, thHi={'GB': 68}), Theta(thLo={'GB': 67}, thHi={'GB': 69}), Theta(thLo={'GB': 67}, thHi={'GB': 70}), Theta(thLo={'GB': 67}, thHi={'GB': 71}), Theta(thLo={'GB': 67}, thHi={'GB': 72}), Theta(thLo={'GB': 67}, thHi={'GB': 73}), Theta(thLo={'GB': 67}, thHi={'GB': 74}), Theta(thLo={'GB': 67}, thHi={'GB': 75}), Theta(thLo={'GB': 67}, thHi={'GB': 76}), Theta(thLo={'GB': 67}, thHi={'GB': 77}), Theta(thLo={'GB': 67}, thHi={'GB': 78}), Theta(thLo={'GB': 67}, thHi={'GB': 79}), Theta(thLo={'GB': 67}, thHi={'GB': 80}), Theta(thLo={'GB': 67}, thHi={'GB': 81}), Theta(thLo={'GB': 67}, thHi={'GB': 82}), Theta(thLo={'GB': 67}, thHi={'GB': 83}), Theta(thLo={'GB': 67}, thHi={'GB': 84}), Theta(thLo={'GB': 67}, thHi={'GB': 85}), Theta(thLo={'GB': 67}, thHi={'GB': 86}), Theta(thLo={'GB': 67}, thHi={'GB': 87}), Theta(thLo={'GB': 67}, thHi={'GB': 88}), Theta(thLo={'GB': 67}, thHi={'GB': 89}), Theta(thLo={'GB': 67}, thHi={'GB': 90}), Theta(thLo={'GB': 67}, thHi={'GB': 91}), Theta(thLo={'GB': 67}, thHi={'GB': 92}), Theta(thLo={'GB': 67}, thHi={'GB': 93}), Theta(thLo={'GB': 67}, thHi={'GB': 94}), Theta(thLo={'GB': 67}, thHi={'GB': 95}), Theta(thLo={'GB': 67}, thHi={'GB': 96}), Theta(thLo={'GB': 67}, thHi={'GB': 97}), Theta(thLo={'GB': 67}, thHi={'GB': 98}), Theta(thLo={'GB': 67}, thHi={'GB': 99}), Theta(thLo={'GB': 68}, thHi={'GB': 10}), Theta(thLo={'GB': 68}, thHi={'GB': 11}), Theta(thLo={'GB': 68}, thHi={'GB': 12}), Theta(thLo={'GB': 68}, thHi={'GB': 13}), Theta(thLo={'GB': 68}, thHi={'GB': 14}), Theta(thLo={'GB': 68}, thHi={'GB': 15}), Theta(thLo={'GB': 68}, thHi={'GB': 16}), Theta(thLo={'GB': 68}, thHi={'GB': 17}), Theta(thLo={'GB': 68}, thHi={'GB': 18}), Theta(thLo={'GB': 68}, thHi={'GB': 19}), Theta(thLo={'GB': 68}, thHi={'GB': 20}), Theta(thLo={'GB': 68}, thHi={'GB': 21}), Theta(thLo={'GB': 68}, thHi={'GB': 22}), Theta(thLo={'GB': 68}, thHi={'GB': 23}), Theta(thLo={'GB': 68}, thHi={'GB': 24}), Theta(thLo={'GB': 68}, thHi={'GB': 25}), Theta(thLo={'GB': 68}, thHi={'GB': 26}), Theta(thLo={'GB': 68}, thHi={'GB': 27}), Theta(thLo={'GB': 68}, thHi={'GB': 28}), Theta(thLo={'GB': 68}, thHi={'GB': 29}), Theta(thLo={'GB': 68}, thHi={'GB': 30}), Theta(thLo={'GB': 68}, thHi={'GB': 31}), Theta(thLo={'GB': 68}, thHi={'GB': 32}), Theta(thLo={'GB': 68}, thHi={'GB': 33}), Theta(thLo={'GB': 68}, thHi={'GB': 34}), Theta(thLo={'GB': 68}, thHi={'GB': 35}), Theta(thLo={'GB': 68}, thHi={'GB': 36}), Theta(thLo={'GB': 68}, thHi={'GB': 37}), Theta(thLo={'GB': 68}, thHi={'GB': 38}), Theta(thLo={'GB': 68}, thHi={'GB': 39}), Theta(thLo={'GB': 68}, thHi={'GB': 40}), Theta(thLo={'GB': 68}, thHi={'GB': 41}), Theta(thLo={'GB': 68}, thHi={'GB': 42}), Theta(thLo={'GB': 68}, thHi={'GB': 43}), Theta(thLo={'GB': 68}, thHi={'GB': 44}), Theta(thLo={'GB': 68}, thHi={'GB': 45}), Theta(thLo={'GB': 68}, thHi={'GB': 46}), Theta(thLo={'GB': 68}, thHi={'GB': 47}), Theta(thLo={'GB': 68}, thHi={'GB': 48}), Theta(thLo={'GB': 68}, thHi={'GB': 49}), Theta(thLo={'GB': 68}, thHi={'GB': 50}), Theta(thLo={'GB': 68}, thHi={'GB': 51}), Theta(thLo={'GB': 68}, thHi={'GB': 52}), Theta(thLo={'GB': 68}, thHi={'GB': 53}), Theta(thLo={'GB': 68}, thHi={'GB': 54}), Theta(thLo={'GB': 68}, thHi={'GB': 55}), Theta(thLo={'GB': 68}, thHi={'GB': 56}), Theta(thLo={'GB': 68}, thHi={'GB': 57}), Theta(thLo={'GB': 68}, thHi={'GB': 58}), Theta(thLo={'GB': 68}, thHi={'GB': 59}), Theta(thLo={'GB': 68}, thHi={'GB': 60}), Theta(thLo={'GB': 68}, thHi={'GB': 61}), Theta(thLo={'GB': 68}, thHi={'GB': 62}), Theta(thLo={'GB': 68}, thHi={'GB': 63}), Theta(thLo={'GB': 68}, thHi={'GB': 64}), Theta(thLo={'GB': 68}, thHi={'GB': 65}), Theta(thLo={'GB': 68}, thHi={'GB': 66}), Theta(thLo={'GB': 68}, thHi={'GB': 67}), Theta(thLo={'GB': 68}, thHi={'GB': 68}), Theta(thLo={'GB': 68}, thHi={'GB': 69}), Theta(thLo={'GB': 68}, thHi={'GB': 70}), Theta(thLo={'GB': 68}, thHi={'GB': 71}), Theta(thLo={'GB': 68}, thHi={'GB': 72}), Theta(thLo={'GB': 68}, thHi={'GB': 73}), Theta(thLo={'GB': 68}, thHi={'GB': 74}), Theta(thLo={'GB': 68}, thHi={'GB': 75}), Theta(thLo={'GB': 68}, thHi={'GB': 76}), Theta(thLo={'GB': 68}, thHi={'GB': 77}), Theta(thLo={'GB': 68}, thHi={'GB': 78}), Theta(thLo={'GB': 68}, thHi={'GB': 79}), Theta(thLo={'GB': 68}, thHi={'GB': 80}), Theta(thLo={'GB': 68}, thHi={'GB': 81}), Theta(thLo={'GB': 68}, thHi={'GB': 82}), Theta(thLo={'GB': 68}, thHi={'GB': 83}), Theta(thLo={'GB': 68}, thHi={'GB': 84}), Theta(thLo={'GB': 68}, thHi={'GB': 85}), Theta(thLo={'GB': 68}, thHi={'GB': 86}), Theta(thLo={'GB': 68}, thHi={'GB': 87}), Theta(thLo={'GB': 68}, thHi={'GB': 88}), Theta(thLo={'GB': 68}, thHi={'GB': 89}), Theta(thLo={'GB': 68}, thHi={'GB': 90}), Theta(thLo={'GB': 68}, thHi={'GB': 91}), Theta(thLo={'GB': 68}, thHi={'GB': 92}), Theta(thLo={'GB': 68}, thHi={'GB': 93}), Theta(thLo={'GB': 68}, thHi={'GB': 94}), Theta(thLo={'GB': 68}, thHi={'GB': 95}), Theta(thLo={'GB': 68}, thHi={'GB': 96}), Theta(thLo={'GB': 68}, thHi={'GB': 97}), Theta(thLo={'GB': 68}, thHi={'GB': 98}), Theta(thLo={'GB': 68}, thHi={'GB': 99}), Theta(thLo={'GB': 69}, thHi={'GB': 10}), Theta(thLo={'GB': 69}, thHi={'GB': 11}), Theta(thLo={'GB': 69}, thHi={'GB': 12}), Theta(thLo={'GB': 69}, thHi={'GB': 13}), Theta(thLo={'GB': 69}, thHi={'GB': 14}), Theta(thLo={'GB': 69}, thHi={'GB': 15}), Theta(thLo={'GB': 69}, thHi={'GB': 16}), Theta(thLo={'GB': 69}, thHi={'GB': 17}), Theta(thLo={'GB': 69}, thHi={'GB': 18}), Theta(thLo={'GB': 69}, thHi={'GB': 19}), Theta(thLo={'GB': 69}, thHi={'GB': 20}), Theta(thLo={'GB': 69}, thHi={'GB': 21}), Theta(thLo={'GB': 69}, thHi={'GB': 22}), Theta(thLo={'GB': 69}, thHi={'GB': 23}), Theta(thLo={'GB': 69}, thHi={'GB': 24}), Theta(thLo={'GB': 69}, thHi={'GB': 25}), Theta(thLo={'GB': 69}, thHi={'GB': 26}), Theta(thLo={'GB': 69}, thHi={'GB': 27}), Theta(thLo={'GB': 69}, thHi={'GB': 28}), Theta(thLo={'GB': 69}, thHi={'GB': 29}), Theta(thLo={'GB': 69}, thHi={'GB': 30}), Theta(thLo={'GB': 69}, thHi={'GB': 31}), Theta(thLo={'GB': 69}, thHi={'GB': 32}), Theta(thLo={'GB': 69}, thHi={'GB': 33}), Theta(thLo={'GB': 69}, thHi={'GB': 34}), Theta(thLo={'GB': 69}, thHi={'GB': 35}), Theta(thLo={'GB': 69}, thHi={'GB': 36}), Theta(thLo={'GB': 69}, thHi={'GB': 37}), Theta(thLo={'GB': 69}, thHi={'GB': 38}), Theta(thLo={'GB': 69}, thHi={'GB': 39}), Theta(thLo={'GB': 69}, thHi={'GB': 40}), Theta(thLo={'GB': 69}, thHi={'GB': 41}), Theta(thLo={'GB': 69}, thHi={'GB': 42}), Theta(thLo={'GB': 69}, thHi={'GB': 43}), Theta(thLo={'GB': 69}, thHi={'GB': 44}), Theta(thLo={'GB': 69}, thHi={'GB': 45}), Theta(thLo={'GB': 69}, thHi={'GB': 46}), Theta(thLo={'GB': 69}, thHi={'GB': 47}), Theta(thLo={'GB': 69}, thHi={'GB': 48}), Theta(thLo={'GB': 69}, thHi={'GB': 49}), Theta(thLo={'GB': 69}, thHi={'GB': 50}), Theta(thLo={'GB': 69}, thHi={'GB': 51}), Theta(thLo={'GB': 69}, thHi={'GB': 52}), Theta(thLo={'GB': 69}, thHi={'GB': 53}), Theta(thLo={'GB': 69}, thHi={'GB': 54}), Theta(thLo={'GB': 69}, thHi={'GB': 55}), Theta(thLo={'GB': 69}, thHi={'GB': 56}), Theta(thLo={'GB': 69}, thHi={'GB': 57}), Theta(thLo={'GB': 69}, thHi={'GB': 58}), Theta(thLo={'GB': 69}, thHi={'GB': 59}), Theta(thLo={'GB': 69}, thHi={'GB': 60}), Theta(thLo={'GB': 69}, thHi={'GB': 61}), Theta(thLo={'GB': 69}, thHi={'GB': 62}), Theta(thLo={'GB': 69}, thHi={'GB': 63}), Theta(thLo={'GB': 69}, thHi={'GB': 64}), Theta(thLo={'GB': 69}, thHi={'GB': 65}), Theta(thLo={'GB': 69}, thHi={'GB': 66}), Theta(thLo={'GB': 69}, thHi={'GB': 67}), Theta(thLo={'GB': 69}, thHi={'GB': 68}), Theta(thLo={'GB': 69}, thHi={'GB': 69}), Theta(thLo={'GB': 69}, thHi={'GB': 70}), Theta(thLo={'GB': 69}, thHi={'GB': 71}), Theta(thLo={'GB': 69}, thHi={'GB': 72}), Theta(thLo={'GB': 69}, thHi={'GB': 73}), Theta(thLo={'GB': 69}, thHi={'GB': 74}), Theta(thLo={'GB': 69}, thHi={'GB': 75}), Theta(thLo={'GB': 69}, thHi={'GB': 76}), Theta(thLo={'GB': 69}, thHi={'GB': 77}), Theta(thLo={'GB': 69}, thHi={'GB': 78}), Theta(thLo={'GB': 69}, thHi={'GB': 79}), Theta(thLo={'GB': 69}, thHi={'GB': 80}), Theta(thLo={'GB': 69}, thHi={'GB': 81}), Theta(thLo={'GB': 69}, thHi={'GB': 82}), Theta(thLo={'GB': 69}, thHi={'GB': 83}), Theta(thLo={'GB': 69}, thHi={'GB': 84}), Theta(thLo={'GB': 69}, thHi={'GB': 85}), Theta(thLo={'GB': 69}, thHi={'GB': 86}), Theta(thLo={'GB': 69}, thHi={'GB': 87}), Theta(thLo={'GB': 69}, thHi={'GB': 88}), Theta(thLo={'GB': 69}, thHi={'GB': 89}), Theta(thLo={'GB': 69}, thHi={'GB': 90}), Theta(thLo={'GB': 69}, thHi={'GB': 91}), Theta(thLo={'GB': 69}, thHi={'GB': 92}), Theta(thLo={'GB': 69}, thHi={'GB': 93}), Theta(thLo={'GB': 69}, thHi={'GB': 94}), Theta(thLo={'GB': 69}, thHi={'GB': 95}), Theta(thLo={'GB': 69}, thHi={'GB': 96}), Theta(thLo={'GB': 69}, thHi={'GB': 97}), Theta(thLo={'GB': 69}, thHi={'GB': 98}), Theta(thLo={'GB': 69}, thHi={'GB': 99}), Theta(thLo={'GB': 70}, thHi={'GB': 10}), Theta(thLo={'GB': 70}, thHi={'GB': 11}), Theta(thLo={'GB': 70}, thHi={'GB': 12}), Theta(thLo={'GB': 70}, thHi={'GB': 13}), Theta(thLo={'GB': 70}, thHi={'GB': 14}), Theta(thLo={'GB': 70}, thHi={'GB': 15}), Theta(thLo={'GB': 70}, thHi={'GB': 16}), Theta(thLo={'GB': 70}, thHi={'GB': 17}), Theta(thLo={'GB': 70}, thHi={'GB': 18}), Theta(thLo={'GB': 70}, thHi={'GB': 19}), Theta(thLo={'GB': 70}, thHi={'GB': 20}), Theta(thLo={'GB': 70}, thHi={'GB': 21}), Theta(thLo={'GB': 70}, thHi={'GB': 22}), Theta(thLo={'GB': 70}, thHi={'GB': 23}), Theta(thLo={'GB': 70}, thHi={'GB': 24}), Theta(thLo={'GB': 70}, thHi={'GB': 25}), Theta(thLo={'GB': 70}, thHi={'GB': 26}), Theta(thLo={'GB': 70}, thHi={'GB': 27}), Theta(thLo={'GB': 70}, thHi={'GB': 28}), Theta(thLo={'GB': 70}, thHi={'GB': 29}), Theta(thLo={'GB': 70}, thHi={'GB': 30}), Theta(thLo={'GB': 70}, thHi={'GB': 31}), Theta(thLo={'GB': 70}, thHi={'GB': 32}), Theta(thLo={'GB': 70}, thHi={'GB': 33}), Theta(thLo={'GB': 70}, thHi={'GB': 34}), Theta(thLo={'GB': 70}, thHi={'GB': 35}), Theta(thLo={'GB': 70}, thHi={'GB': 36}), Theta(thLo={'GB': 70}, thHi={'GB': 37}), Theta(thLo={'GB': 70}, thHi={'GB': 38}), Theta(thLo={'GB': 70}, thHi={'GB': 39}), Theta(thLo={'GB': 70}, thHi={'GB': 40}), Theta(thLo={'GB': 70}, thHi={'GB': 41}), Theta(thLo={'GB': 70}, thHi={'GB': 42}), Theta(thLo={'GB': 70}, thHi={'GB': 43}), Theta(thLo={'GB': 70}, thHi={'GB': 44}), Theta(thLo={'GB': 70}, thHi={'GB': 45}), Theta(thLo={'GB': 70}, thHi={'GB': 46}), Theta(thLo={'GB': 70}, thHi={'GB': 47}), Theta(thLo={'GB': 70}, thHi={'GB': 48}), Theta(thLo={'GB': 70}, thHi={'GB': 49}), Theta(thLo={'GB': 70}, thHi={'GB': 50}), Theta(thLo={'GB': 70}, thHi={'GB': 51}), Theta(thLo={'GB': 70}, thHi={'GB': 52}), Theta(thLo={'GB': 70}, thHi={'GB': 53}), Theta(thLo={'GB': 70}, thHi={'GB': 54}), Theta(thLo={'GB': 70}, thHi={'GB': 55}), Theta(thLo={'GB': 70}, thHi={'GB': 56}), Theta(thLo={'GB': 70}, thHi={'GB': 57}), Theta(thLo={'GB': 70}, thHi={'GB': 58}), Theta(thLo={'GB': 70}, thHi={'GB': 59}), Theta(thLo={'GB': 70}, thHi={'GB': 60}), Theta(thLo={'GB': 70}, thHi={'GB': 61}), Theta(thLo={'GB': 70}, thHi={'GB': 62}), Theta(thLo={'GB': 70}, thHi={'GB': 63}), Theta(thLo={'GB': 70}, thHi={'GB': 64}), Theta(thLo={'GB': 70}, thHi={'GB': 65}), Theta(thLo={'GB': 70}, thHi={'GB': 66}), Theta(thLo={'GB': 70}, thHi={'GB': 67}), Theta(thLo={'GB': 70}, thHi={'GB': 68}), Theta(thLo={'GB': 70}, thHi={'GB': 69}), Theta(thLo={'GB': 70}, thHi={'GB': 70}), Theta(thLo={'GB': 70}, thHi={'GB': 71}), Theta(thLo={'GB': 70}, thHi={'GB': 72}), Theta(thLo={'GB': 70}, thHi={'GB': 73}), Theta(thLo={'GB': 70}, thHi={'GB': 74}), Theta(thLo={'GB': 70}, thHi={'GB': 75}), Theta(thLo={'GB': 70}, thHi={'GB': 76}), Theta(thLo={'GB': 70}, thHi={'GB': 77}), Theta(thLo={'GB': 70}, thHi={'GB': 78}), Theta(thLo={'GB': 70}, thHi={'GB': 79}), Theta(thLo={'GB': 70}, thHi={'GB': 80}), Theta(thLo={'GB': 70}, thHi={'GB': 81}), Theta(thLo={'GB': 70}, thHi={'GB': 82}), Theta(thLo={'GB': 70}, thHi={'GB': 83}), Theta(thLo={'GB': 70}, thHi={'GB': 84}), Theta(thLo={'GB': 70}, thHi={'GB': 85}), Theta(thLo={'GB': 70}, thHi={'GB': 86}), Theta(thLo={'GB': 70}, thHi={'GB': 87}), Theta(thLo={'GB': 70}, thHi={'GB': 88}), Theta(thLo={'GB': 70}, thHi={'GB': 89}), Theta(thLo={'GB': 70}, thHi={'GB': 90}), Theta(thLo={'GB': 70}, thHi={'GB': 91}), Theta(thLo={'GB': 70}, thHi={'GB': 92}), Theta(thLo={'GB': 70}, thHi={'GB': 93}), Theta(thLo={'GB': 70}, thHi={'GB': 94}), Theta(thLo={'GB': 70}, thHi={'GB': 95}), Theta(thLo={'GB': 70}, thHi={'GB': 96}), Theta(thLo={'GB': 70}, thHi={'GB': 97}), Theta(thLo={'GB': 70}, thHi={'GB': 98}), Theta(thLo={'GB': 70}, thHi={'GB': 99}), Theta(thLo={'GB': 71}, thHi={'GB': 10}), Theta(thLo={'GB': 71}, thHi={'GB': 11}), Theta(thLo={'GB': 71}, thHi={'GB': 12}), Theta(thLo={'GB': 71}, thHi={'GB': 13}), Theta(thLo={'GB': 71}, thHi={'GB': 14}), Theta(thLo={'GB': 71}, thHi={'GB': 15}), Theta(thLo={'GB': 71}, thHi={'GB': 16}), Theta(thLo={'GB': 71}, thHi={'GB': 17}), Theta(thLo={'GB': 71}, thHi={'GB': 18}), Theta(thLo={'GB': 71}, thHi={'GB': 19}), Theta(thLo={'GB': 71}, thHi={'GB': 20}), Theta(thLo={'GB': 71}, thHi={'GB': 21}), Theta(thLo={'GB': 71}, thHi={'GB': 22}), Theta(thLo={'GB': 71}, thHi={'GB': 23}), Theta(thLo={'GB': 71}, thHi={'GB': 24}), Theta(thLo={'GB': 71}, thHi={'GB': 25}), Theta(thLo={'GB': 71}, thHi={'GB': 26}), Theta(thLo={'GB': 71}, thHi={'GB': 27}), Theta(thLo={'GB': 71}, thHi={'GB': 28}), Theta(thLo={'GB': 71}, thHi={'GB': 29}), Theta(thLo={'GB': 71}, thHi={'GB': 30}), Theta(thLo={'GB': 71}, thHi={'GB': 31}), Theta(thLo={'GB': 71}, thHi={'GB': 32}), Theta(thLo={'GB': 71}, thHi={'GB': 33}), Theta(thLo={'GB': 71}, thHi={'GB': 34}), Theta(thLo={'GB': 71}, thHi={'GB': 35}), Theta(thLo={'GB': 71}, thHi={'GB': 36}), Theta(thLo={'GB': 71}, thHi={'GB': 37}), Theta(thLo={'GB': 71}, thHi={'GB': 38}), Theta(thLo={'GB': 71}, thHi={'GB': 39}), Theta(thLo={'GB': 71}, thHi={'GB': 40}), Theta(thLo={'GB': 71}, thHi={'GB': 41}), Theta(thLo={'GB': 71}, thHi={'GB': 42}), Theta(thLo={'GB': 71}, thHi={'GB': 43}), Theta(thLo={'GB': 71}, thHi={'GB': 44}), Theta(thLo={'GB': 71}, thHi={'GB': 45}), Theta(thLo={'GB': 71}, thHi={'GB': 46}), Theta(thLo={'GB': 71}, thHi={'GB': 47}), Theta(thLo={'GB': 71}, thHi={'GB': 48}), Theta(thLo={'GB': 71}, thHi={'GB': 49}), Theta(thLo={'GB': 71}, thHi={'GB': 50}), Theta(thLo={'GB': 71}, thHi={'GB': 51}), Theta(thLo={'GB': 71}, thHi={'GB': 52}), Theta(thLo={'GB': 71}, thHi={'GB': 53}), Theta(thLo={'GB': 71}, thHi={'GB': 54}), Theta(thLo={'GB': 71}, thHi={'GB': 55}), Theta(thLo={'GB': 71}, thHi={'GB': 56}), Theta(thLo={'GB': 71}, thHi={'GB': 57}), Theta(thLo={'GB': 71}, thHi={'GB': 58}), Theta(thLo={'GB': 71}, thHi={'GB': 59}), Theta(thLo={'GB': 71}, thHi={'GB': 60}), Theta(thLo={'GB': 71}, thHi={'GB': 61}), Theta(thLo={'GB': 71}, thHi={'GB': 62}), Theta(thLo={'GB': 71}, thHi={'GB': 63}), Theta(thLo={'GB': 71}, thHi={'GB': 64}), Theta(thLo={'GB': 71}, thHi={'GB': 65}), Theta(thLo={'GB': 71}, thHi={'GB': 66}), Theta(thLo={'GB': 71}, thHi={'GB': 67}), Theta(thLo={'GB': 71}, thHi={'GB': 68}), Theta(thLo={'GB': 71}, thHi={'GB': 69}), Theta(thLo={'GB': 71}, thHi={'GB': 70}), Theta(thLo={'GB': 71}, thHi={'GB': 71}), Theta(thLo={'GB': 71}, thHi={'GB': 72}), Theta(thLo={'GB': 71}, thHi={'GB': 73}), Theta(thLo={'GB': 71}, thHi={'GB': 74}), Theta(thLo={'GB': 71}, thHi={'GB': 75}), Theta(thLo={'GB': 71}, thHi={'GB': 76}), Theta(thLo={'GB': 71}, thHi={'GB': 77}), Theta(thLo={'GB': 71}, thHi={'GB': 78}), Theta(thLo={'GB': 71}, thHi={'GB': 79}), Theta(thLo={'GB': 71}, thHi={'GB': 80}), Theta(thLo={'GB': 71}, thHi={'GB': 81}), Theta(thLo={'GB': 71}, thHi={'GB': 82}), Theta(thLo={'GB': 71}, thHi={'GB': 83}), Theta(thLo={'GB': 71}, thHi={'GB': 84}), Theta(thLo={'GB': 71}, thHi={'GB': 85}), Theta(thLo={'GB': 71}, thHi={'GB': 86}), Theta(thLo={'GB': 71}, thHi={'GB': 87}), Theta(thLo={'GB': 71}, thHi={'GB': 88}), Theta(thLo={'GB': 71}, thHi={'GB': 89}), Theta(thLo={'GB': 71}, thHi={'GB': 90}), Theta(thLo={'GB': 71}, thHi={'GB': 91}), Theta(thLo={'GB': 71}, thHi={'GB': 92}), Theta(thLo={'GB': 71}, thHi={'GB': 93}), Theta(thLo={'GB': 71}, thHi={'GB': 94}), Theta(thLo={'GB': 71}, thHi={'GB': 95}), Theta(thLo={'GB': 71}, thHi={'GB': 96}), Theta(thLo={'GB': 71}, thHi={'GB': 97}), Theta(thLo={'GB': 71}, thHi={'GB': 98}), Theta(thLo={'GB': 71}, thHi={'GB': 99}), Theta(thLo={'GB': 72}, thHi={'GB': 10}), Theta(thLo={'GB': 72}, thHi={'GB': 11}), Theta(thLo={'GB': 72}, thHi={'GB': 12}), Theta(thLo={'GB': 72}, thHi={'GB': 13}), Theta(thLo={'GB': 72}, thHi={'GB': 14}), Theta(thLo={'GB': 72}, thHi={'GB': 15}), Theta(thLo={'GB': 72}, thHi={'GB': 16}), Theta(thLo={'GB': 72}, thHi={'GB': 17}), Theta(thLo={'GB': 72}, thHi={'GB': 18}), Theta(thLo={'GB': 72}, thHi={'GB': 19}), Theta(thLo={'GB': 72}, thHi={'GB': 20}), Theta(thLo={'GB': 72}, thHi={'GB': 21}), Theta(thLo={'GB': 72}, thHi={'GB': 22}), Theta(thLo={'GB': 72}, thHi={'GB': 23}), Theta(thLo={'GB': 72}, thHi={'GB': 24}), Theta(thLo={'GB': 72}, thHi={'GB': 25}), Theta(thLo={'GB': 72}, thHi={'GB': 26}), Theta(thLo={'GB': 72}, thHi={'GB': 27}), Theta(thLo={'GB': 72}, thHi={'GB': 28}), Theta(thLo={'GB': 72}, thHi={'GB': 29}), Theta(thLo={'GB': 72}, thHi={'GB': 30}), Theta(thLo={'GB': 72}, thHi={'GB': 31}), Theta(thLo={'GB': 72}, thHi={'GB': 32}), Theta(thLo={'GB': 72}, thHi={'GB': 33}), Theta(thLo={'GB': 72}, thHi={'GB': 34}), Theta(thLo={'GB': 72}, thHi={'GB': 35}), Theta(thLo={'GB': 72}, thHi={'GB': 36}), Theta(thLo={'GB': 72}, thHi={'GB': 37}), Theta(thLo={'GB': 72}, thHi={'GB': 38}), Theta(thLo={'GB': 72}, thHi={'GB': 39}), Theta(thLo={'GB': 72}, thHi={'GB': 40}), Theta(thLo={'GB': 72}, thHi={'GB': 41}), Theta(thLo={'GB': 72}, thHi={'GB': 42}), Theta(thLo={'GB': 72}, thHi={'GB': 43}), Theta(thLo={'GB': 72}, thHi={'GB': 44}), Theta(thLo={'GB': 72}, thHi={'GB': 45}), Theta(thLo={'GB': 72}, thHi={'GB': 46}), Theta(thLo={'GB': 72}, thHi={'GB': 47}), Theta(thLo={'GB': 72}, thHi={'GB': 48}), Theta(thLo={'GB': 72}, thHi={'GB': 49}), Theta(thLo={'GB': 72}, thHi={'GB': 50}), Theta(thLo={'GB': 72}, thHi={'GB': 51}), Theta(thLo={'GB': 72}, thHi={'GB': 52}), Theta(thLo={'GB': 72}, thHi={'GB': 53}), Theta(thLo={'GB': 72}, thHi={'GB': 54}), Theta(thLo={'GB': 72}, thHi={'GB': 55}), Theta(thLo={'GB': 72}, thHi={'GB': 56}), Theta(thLo={'GB': 72}, thHi={'GB': 57}), Theta(thLo={'GB': 72}, thHi={'GB': 58}), Theta(thLo={'GB': 72}, thHi={'GB': 59}), Theta(thLo={'GB': 72}, thHi={'GB': 60}), Theta(thLo={'GB': 72}, thHi={'GB': 61}), Theta(thLo={'GB': 72}, thHi={'GB': 62}), Theta(thLo={'GB': 72}, thHi={'GB': 63}), Theta(thLo={'GB': 72}, thHi={'GB': 64}), Theta(thLo={'GB': 72}, thHi={'GB': 65}), Theta(thLo={'GB': 72}, thHi={'GB': 66}), Theta(thLo={'GB': 72}, thHi={'GB': 67}), Theta(thLo={'GB': 72}, thHi={'GB': 68}), Theta(thLo={'GB': 72}, thHi={'GB': 69}), Theta(thLo={'GB': 72}, thHi={'GB': 70}), Theta(thLo={'GB': 72}, thHi={'GB': 71}), Theta(thLo={'GB': 72}, thHi={'GB': 72}), Theta(thLo={'GB': 72}, thHi={'GB': 73}), Theta(thLo={'GB': 72}, thHi={'GB': 74}), Theta(thLo={'GB': 72}, thHi={'GB': 75}), Theta(thLo={'GB': 72}, thHi={'GB': 76}), Theta(thLo={'GB': 72}, thHi={'GB': 77}), Theta(thLo={'GB': 72}, thHi={'GB': 78}), Theta(thLo={'GB': 72}, thHi={'GB': 79}), Theta(thLo={'GB': 72}, thHi={'GB': 80}), Theta(thLo={'GB': 72}, thHi={'GB': 81}), Theta(thLo={'GB': 72}, thHi={'GB': 82}), Theta(thLo={'GB': 72}, thHi={'GB': 83}), Theta(thLo={'GB': 72}, thHi={'GB': 84}), Theta(thLo={'GB': 72}, thHi={'GB': 85}), Theta(thLo={'GB': 72}, thHi={'GB': 86}), Theta(thLo={'GB': 72}, thHi={'GB': 87}), Theta(thLo={'GB': 72}, thHi={'GB': 88}), Theta(thLo={'GB': 72}, thHi={'GB': 89}), Theta(thLo={'GB': 72}, thHi={'GB': 90}), Theta(thLo={'GB': 72}, thHi={'GB': 91}), Theta(thLo={'GB': 72}, thHi={'GB': 92}), Theta(thLo={'GB': 72}, thHi={'GB': 93}), Theta(thLo={'GB': 72}, thHi={'GB': 94}), Theta(thLo={'GB': 72}, thHi={'GB': 95}), Theta(thLo={'GB': 72}, thHi={'GB': 96}), Theta(thLo={'GB': 72}, thHi={'GB': 97}), Theta(thLo={'GB': 72}, thHi={'GB': 98}), Theta(thLo={'GB': 72}, thHi={'GB': 99}), Theta(thLo={'GB': 73}, thHi={'GB': 10}), Theta(thLo={'GB': 73}, thHi={'GB': 11}), Theta(thLo={'GB': 73}, thHi={'GB': 12}), Theta(thLo={'GB': 73}, thHi={'GB': 13}), Theta(thLo={'GB': 73}, thHi={'GB': 14}), Theta(thLo={'GB': 73}, thHi={'GB': 15}), Theta(thLo={'GB': 73}, thHi={'GB': 16}), Theta(thLo={'GB': 73}, thHi={'GB': 17}), Theta(thLo={'GB': 73}, thHi={'GB': 18}), Theta(thLo={'GB': 73}, thHi={'GB': 19}), Theta(thLo={'GB': 73}, thHi={'GB': 20}), Theta(thLo={'GB': 73}, thHi={'GB': 21}), Theta(thLo={'GB': 73}, thHi={'GB': 22}), Theta(thLo={'GB': 73}, thHi={'GB': 23}), Theta(thLo={'GB': 73}, thHi={'GB': 24}), Theta(thLo={'GB': 73}, thHi={'GB': 25}), Theta(thLo={'GB': 73}, thHi={'GB': 26}), Theta(thLo={'GB': 73}, thHi={'GB': 27}), Theta(thLo={'GB': 73}, thHi={'GB': 28}), Theta(thLo={'GB': 73}, thHi={'GB': 29}), Theta(thLo={'GB': 73}, thHi={'GB': 30}), Theta(thLo={'GB': 73}, thHi={'GB': 31}), Theta(thLo={'GB': 73}, thHi={'GB': 32}), Theta(thLo={'GB': 73}, thHi={'GB': 33}), Theta(thLo={'GB': 73}, thHi={'GB': 34}), Theta(thLo={'GB': 73}, thHi={'GB': 35}), Theta(thLo={'GB': 73}, thHi={'GB': 36}), Theta(thLo={'GB': 73}, thHi={'GB': 37}), Theta(thLo={'GB': 73}, thHi={'GB': 38}), Theta(thLo={'GB': 73}, thHi={'GB': 39}), Theta(thLo={'GB': 73}, thHi={'GB': 40}), Theta(thLo={'GB': 73}, thHi={'GB': 41}), Theta(thLo={'GB': 73}, thHi={'GB': 42}), Theta(thLo={'GB': 73}, thHi={'GB': 43}), Theta(thLo={'GB': 73}, thHi={'GB': 44}), Theta(thLo={'GB': 73}, thHi={'GB': 45}), Theta(thLo={'GB': 73}, thHi={'GB': 46}), Theta(thLo={'GB': 73}, thHi={'GB': 47}), Theta(thLo={'GB': 73}, thHi={'GB': 48}), Theta(thLo={'GB': 73}, thHi={'GB': 49}), Theta(thLo={'GB': 73}, thHi={'GB': 50}), Theta(thLo={'GB': 73}, thHi={'GB': 51}), Theta(thLo={'GB': 73}, thHi={'GB': 52}), Theta(thLo={'GB': 73}, thHi={'GB': 53}), Theta(thLo={'GB': 73}, thHi={'GB': 54}), Theta(thLo={'GB': 73}, thHi={'GB': 55}), Theta(thLo={'GB': 73}, thHi={'GB': 56}), Theta(thLo={'GB': 73}, thHi={'GB': 57}), Theta(thLo={'GB': 73}, thHi={'GB': 58}), Theta(thLo={'GB': 73}, thHi={'GB': 59}), Theta(thLo={'GB': 73}, thHi={'GB': 60}), Theta(thLo={'GB': 73}, thHi={'GB': 61}), Theta(thLo={'GB': 73}, thHi={'GB': 62}), Theta(thLo={'GB': 73}, thHi={'GB': 63}), Theta(thLo={'GB': 73}, thHi={'GB': 64}), Theta(thLo={'GB': 73}, thHi={'GB': 65}), Theta(thLo={'GB': 73}, thHi={'GB': 66}), Theta(thLo={'GB': 73}, thHi={'GB': 67}), Theta(thLo={'GB': 73}, thHi={'GB': 68}), Theta(thLo={'GB': 73}, thHi={'GB': 69}), Theta(thLo={'GB': 73}, thHi={'GB': 70}), Theta(thLo={'GB': 73}, thHi={'GB': 71}), Theta(thLo={'GB': 73}, thHi={'GB': 72}), Theta(thLo={'GB': 73}, thHi={'GB': 73}), Theta(thLo={'GB': 73}, thHi={'GB': 74}), Theta(thLo={'GB': 73}, thHi={'GB': 75}), Theta(thLo={'GB': 73}, thHi={'GB': 76}), Theta(thLo={'GB': 73}, thHi={'GB': 77}), Theta(thLo={'GB': 73}, thHi={'GB': 78}), Theta(thLo={'GB': 73}, thHi={'GB': 79}), Theta(thLo={'GB': 73}, thHi={'GB': 80}), Theta(thLo={'GB': 73}, thHi={'GB': 81}), Theta(thLo={'GB': 73}, thHi={'GB': 82}), Theta(thLo={'GB': 73}, thHi={'GB': 83}), Theta(thLo={'GB': 73}, thHi={'GB': 84}), Theta(thLo={'GB': 73}, thHi={'GB': 85}), Theta(thLo={'GB': 73}, thHi={'GB': 86}), Theta(thLo={'GB': 73}, thHi={'GB': 87}), Theta(thLo={'GB': 73}, thHi={'GB': 88}), Theta(thLo={'GB': 73}, thHi={'GB': 89}), Theta(thLo={'GB': 73}, thHi={'GB': 90}), Theta(thLo={'GB': 73}, thHi={'GB': 91}), Theta(thLo={'GB': 73}, thHi={'GB': 92}), Theta(thLo={'GB': 73}, thHi={'GB': 93}), Theta(thLo={'GB': 73}, thHi={'GB': 94}), Theta(thLo={'GB': 73}, thHi={'GB': 95}), Theta(thLo={'GB': 73}, thHi={'GB': 96}), Theta(thLo={'GB': 73}, thHi={'GB': 97}), Theta(thLo={'GB': 73}, thHi={'GB': 98}), Theta(thLo={'GB': 73}, thHi={'GB': 99}), Theta(thLo={'GB': 74}, thHi={'GB': 10}), Theta(thLo={'GB': 74}, thHi={'GB': 11}), Theta(thLo={'GB': 74}, thHi={'GB': 12}), Theta(thLo={'GB': 74}, thHi={'GB': 13}), Theta(thLo={'GB': 74}, thHi={'GB': 14}), Theta(thLo={'GB': 74}, thHi={'GB': 15}), Theta(thLo={'GB': 74}, thHi={'GB': 16}), Theta(thLo={'GB': 74}, thHi={'GB': 17}), Theta(thLo={'GB': 74}, thHi={'GB': 18}), Theta(thLo={'GB': 74}, thHi={'GB': 19}), Theta(thLo={'GB': 74}, thHi={'GB': 20}), Theta(thLo={'GB': 74}, thHi={'GB': 21}), Theta(thLo={'GB': 74}, thHi={'GB': 22}), Theta(thLo={'GB': 74}, thHi={'GB': 23}), Theta(thLo={'GB': 74}, thHi={'GB': 24}), Theta(thLo={'GB': 74}, thHi={'GB': 25}), Theta(thLo={'GB': 74}, thHi={'GB': 26}), Theta(thLo={'GB': 74}, thHi={'GB': 27}), Theta(thLo={'GB': 74}, thHi={'GB': 28}), Theta(thLo={'GB': 74}, thHi={'GB': 29}), Theta(thLo={'GB': 74}, thHi={'GB': 30}), Theta(thLo={'GB': 74}, thHi={'GB': 31}), Theta(thLo={'GB': 74}, thHi={'GB': 32}), Theta(thLo={'GB': 74}, thHi={'GB': 33}), Theta(thLo={'GB': 74}, thHi={'GB': 34}), Theta(thLo={'GB': 74}, thHi={'GB': 35}), Theta(thLo={'GB': 74}, thHi={'GB': 36}), Theta(thLo={'GB': 74}, thHi={'GB': 37}), Theta(thLo={'GB': 74}, thHi={'GB': 38}), Theta(thLo={'GB': 74}, thHi={'GB': 39}), Theta(thLo={'GB': 74}, thHi={'GB': 40}), Theta(thLo={'GB': 74}, thHi={'GB': 41}), Theta(thLo={'GB': 74}, thHi={'GB': 42}), Theta(thLo={'GB': 74}, thHi={'GB': 43}), Theta(thLo={'GB': 74}, thHi={'GB': 44}), Theta(thLo={'GB': 74}, thHi={'GB': 45}), Theta(thLo={'GB': 74}, thHi={'GB': 46}), Theta(thLo={'GB': 74}, thHi={'GB': 47}), Theta(thLo={'GB': 74}, thHi={'GB': 48}), Theta(thLo={'GB': 74}, thHi={'GB': 49}), Theta(thLo={'GB': 74}, thHi={'GB': 50}), Theta(thLo={'GB': 74}, thHi={'GB': 51}), Theta(thLo={'GB': 74}, thHi={'GB': 52}), Theta(thLo={'GB': 74}, thHi={'GB': 53}), Theta(thLo={'GB': 74}, thHi={'GB': 54}), Theta(thLo={'GB': 74}, thHi={'GB': 55}), Theta(thLo={'GB': 74}, thHi={'GB': 56}), Theta(thLo={'GB': 74}, thHi={'GB': 57}), Theta(thLo={'GB': 74}, thHi={'GB': 58}), Theta(thLo={'GB': 74}, thHi={'GB': 59}), Theta(thLo={'GB': 74}, thHi={'GB': 60}), Theta(thLo={'GB': 74}, thHi={'GB': 61}), Theta(thLo={'GB': 74}, thHi={'GB': 62}), Theta(thLo={'GB': 74}, thHi={'GB': 63}), Theta(thLo={'GB': 74}, thHi={'GB': 64}), Theta(thLo={'GB': 74}, thHi={'GB': 65}), Theta(thLo={'GB': 74}, thHi={'GB': 66}), Theta(thLo={'GB': 74}, thHi={'GB': 67}), Theta(thLo={'GB': 74}, thHi={'GB': 68}), Theta(thLo={'GB': 74}, thHi={'GB': 69}), Theta(thLo={'GB': 74}, thHi={'GB': 70}), Theta(thLo={'GB': 74}, thHi={'GB': 71}), Theta(thLo={'GB': 74}, thHi={'GB': 72}), Theta(thLo={'GB': 74}, thHi={'GB': 73}), Theta(thLo={'GB': 74}, thHi={'GB': 74}), Theta(thLo={'GB': 74}, thHi={'GB': 75}), Theta(thLo={'GB': 74}, thHi={'GB': 76}), Theta(thLo={'GB': 74}, thHi={'GB': 77}), Theta(thLo={'GB': 74}, thHi={'GB': 78}), Theta(thLo={'GB': 74}, thHi={'GB': 79}), Theta(thLo={'GB': 74}, thHi={'GB': 80}), Theta(thLo={'GB': 74}, thHi={'GB': 81}), Theta(thLo={'GB': 74}, thHi={'GB': 82}), Theta(thLo={'GB': 74}, thHi={'GB': 83}), Theta(thLo={'GB': 74}, thHi={'GB': 84}), Theta(thLo={'GB': 74}, thHi={'GB': 85}), Theta(thLo={'GB': 74}, thHi={'GB': 86}), Theta(thLo={'GB': 74}, thHi={'GB': 87}), Theta(thLo={'GB': 74}, thHi={'GB': 88}), Theta(thLo={'GB': 74}, thHi={'GB': 89}), Theta(thLo={'GB': 74}, thHi={'GB': 90}), Theta(thLo={'GB': 74}, thHi={'GB': 91}), Theta(thLo={'GB': 74}, thHi={'GB': 92}), Theta(thLo={'GB': 74}, thHi={'GB': 93}), Theta(thLo={'GB': 74}, thHi={'GB': 94}), Theta(thLo={'GB': 74}, thHi={'GB': 95}), Theta(thLo={'GB': 74}, thHi={'GB': 96}), Theta(thLo={'GB': 74}, thHi={'GB': 97}), Theta(thLo={'GB': 74}, thHi={'GB': 98}), Theta(thLo={'GB': 74}, thHi={'GB': 99}), Theta(thLo={'GB': 75}, thHi={'GB': 10}), Theta(thLo={'GB': 75}, thHi={'GB': 11}), Theta(thLo={'GB': 75}, thHi={'GB': 12}), Theta(thLo={'GB': 75}, thHi={'GB': 13}), Theta(thLo={'GB': 75}, thHi={'GB': 14}), Theta(thLo={'GB': 75}, thHi={'GB': 15}), Theta(thLo={'GB': 75}, thHi={'GB': 16}), Theta(thLo={'GB': 75}, thHi={'GB': 17}), Theta(thLo={'GB': 75}, thHi={'GB': 18}), Theta(thLo={'GB': 75}, thHi={'GB': 19}), Theta(thLo={'GB': 75}, thHi={'GB': 20}), Theta(thLo={'GB': 75}, thHi={'GB': 21}), Theta(thLo={'GB': 75}, thHi={'GB': 22}), Theta(thLo={'GB': 75}, thHi={'GB': 23}), Theta(thLo={'GB': 75}, thHi={'GB': 24}), Theta(thLo={'GB': 75}, thHi={'GB': 25}), Theta(thLo={'GB': 75}, thHi={'GB': 26}), Theta(thLo={'GB': 75}, thHi={'GB': 27}), Theta(thLo={'GB': 75}, thHi={'GB': 28}), Theta(thLo={'GB': 75}, thHi={'GB': 29}), Theta(thLo={'GB': 75}, thHi={'GB': 30}), Theta(thLo={'GB': 75}, thHi={'GB': 31}), Theta(thLo={'GB': 75}, thHi={'GB': 32}), Theta(thLo={'GB': 75}, thHi={'GB': 33}), Theta(thLo={'GB': 75}, thHi={'GB': 34}), Theta(thLo={'GB': 75}, thHi={'GB': 35}), Theta(thLo={'GB': 75}, thHi={'GB': 36}), Theta(thLo={'GB': 75}, thHi={'GB': 37}), Theta(thLo={'GB': 75}, thHi={'GB': 38}), Theta(thLo={'GB': 75}, thHi={'GB': 39}), Theta(thLo={'GB': 75}, thHi={'GB': 40}), Theta(thLo={'GB': 75}, thHi={'GB': 41}), Theta(thLo={'GB': 75}, thHi={'GB': 42}), Theta(thLo={'GB': 75}, thHi={'GB': 43}), Theta(thLo={'GB': 75}, thHi={'GB': 44}), Theta(thLo={'GB': 75}, thHi={'GB': 45}), Theta(thLo={'GB': 75}, thHi={'GB': 46}), Theta(thLo={'GB': 75}, thHi={'GB': 47}), Theta(thLo={'GB': 75}, thHi={'GB': 48}), Theta(thLo={'GB': 75}, thHi={'GB': 49}), Theta(thLo={'GB': 75}, thHi={'GB': 50}), Theta(thLo={'GB': 75}, thHi={'GB': 51}), Theta(thLo={'GB': 75}, thHi={'GB': 52}), Theta(thLo={'GB': 75}, thHi={'GB': 53}), Theta(thLo={'GB': 75}, thHi={'GB': 54}), Theta(thLo={'GB': 75}, thHi={'GB': 55}), Theta(thLo={'GB': 75}, thHi={'GB': 56}), Theta(thLo={'GB': 75}, thHi={'GB': 57}), Theta(thLo={'GB': 75}, thHi={'GB': 58}), Theta(thLo={'GB': 75}, thHi={'GB': 59}), Theta(thLo={'GB': 75}, thHi={'GB': 60}), Theta(thLo={'GB': 75}, thHi={'GB': 61}), Theta(thLo={'GB': 75}, thHi={'GB': 62}), Theta(thLo={'GB': 75}, thHi={'GB': 63}), Theta(thLo={'GB': 75}, thHi={'GB': 64}), Theta(thLo={'GB': 75}, thHi={'GB': 65}), Theta(thLo={'GB': 75}, thHi={'GB': 66}), Theta(thLo={'GB': 75}, thHi={'GB': 67}), Theta(thLo={'GB': 75}, thHi={'GB': 68}), Theta(thLo={'GB': 75}, thHi={'GB': 69}), Theta(thLo={'GB': 75}, thHi={'GB': 70}), Theta(thLo={'GB': 75}, thHi={'GB': 71}), Theta(thLo={'GB': 75}, thHi={'GB': 72}), Theta(thLo={'GB': 75}, thHi={'GB': 73}), Theta(thLo={'GB': 75}, thHi={'GB': 74}), Theta(thLo={'GB': 75}, thHi={'GB': 75}), Theta(thLo={'GB': 75}, thHi={'GB': 76}), Theta(thLo={'GB': 75}, thHi={'GB': 77}), Theta(thLo={'GB': 75}, thHi={'GB': 78}), Theta(thLo={'GB': 75}, thHi={'GB': 79}), Theta(thLo={'GB': 75}, thHi={'GB': 80}), Theta(thLo={'GB': 75}, thHi={'GB': 81}), Theta(thLo={'GB': 75}, thHi={'GB': 82}), Theta(thLo={'GB': 75}, thHi={'GB': 83}), Theta(thLo={'GB': 75}, thHi={'GB': 84}), Theta(thLo={'GB': 75}, thHi={'GB': 85}), Theta(thLo={'GB': 75}, thHi={'GB': 86}), Theta(thLo={'GB': 75}, thHi={'GB': 87}), Theta(thLo={'GB': 75}, thHi={'GB': 88}), Theta(thLo={'GB': 75}, thHi={'GB': 89}), Theta(thLo={'GB': 75}, thHi={'GB': 90}), Theta(thLo={'GB': 75}, thHi={'GB': 91}), Theta(thLo={'GB': 75}, thHi={'GB': 92}), Theta(thLo={'GB': 75}, thHi={'GB': 93}), Theta(thLo={'GB': 75}, thHi={'GB': 94}), Theta(thLo={'GB': 75}, thHi={'GB': 95}), Theta(thLo={'GB': 75}, thHi={'GB': 96}), Theta(thLo={'GB': 75}, thHi={'GB': 97}), Theta(thLo={'GB': 75}, thHi={'GB': 98}), Theta(thLo={'GB': 75}, thHi={'GB': 99}), Theta(thLo={'GB': 76}, thHi={'GB': 10}), Theta(thLo={'GB': 76}, thHi={'GB': 11}), Theta(thLo={'GB': 76}, thHi={'GB': 12}), Theta(thLo={'GB': 76}, thHi={'GB': 13}), Theta(thLo={'GB': 76}, thHi={'GB': 14}), Theta(thLo={'GB': 76}, thHi={'GB': 15}), Theta(thLo={'GB': 76}, thHi={'GB': 16}), Theta(thLo={'GB': 76}, thHi={'GB': 17}), Theta(thLo={'GB': 76}, thHi={'GB': 18}), Theta(thLo={'GB': 76}, thHi={'GB': 19}), Theta(thLo={'GB': 76}, thHi={'GB': 20}), Theta(thLo={'GB': 76}, thHi={'GB': 21}), Theta(thLo={'GB': 76}, thHi={'GB': 22}), Theta(thLo={'GB': 76}, thHi={'GB': 23}), Theta(thLo={'GB': 76}, thHi={'GB': 24}), Theta(thLo={'GB': 76}, thHi={'GB': 25}), Theta(thLo={'GB': 76}, thHi={'GB': 26}), Theta(thLo={'GB': 76}, thHi={'GB': 27}), Theta(thLo={'GB': 76}, thHi={'GB': 28}), Theta(thLo={'GB': 76}, thHi={'GB': 29}), Theta(thLo={'GB': 76}, thHi={'GB': 30}), Theta(thLo={'GB': 76}, thHi={'GB': 31}), Theta(thLo={'GB': 76}, thHi={'GB': 32}), Theta(thLo={'GB': 76}, thHi={'GB': 33}), Theta(thLo={'GB': 76}, thHi={'GB': 34}), Theta(thLo={'GB': 76}, thHi={'GB': 35}), Theta(thLo={'GB': 76}, thHi={'GB': 36}), Theta(thLo={'GB': 76}, thHi={'GB': 37}), Theta(thLo={'GB': 76}, thHi={'GB': 38}), Theta(thLo={'GB': 76}, thHi={'GB': 39}), Theta(thLo={'GB': 76}, thHi={'GB': 40}), Theta(thLo={'GB': 76}, thHi={'GB': 41}), Theta(thLo={'GB': 76}, thHi={'GB': 42}), Theta(thLo={'GB': 76}, thHi={'GB': 43}), Theta(thLo={'GB': 76}, thHi={'GB': 44}), Theta(thLo={'GB': 76}, thHi={'GB': 45}), Theta(thLo={'GB': 76}, thHi={'GB': 46}), Theta(thLo={'GB': 76}, thHi={'GB': 47}), Theta(thLo={'GB': 76}, thHi={'GB': 48}), Theta(thLo={'GB': 76}, thHi={'GB': 49}), Theta(thLo={'GB': 76}, thHi={'GB': 50}), Theta(thLo={'GB': 76}, thHi={'GB': 51}), Theta(thLo={'GB': 76}, thHi={'GB': 52}), Theta(thLo={'GB': 76}, thHi={'GB': 53}), Theta(thLo={'GB': 76}, thHi={'GB': 54}), Theta(thLo={'GB': 76}, thHi={'GB': 55}), Theta(thLo={'GB': 76}, thHi={'GB': 56}), Theta(thLo={'GB': 76}, thHi={'GB': 57}), Theta(thLo={'GB': 76}, thHi={'GB': 58}), Theta(thLo={'GB': 76}, thHi={'GB': 59}), Theta(thLo={'GB': 76}, thHi={'GB': 60}), Theta(thLo={'GB': 76}, thHi={'GB': 61}), Theta(thLo={'GB': 76}, thHi={'GB': 62}), Theta(thLo={'GB': 76}, thHi={'GB': 63}), Theta(thLo={'GB': 76}, thHi={'GB': 64}), Theta(thLo={'GB': 76}, thHi={'GB': 65}), Theta(thLo={'GB': 76}, thHi={'GB': 66}), Theta(thLo={'GB': 76}, thHi={'GB': 67}), Theta(thLo={'GB': 76}, thHi={'GB': 68}), Theta(thLo={'GB': 76}, thHi={'GB': 69}), Theta(thLo={'GB': 76}, thHi={'GB': 70}), Theta(thLo={'GB': 76}, thHi={'GB': 71}), Theta(thLo={'GB': 76}, thHi={'GB': 72}), Theta(thLo={'GB': 76}, thHi={'GB': 73}), Theta(thLo={'GB': 76}, thHi={'GB': 74}), Theta(thLo={'GB': 76}, thHi={'GB': 75}), Theta(thLo={'GB': 76}, thHi={'GB': 76}), Theta(thLo={'GB': 76}, thHi={'GB': 77}), Theta(thLo={'GB': 76}, thHi={'GB': 78}), Theta(thLo={'GB': 76}, thHi={'GB': 79}), Theta(thLo={'GB': 76}, thHi={'GB': 80}), Theta(thLo={'GB': 76}, thHi={'GB': 81}), Theta(thLo={'GB': 76}, thHi={'GB': 82}), Theta(thLo={'GB': 76}, thHi={'GB': 83}), Theta(thLo={'GB': 76}, thHi={'GB': 84}), Theta(thLo={'GB': 76}, thHi={'GB': 85}), Theta(thLo={'GB': 76}, thHi={'GB': 86}), Theta(thLo={'GB': 76}, thHi={'GB': 87}), Theta(thLo={'GB': 76}, thHi={'GB': 88}), Theta(thLo={'GB': 76}, thHi={'GB': 89}), Theta(thLo={'GB': 76}, thHi={'GB': 90}), Theta(thLo={'GB': 76}, thHi={'GB': 91}), Theta(thLo={'GB': 76}, thHi={'GB': 92}), Theta(thLo={'GB': 76}, thHi={'GB': 93}), Theta(thLo={'GB': 76}, thHi={'GB': 94}), Theta(thLo={'GB': 76}, thHi={'GB': 95}), Theta(thLo={'GB': 76}, thHi={'GB': 96}), Theta(thLo={'GB': 76}, thHi={'GB': 97}), Theta(thLo={'GB': 76}, thHi={'GB': 98}), Theta(thLo={'GB': 76}, thHi={'GB': 99}), Theta(thLo={'GB': 77}, thHi={'GB': 10}), Theta(thLo={'GB': 77}, thHi={'GB': 11}), Theta(thLo={'GB': 77}, thHi={'GB': 12}), Theta(thLo={'GB': 77}, thHi={'GB': 13}), Theta(thLo={'GB': 77}, thHi={'GB': 14}), Theta(thLo={'GB': 77}, thHi={'GB': 15}), Theta(thLo={'GB': 77}, thHi={'GB': 16}), Theta(thLo={'GB': 77}, thHi={'GB': 17}), Theta(thLo={'GB': 77}, thHi={'GB': 18}), Theta(thLo={'GB': 77}, thHi={'GB': 19}), Theta(thLo={'GB': 77}, thHi={'GB': 20}), Theta(thLo={'GB': 77}, thHi={'GB': 21}), Theta(thLo={'GB': 77}, thHi={'GB': 22}), Theta(thLo={'GB': 77}, thHi={'GB': 23}), Theta(thLo={'GB': 77}, thHi={'GB': 24}), Theta(thLo={'GB': 77}, thHi={'GB': 25}), Theta(thLo={'GB': 77}, thHi={'GB': 26}), Theta(thLo={'GB': 77}, thHi={'GB': 27}), Theta(thLo={'GB': 77}, thHi={'GB': 28}), Theta(thLo={'GB': 77}, thHi={'GB': 29}), Theta(thLo={'GB': 77}, thHi={'GB': 30}), Theta(thLo={'GB': 77}, thHi={'GB': 31}), Theta(thLo={'GB': 77}, thHi={'GB': 32}), Theta(thLo={'GB': 77}, thHi={'GB': 33}), Theta(thLo={'GB': 77}, thHi={'GB': 34}), Theta(thLo={'GB': 77}, thHi={'GB': 35}), Theta(thLo={'GB': 77}, thHi={'GB': 36}), Theta(thLo={'GB': 77}, thHi={'GB': 37}), Theta(thLo={'GB': 77}, thHi={'GB': 38}), Theta(thLo={'GB': 77}, thHi={'GB': 39}), Theta(thLo={'GB': 77}, thHi={'GB': 40}), Theta(thLo={'GB': 77}, thHi={'GB': 41}), Theta(thLo={'GB': 77}, thHi={'GB': 42}), Theta(thLo={'GB': 77}, thHi={'GB': 43}), Theta(thLo={'GB': 77}, thHi={'GB': 44}), Theta(thLo={'GB': 77}, thHi={'GB': 45}), Theta(thLo={'GB': 77}, thHi={'GB': 46}), Theta(thLo={'GB': 77}, thHi={'GB': 47}), Theta(thLo={'GB': 77}, thHi={'GB': 48}), Theta(thLo={'GB': 77}, thHi={'GB': 49}), Theta(thLo={'GB': 77}, thHi={'GB': 50}), Theta(thLo={'GB': 77}, thHi={'GB': 51}), Theta(thLo={'GB': 77}, thHi={'GB': 52}), Theta(thLo={'GB': 77}, thHi={'GB': 53}), Theta(thLo={'GB': 77}, thHi={'GB': 54}), Theta(thLo={'GB': 77}, thHi={'GB': 55}), Theta(thLo={'GB': 77}, thHi={'GB': 56}), Theta(thLo={'GB': 77}, thHi={'GB': 57}), Theta(thLo={'GB': 77}, thHi={'GB': 58}), Theta(thLo={'GB': 77}, thHi={'GB': 59}), Theta(thLo={'GB': 77}, thHi={'GB': 60}), Theta(thLo={'GB': 77}, thHi={'GB': 61}), Theta(thLo={'GB': 77}, thHi={'GB': 62}), Theta(thLo={'GB': 77}, thHi={'GB': 63}), Theta(thLo={'GB': 77}, thHi={'GB': 64}), Theta(thLo={'GB': 77}, thHi={'GB': 65}), Theta(thLo={'GB': 77}, thHi={'GB': 66}), Theta(thLo={'GB': 77}, thHi={'GB': 67}), Theta(thLo={'GB': 77}, thHi={'GB': 68}), Theta(thLo={'GB': 77}, thHi={'GB': 69}), Theta(thLo={'GB': 77}, thHi={'GB': 70}), Theta(thLo={'GB': 77}, thHi={'GB': 71}), Theta(thLo={'GB': 77}, thHi={'GB': 72}), Theta(thLo={'GB': 77}, thHi={'GB': 73}), Theta(thLo={'GB': 77}, thHi={'GB': 74}), Theta(thLo={'GB': 77}, thHi={'GB': 75}), Theta(thLo={'GB': 77}, thHi={'GB': 76}), Theta(thLo={'GB': 77}, thHi={'GB': 77}), Theta(thLo={'GB': 77}, thHi={'GB': 78}), Theta(thLo={'GB': 77}, thHi={'GB': 79}), Theta(thLo={'GB': 77}, thHi={'GB': 80}), Theta(thLo={'GB': 77}, thHi={'GB': 81}), Theta(thLo={'GB': 77}, thHi={'GB': 82}), Theta(thLo={'GB': 77}, thHi={'GB': 83}), Theta(thLo={'GB': 77}, thHi={'GB': 84}), Theta(thLo={'GB': 77}, thHi={'GB': 85}), Theta(thLo={'GB': 77}, thHi={'GB': 86}), Theta(thLo={'GB': 77}, thHi={'GB': 87}), Theta(thLo={'GB': 77}, thHi={'GB': 88}), Theta(thLo={'GB': 77}, thHi={'GB': 89}), Theta(thLo={'GB': 77}, thHi={'GB': 90}), Theta(thLo={'GB': 77}, thHi={'GB': 91}), Theta(thLo={'GB': 77}, thHi={'GB': 92}), Theta(thLo={'GB': 77}, thHi={'GB': 93}), Theta(thLo={'GB': 77}, thHi={'GB': 94}), Theta(thLo={'GB': 77}, thHi={'GB': 95}), Theta(thLo={'GB': 77}, thHi={'GB': 96}), Theta(thLo={'GB': 77}, thHi={'GB': 97}), Theta(thLo={'GB': 77}, thHi={'GB': 98}), Theta(thLo={'GB': 77}, thHi={'GB': 99}), Theta(thLo={'GB': 78}, thHi={'GB': 10}), Theta(thLo={'GB': 78}, thHi={'GB': 11}), Theta(thLo={'GB': 78}, thHi={'GB': 12}), Theta(thLo={'GB': 78}, thHi={'GB': 13}), Theta(thLo={'GB': 78}, thHi={'GB': 14}), Theta(thLo={'GB': 78}, thHi={'GB': 15}), Theta(thLo={'GB': 78}, thHi={'GB': 16}), Theta(thLo={'GB': 78}, thHi={'GB': 17}), Theta(thLo={'GB': 78}, thHi={'GB': 18}), Theta(thLo={'GB': 78}, thHi={'GB': 19}), Theta(thLo={'GB': 78}, thHi={'GB': 20}), Theta(thLo={'GB': 78}, thHi={'GB': 21}), Theta(thLo={'GB': 78}, thHi={'GB': 22}), Theta(thLo={'GB': 78}, thHi={'GB': 23}), Theta(thLo={'GB': 78}, thHi={'GB': 24}), Theta(thLo={'GB': 78}, thHi={'GB': 25}), Theta(thLo={'GB': 78}, thHi={'GB': 26}), Theta(thLo={'GB': 78}, thHi={'GB': 27}), Theta(thLo={'GB': 78}, thHi={'GB': 28}), Theta(thLo={'GB': 78}, thHi={'GB': 29}), Theta(thLo={'GB': 78}, thHi={'GB': 30}), Theta(thLo={'GB': 78}, thHi={'GB': 31}), Theta(thLo={'GB': 78}, thHi={'GB': 32}), Theta(thLo={'GB': 78}, thHi={'GB': 33}), Theta(thLo={'GB': 78}, thHi={'GB': 34}), Theta(thLo={'GB': 78}, thHi={'GB': 35}), Theta(thLo={'GB': 78}, thHi={'GB': 36}), Theta(thLo={'GB': 78}, thHi={'GB': 37}), Theta(thLo={'GB': 78}, thHi={'GB': 38}), Theta(thLo={'GB': 78}, thHi={'GB': 39}), Theta(thLo={'GB': 78}, thHi={'GB': 40}), Theta(thLo={'GB': 78}, thHi={'GB': 41}), Theta(thLo={'GB': 78}, thHi={'GB': 42}), Theta(thLo={'GB': 78}, thHi={'GB': 43}), Theta(thLo={'GB': 78}, thHi={'GB': 44}), Theta(thLo={'GB': 78}, thHi={'GB': 45}), Theta(thLo={'GB': 78}, thHi={'GB': 46}), Theta(thLo={'GB': 78}, thHi={'GB': 47}), Theta(thLo={'GB': 78}, thHi={'GB': 48}), Theta(thLo={'GB': 78}, thHi={'GB': 49}), Theta(thLo={'GB': 78}, thHi={'GB': 50}), Theta(thLo={'GB': 78}, thHi={'GB': 51}), Theta(thLo={'GB': 78}, thHi={'GB': 52}), Theta(thLo={'GB': 78}, thHi={'GB': 53}), Theta(thLo={'GB': 78}, thHi={'GB': 54}), Theta(thLo={'GB': 78}, thHi={'GB': 55}), Theta(thLo={'GB': 78}, thHi={'GB': 56}), Theta(thLo={'GB': 78}, thHi={'GB': 57}), Theta(thLo={'GB': 78}, thHi={'GB': 58}), Theta(thLo={'GB': 78}, thHi={'GB': 59}), Theta(thLo={'GB': 78}, thHi={'GB': 60}), Theta(thLo={'GB': 78}, thHi={'GB': 61}), Theta(thLo={'GB': 78}, thHi={'GB': 62}), Theta(thLo={'GB': 78}, thHi={'GB': 63}), Theta(thLo={'GB': 78}, thHi={'GB': 64}), Theta(thLo={'GB': 78}, thHi={'GB': 65}), Theta(thLo={'GB': 78}, thHi={'GB': 66}), Theta(thLo={'GB': 78}, thHi={'GB': 67}), Theta(thLo={'GB': 78}, thHi={'GB': 68}), Theta(thLo={'GB': 78}, thHi={'GB': 69}), Theta(thLo={'GB': 78}, thHi={'GB': 70}), Theta(thLo={'GB': 78}, thHi={'GB': 71}), Theta(thLo={'GB': 78}, thHi={'GB': 72}), Theta(thLo={'GB': 78}, thHi={'GB': 73}), Theta(thLo={'GB': 78}, thHi={'GB': 74}), Theta(thLo={'GB': 78}, thHi={'GB': 75}), Theta(thLo={'GB': 78}, thHi={'GB': 76}), Theta(thLo={'GB': 78}, thHi={'GB': 77}), Theta(thLo={'GB': 78}, thHi={'GB': 78}), Theta(thLo={'GB': 78}, thHi={'GB': 79}), Theta(thLo={'GB': 78}, thHi={'GB': 80}), Theta(thLo={'GB': 78}, thHi={'GB': 81}), Theta(thLo={'GB': 78}, thHi={'GB': 82}), Theta(thLo={'GB': 78}, thHi={'GB': 83}), Theta(thLo={'GB': 78}, thHi={'GB': 84}), Theta(thLo={'GB': 78}, thHi={'GB': 85}), Theta(thLo={'GB': 78}, thHi={'GB': 86}), Theta(thLo={'GB': 78}, thHi={'GB': 87}), Theta(thLo={'GB': 78}, thHi={'GB': 88}), Theta(thLo={'GB': 78}, thHi={'GB': 89}), Theta(thLo={'GB': 78}, thHi={'GB': 90}), Theta(thLo={'GB': 78}, thHi={'GB': 91}), Theta(thLo={'GB': 78}, thHi={'GB': 92}), Theta(thLo={'GB': 78}, thHi={'GB': 93}), Theta(thLo={'GB': 78}, thHi={'GB': 94}), Theta(thLo={'GB': 78}, thHi={'GB': 95}), Theta(thLo={'GB': 78}, thHi={'GB': 96}), Theta(thLo={'GB': 78}, thHi={'GB': 97}), Theta(thLo={'GB': 78}, thHi={'GB': 98}), Theta(thLo={'GB': 78}, thHi={'GB': 99}), Theta(thLo={'GB': 79}, thHi={'GB': 10}), Theta(thLo={'GB': 79}, thHi={'GB': 11}), Theta(thLo={'GB': 79}, thHi={'GB': 12}), Theta(thLo={'GB': 79}, thHi={'GB': 13}), Theta(thLo={'GB': 79}, thHi={'GB': 14}), Theta(thLo={'GB': 79}, thHi={'GB': 15}), Theta(thLo={'GB': 79}, thHi={'GB': 16}), Theta(thLo={'GB': 79}, thHi={'GB': 17}), Theta(thLo={'GB': 79}, thHi={'GB': 18}), Theta(thLo={'GB': 79}, thHi={'GB': 19}), Theta(thLo={'GB': 79}, thHi={'GB': 20}), Theta(thLo={'GB': 79}, thHi={'GB': 21}), Theta(thLo={'GB': 79}, thHi={'GB': 22}), Theta(thLo={'GB': 79}, thHi={'GB': 23}), Theta(thLo={'GB': 79}, thHi={'GB': 24}), Theta(thLo={'GB': 79}, thHi={'GB': 25}), Theta(thLo={'GB': 79}, thHi={'GB': 26}), Theta(thLo={'GB': 79}, thHi={'GB': 27}), Theta(thLo={'GB': 79}, thHi={'GB': 28}), Theta(thLo={'GB': 79}, thHi={'GB': 29}), Theta(thLo={'GB': 79}, thHi={'GB': 30}), Theta(thLo={'GB': 79}, thHi={'GB': 31}), Theta(thLo={'GB': 79}, thHi={'GB': 32}), Theta(thLo={'GB': 79}, thHi={'GB': 33}), Theta(thLo={'GB': 79}, thHi={'GB': 34}), Theta(thLo={'GB': 79}, thHi={'GB': 35}), Theta(thLo={'GB': 79}, thHi={'GB': 36}), Theta(thLo={'GB': 79}, thHi={'GB': 37}), Theta(thLo={'GB': 79}, thHi={'GB': 38}), Theta(thLo={'GB': 79}, thHi={'GB': 39}), Theta(thLo={'GB': 79}, thHi={'GB': 40}), Theta(thLo={'GB': 79}, thHi={'GB': 41}), Theta(thLo={'GB': 79}, thHi={'GB': 42}), Theta(thLo={'GB': 79}, thHi={'GB': 43}), Theta(thLo={'GB': 79}, thHi={'GB': 44}), Theta(thLo={'GB': 79}, thHi={'GB': 45}), Theta(thLo={'GB': 79}, thHi={'GB': 46}), Theta(thLo={'GB': 79}, thHi={'GB': 47}), Theta(thLo={'GB': 79}, thHi={'GB': 48}), Theta(thLo={'GB': 79}, thHi={'GB': 49}), Theta(thLo={'GB': 79}, thHi={'GB': 50}), Theta(thLo={'GB': 79}, thHi={'GB': 51}), Theta(thLo={'GB': 79}, thHi={'GB': 52}), Theta(thLo={'GB': 79}, thHi={'GB': 53}), Theta(thLo={'GB': 79}, thHi={'GB': 54}), Theta(thLo={'GB': 79}, thHi={'GB': 55}), Theta(thLo={'GB': 79}, thHi={'GB': 56}), Theta(thLo={'GB': 79}, thHi={'GB': 57}), Theta(thLo={'GB': 79}, thHi={'GB': 58}), Theta(thLo={'GB': 79}, thHi={'GB': 59}), Theta(thLo={'GB': 79}, thHi={'GB': 60}), Theta(thLo={'GB': 79}, thHi={'GB': 61}), Theta(thLo={'GB': 79}, thHi={'GB': 62}), Theta(thLo={'GB': 79}, thHi={'GB': 63}), Theta(thLo={'GB': 79}, thHi={'GB': 64}), Theta(thLo={'GB': 79}, thHi={'GB': 65}), Theta(thLo={'GB': 79}, thHi={'GB': 66}), Theta(thLo={'GB': 79}, thHi={'GB': 67}), Theta(thLo={'GB': 79}, thHi={'GB': 68}), Theta(thLo={'GB': 79}, thHi={'GB': 69}), Theta(thLo={'GB': 79}, thHi={'GB': 70}), Theta(thLo={'GB': 79}, thHi={'GB': 71}), Theta(thLo={'GB': 79}, thHi={'GB': 72}), Theta(thLo={'GB': 79}, thHi={'GB': 73}), Theta(thLo={'GB': 79}, thHi={'GB': 74}), Theta(thLo={'GB': 79}, thHi={'GB': 75}), Theta(thLo={'GB': 79}, thHi={'GB': 76}), Theta(thLo={'GB': 79}, thHi={'GB': 77}), Theta(thLo={'GB': 79}, thHi={'GB': 78}), Theta(thLo={'GB': 79}, thHi={'GB': 79}), Theta(thLo={'GB': 79}, thHi={'GB': 80}), Theta(thLo={'GB': 79}, thHi={'GB': 81}), Theta(thLo={'GB': 79}, thHi={'GB': 82}), Theta(thLo={'GB': 79}, thHi={'GB': 83}), Theta(thLo={'GB': 79}, thHi={'GB': 84}), Theta(thLo={'GB': 79}, thHi={'GB': 85}), Theta(thLo={'GB': 79}, thHi={'GB': 86}), Theta(thLo={'GB': 79}, thHi={'GB': 87}), Theta(thLo={'GB': 79}, thHi={'GB': 88}), Theta(thLo={'GB': 79}, thHi={'GB': 89}), Theta(thLo={'GB': 79}, thHi={'GB': 90}), Theta(thLo={'GB': 79}, thHi={'GB': 91}), Theta(thLo={'GB': 79}, thHi={'GB': 92}), Theta(thLo={'GB': 79}, thHi={'GB': 93}), Theta(thLo={'GB': 79}, thHi={'GB': 94}), Theta(thLo={'GB': 79}, thHi={'GB': 95}), Theta(thLo={'GB': 79}, thHi={'GB': 96}), Theta(thLo={'GB': 79}, thHi={'GB': 97}), Theta(thLo={'GB': 79}, thHi={'GB': 98}), Theta(thLo={'GB': 79}, thHi={'GB': 99}), Theta(thLo={'GB': 80}, thHi={'GB': 10}), Theta(thLo={'GB': 80}, thHi={'GB': 11}), Theta(thLo={'GB': 80}, thHi={'GB': 12}), Theta(thLo={'GB': 80}, thHi={'GB': 13}), Theta(thLo={'GB': 80}, thHi={'GB': 14}), Theta(thLo={'GB': 80}, thHi={'GB': 15}), Theta(thLo={'GB': 80}, thHi={'GB': 16}), Theta(thLo={'GB': 80}, thHi={'GB': 17}), Theta(thLo={'GB': 80}, thHi={'GB': 18}), Theta(thLo={'GB': 80}, thHi={'GB': 19}), Theta(thLo={'GB': 80}, thHi={'GB': 20}), Theta(thLo={'GB': 80}, thHi={'GB': 21}), Theta(thLo={'GB': 80}, thHi={'GB': 22}), Theta(thLo={'GB': 80}, thHi={'GB': 23}), Theta(thLo={'GB': 80}, thHi={'GB': 24}), Theta(thLo={'GB': 80}, thHi={'GB': 25}), Theta(thLo={'GB': 80}, thHi={'GB': 26}), Theta(thLo={'GB': 80}, thHi={'GB': 27}), Theta(thLo={'GB': 80}, thHi={'GB': 28}), Theta(thLo={'GB': 80}, thHi={'GB': 29}), Theta(thLo={'GB': 80}, thHi={'GB': 30}), Theta(thLo={'GB': 80}, thHi={'GB': 31}), Theta(thLo={'GB': 80}, thHi={'GB': 32}), Theta(thLo={'GB': 80}, thHi={'GB': 33}), Theta(thLo={'GB': 80}, thHi={'GB': 34}), Theta(thLo={'GB': 80}, thHi={'GB': 35}), Theta(thLo={'GB': 80}, thHi={'GB': 36}), Theta(thLo={'GB': 80}, thHi={'GB': 37}), Theta(thLo={'GB': 80}, thHi={'GB': 38}), Theta(thLo={'GB': 80}, thHi={'GB': 39}), Theta(thLo={'GB': 80}, thHi={'GB': 40}), Theta(thLo={'GB': 80}, thHi={'GB': 41}), Theta(thLo={'GB': 80}, thHi={'GB': 42}), Theta(thLo={'GB': 80}, thHi={'GB': 43}), Theta(thLo={'GB': 80}, thHi={'GB': 44}), Theta(thLo={'GB': 80}, thHi={'GB': 45}), Theta(thLo={'GB': 80}, thHi={'GB': 46}), Theta(thLo={'GB': 80}, thHi={'GB': 47}), Theta(thLo={'GB': 80}, thHi={'GB': 48}), Theta(thLo={'GB': 80}, thHi={'GB': 49}), Theta(thLo={'GB': 80}, thHi={'GB': 50}), Theta(thLo={'GB': 80}, thHi={'GB': 51}), Theta(thLo={'GB': 80}, thHi={'GB': 52}), Theta(thLo={'GB': 80}, thHi={'GB': 53}), Theta(thLo={'GB': 80}, thHi={'GB': 54}), Theta(thLo={'GB': 80}, thHi={'GB': 55}), Theta(thLo={'GB': 80}, thHi={'GB': 56}), Theta(thLo={'GB': 80}, thHi={'GB': 57}), Theta(thLo={'GB': 80}, thHi={'GB': 58}), Theta(thLo={'GB': 80}, thHi={'GB': 59}), Theta(thLo={'GB': 80}, thHi={'GB': 60}), Theta(thLo={'GB': 80}, thHi={'GB': 61}), Theta(thLo={'GB': 80}, thHi={'GB': 62}), Theta(thLo={'GB': 80}, thHi={'GB': 63}), Theta(thLo={'GB': 80}, thHi={'GB': 64}), Theta(thLo={'GB': 80}, thHi={'GB': 65}), Theta(thLo={'GB': 80}, thHi={'GB': 66}), Theta(thLo={'GB': 80}, thHi={'GB': 67}), Theta(thLo={'GB': 80}, thHi={'GB': 68}), Theta(thLo={'GB': 80}, thHi={'GB': 69}), Theta(thLo={'GB': 80}, thHi={'GB': 70}), Theta(thLo={'GB': 80}, thHi={'GB': 71}), Theta(thLo={'GB': 80}, thHi={'GB': 72}), Theta(thLo={'GB': 80}, thHi={'GB': 73}), Theta(thLo={'GB': 80}, thHi={'GB': 74}), Theta(thLo={'GB': 80}, thHi={'GB': 75}), Theta(thLo={'GB': 80}, thHi={'GB': 76}), Theta(thLo={'GB': 80}, thHi={'GB': 77}), Theta(thLo={'GB': 80}, thHi={'GB': 78}), Theta(thLo={'GB': 80}, thHi={'GB': 79}), Theta(thLo={'GB': 80}, thHi={'GB': 80}), Theta(thLo={'GB': 80}, thHi={'GB': 81}), Theta(thLo={'GB': 80}, thHi={'GB': 82}), Theta(thLo={'GB': 80}, thHi={'GB': 83}), Theta(thLo={'GB': 80}, thHi={'GB': 84}), Theta(thLo={'GB': 80}, thHi={'GB': 85}), Theta(thLo={'GB': 80}, thHi={'GB': 86}), Theta(thLo={'GB': 80}, thHi={'GB': 87}), Theta(thLo={'GB': 80}, thHi={'GB': 88}), Theta(thLo={'GB': 80}, thHi={'GB': 89}), Theta(thLo={'GB': 80}, thHi={'GB': 90}), Theta(thLo={'GB': 80}, thHi={'GB': 91}), Theta(thLo={'GB': 80}, thHi={'GB': 92}), Theta(thLo={'GB': 80}, thHi={'GB': 93}), Theta(thLo={'GB': 80}, thHi={'GB': 94}), Theta(thLo={'GB': 80}, thHi={'GB': 95}), Theta(thLo={'GB': 80}, thHi={'GB': 96}), Theta(thLo={'GB': 80}, thHi={'GB': 97}), Theta(thLo={'GB': 80}, thHi={'GB': 98}), Theta(thLo={'GB': 80}, thHi={'GB': 99}), Theta(thLo={'GB': 81}, thHi={'GB': 10}), Theta(thLo={'GB': 81}, thHi={'GB': 11}), Theta(thLo={'GB': 81}, thHi={'GB': 12}), Theta(thLo={'GB': 81}, thHi={'GB': 13}), Theta(thLo={'GB': 81}, thHi={'GB': 14}), Theta(thLo={'GB': 81}, thHi={'GB': 15}), Theta(thLo={'GB': 81}, thHi={'GB': 16}), Theta(thLo={'GB': 81}, thHi={'GB': 17}), Theta(thLo={'GB': 81}, thHi={'GB': 18}), Theta(thLo={'GB': 81}, thHi={'GB': 19}), Theta(thLo={'GB': 81}, thHi={'GB': 20}), Theta(thLo={'GB': 81}, thHi={'GB': 21}), Theta(thLo={'GB': 81}, thHi={'GB': 22}), Theta(thLo={'GB': 81}, thHi={'GB': 23}), Theta(thLo={'GB': 81}, thHi={'GB': 24}), Theta(thLo={'GB': 81}, thHi={'GB': 25}), Theta(thLo={'GB': 81}, thHi={'GB': 26}), Theta(thLo={'GB': 81}, thHi={'GB': 27}), Theta(thLo={'GB': 81}, thHi={'GB': 28}), Theta(thLo={'GB': 81}, thHi={'GB': 29}), Theta(thLo={'GB': 81}, thHi={'GB': 30}), Theta(thLo={'GB': 81}, thHi={'GB': 31}), Theta(thLo={'GB': 81}, thHi={'GB': 32}), Theta(thLo={'GB': 81}, thHi={'GB': 33}), Theta(thLo={'GB': 81}, thHi={'GB': 34}), Theta(thLo={'GB': 81}, thHi={'GB': 35}), Theta(thLo={'GB': 81}, thHi={'GB': 36}), Theta(thLo={'GB': 81}, thHi={'GB': 37}), Theta(thLo={'GB': 81}, thHi={'GB': 38}), Theta(thLo={'GB': 81}, thHi={'GB': 39}), Theta(thLo={'GB': 81}, thHi={'GB': 40}), Theta(thLo={'GB': 81}, thHi={'GB': 41}), Theta(thLo={'GB': 81}, thHi={'GB': 42}), Theta(thLo={'GB': 81}, thHi={'GB': 43}), Theta(thLo={'GB': 81}, thHi={'GB': 44}), Theta(thLo={'GB': 81}, thHi={'GB': 45}), Theta(thLo={'GB': 81}, thHi={'GB': 46}), Theta(thLo={'GB': 81}, thHi={'GB': 47}), Theta(thLo={'GB': 81}, thHi={'GB': 48}), Theta(thLo={'GB': 81}, thHi={'GB': 49}), Theta(thLo={'GB': 81}, thHi={'GB': 50}), Theta(thLo={'GB': 81}, thHi={'GB': 51}), Theta(thLo={'GB': 81}, thHi={'GB': 52}), Theta(thLo={'GB': 81}, thHi={'GB': 53}), Theta(thLo={'GB': 81}, thHi={'GB': 54}), Theta(thLo={'GB': 81}, thHi={'GB': 55}), Theta(thLo={'GB': 81}, thHi={'GB': 56}), Theta(thLo={'GB': 81}, thHi={'GB': 57}), Theta(thLo={'GB': 81}, thHi={'GB': 58}), Theta(thLo={'GB': 81}, thHi={'GB': 59}), Theta(thLo={'GB': 81}, thHi={'GB': 60}), Theta(thLo={'GB': 81}, thHi={'GB': 61}), Theta(thLo={'GB': 81}, thHi={'GB': 62}), Theta(thLo={'GB': 81}, thHi={'GB': 63}), Theta(thLo={'GB': 81}, thHi={'GB': 64}), Theta(thLo={'GB': 81}, thHi={'GB': 65}), Theta(thLo={'GB': 81}, thHi={'GB': 66}), Theta(thLo={'GB': 81}, thHi={'GB': 67}), Theta(thLo={'GB': 81}, thHi={'GB': 68}), Theta(thLo={'GB': 81}, thHi={'GB': 69}), Theta(thLo={'GB': 81}, thHi={'GB': 70}), Theta(thLo={'GB': 81}, thHi={'GB': 71}), Theta(thLo={'GB': 81}, thHi={'GB': 72}), Theta(thLo={'GB': 81}, thHi={'GB': 73}), Theta(thLo={'GB': 81}, thHi={'GB': 74}), Theta(thLo={'GB': 81}, thHi={'GB': 75}), Theta(thLo={'GB': 81}, thHi={'GB': 76}), Theta(thLo={'GB': 81}, thHi={'GB': 77}), Theta(thLo={'GB': 81}, thHi={'GB': 78}), Theta(thLo={'GB': 81}, thHi={'GB': 79}), Theta(thLo={'GB': 81}, thHi={'GB': 80}), Theta(thLo={'GB': 81}, thHi={'GB': 81}), Theta(thLo={'GB': 81}, thHi={'GB': 82}), Theta(thLo={'GB': 81}, thHi={'GB': 83}), Theta(thLo={'GB': 81}, thHi={'GB': 84}), Theta(thLo={'GB': 81}, thHi={'GB': 85}), Theta(thLo={'GB': 81}, thHi={'GB': 86}), Theta(thLo={'GB': 81}, thHi={'GB': 87}), Theta(thLo={'GB': 81}, thHi={'GB': 88}), Theta(thLo={'GB': 81}, thHi={'GB': 89}), Theta(thLo={'GB': 81}, thHi={'GB': 90}), Theta(thLo={'GB': 81}, thHi={'GB': 91}), Theta(thLo={'GB': 81}, thHi={'GB': 92}), Theta(thLo={'GB': 81}, thHi={'GB': 93}), Theta(thLo={'GB': 81}, thHi={'GB': 94}), Theta(thLo={'GB': 81}, thHi={'GB': 95}), Theta(thLo={'GB': 81}, thHi={'GB': 96}), Theta(thLo={'GB': 81}, thHi={'GB': 97}), Theta(thLo={'GB': 81}, thHi={'GB': 98}), Theta(thLo={'GB': 81}, thHi={'GB': 99}), Theta(thLo={'GB': 82}, thHi={'GB': 10}), Theta(thLo={'GB': 82}, thHi={'GB': 11}), Theta(thLo={'GB': 82}, thHi={'GB': 12}), Theta(thLo={'GB': 82}, thHi={'GB': 13}), Theta(thLo={'GB': 82}, thHi={'GB': 14}), Theta(thLo={'GB': 82}, thHi={'GB': 15}), Theta(thLo={'GB': 82}, thHi={'GB': 16}), Theta(thLo={'GB': 82}, thHi={'GB': 17}), Theta(thLo={'GB': 82}, thHi={'GB': 18}), Theta(thLo={'GB': 82}, thHi={'GB': 19}), Theta(thLo={'GB': 82}, thHi={'GB': 20}), Theta(thLo={'GB': 82}, thHi={'GB': 21}), Theta(thLo={'GB': 82}, thHi={'GB': 22}), Theta(thLo={'GB': 82}, thHi={'GB': 23}), Theta(thLo={'GB': 82}, thHi={'GB': 24}), Theta(thLo={'GB': 82}, thHi={'GB': 25}), Theta(thLo={'GB': 82}, thHi={'GB': 26}), Theta(thLo={'GB': 82}, thHi={'GB': 27}), Theta(thLo={'GB': 82}, thHi={'GB': 28}), Theta(thLo={'GB': 82}, thHi={'GB': 29}), Theta(thLo={'GB': 82}, thHi={'GB': 30}), Theta(thLo={'GB': 82}, thHi={'GB': 31}), Theta(thLo={'GB': 82}, thHi={'GB': 32}), Theta(thLo={'GB': 82}, thHi={'GB': 33}), Theta(thLo={'GB': 82}, thHi={'GB': 34}), Theta(thLo={'GB': 82}, thHi={'GB': 35}), Theta(thLo={'GB': 82}, thHi={'GB': 36}), Theta(thLo={'GB': 82}, thHi={'GB': 37}), Theta(thLo={'GB': 82}, thHi={'GB': 38}), Theta(thLo={'GB': 82}, thHi={'GB': 39}), Theta(thLo={'GB': 82}, thHi={'GB': 40}), Theta(thLo={'GB': 82}, thHi={'GB': 41}), Theta(thLo={'GB': 82}, thHi={'GB': 42}), Theta(thLo={'GB': 82}, thHi={'GB': 43}), Theta(thLo={'GB': 82}, thHi={'GB': 44}), Theta(thLo={'GB': 82}, thHi={'GB': 45}), Theta(thLo={'GB': 82}, thHi={'GB': 46}), Theta(thLo={'GB': 82}, thHi={'GB': 47}), Theta(thLo={'GB': 82}, thHi={'GB': 48}), Theta(thLo={'GB': 82}, thHi={'GB': 49}), Theta(thLo={'GB': 82}, thHi={'GB': 50}), Theta(thLo={'GB': 82}, thHi={'GB': 51}), Theta(thLo={'GB': 82}, thHi={'GB': 52}), Theta(thLo={'GB': 82}, thHi={'GB': 53}), Theta(thLo={'GB': 82}, thHi={'GB': 54}), Theta(thLo={'GB': 82}, thHi={'GB': 55}), Theta(thLo={'GB': 82}, thHi={'GB': 56}), Theta(thLo={'GB': 82}, thHi={'GB': 57}), Theta(thLo={'GB': 82}, thHi={'GB': 58}), Theta(thLo={'GB': 82}, thHi={'GB': 59}), Theta(thLo={'GB': 82}, thHi={'GB': 60}), Theta(thLo={'GB': 82}, thHi={'GB': 61}), Theta(thLo={'GB': 82}, thHi={'GB': 62}), Theta(thLo={'GB': 82}, thHi={'GB': 63}), Theta(thLo={'GB': 82}, thHi={'GB': 64}), Theta(thLo={'GB': 82}, thHi={'GB': 65}), Theta(thLo={'GB': 82}, thHi={'GB': 66}), Theta(thLo={'GB': 82}, thHi={'GB': 67}), Theta(thLo={'GB': 82}, thHi={'GB': 68}), Theta(thLo={'GB': 82}, thHi={'GB': 69}), Theta(thLo={'GB': 82}, thHi={'GB': 70}), Theta(thLo={'GB': 82}, thHi={'GB': 71}), Theta(thLo={'GB': 82}, thHi={'GB': 72}), Theta(thLo={'GB': 82}, thHi={'GB': 73}), Theta(thLo={'GB': 82}, thHi={'GB': 74}), Theta(thLo={'GB': 82}, thHi={'GB': 75}), Theta(thLo={'GB': 82}, thHi={'GB': 76}), Theta(thLo={'GB': 82}, thHi={'GB': 77}), Theta(thLo={'GB': 82}, thHi={'GB': 78}), Theta(thLo={'GB': 82}, thHi={'GB': 79}), Theta(thLo={'GB': 82}, thHi={'GB': 80}), Theta(thLo={'GB': 82}, thHi={'GB': 81}), Theta(thLo={'GB': 82}, thHi={'GB': 82}), Theta(thLo={'GB': 82}, thHi={'GB': 83}), Theta(thLo={'GB': 82}, thHi={'GB': 84}), Theta(thLo={'GB': 82}, thHi={'GB': 85}), Theta(thLo={'GB': 82}, thHi={'GB': 86}), Theta(thLo={'GB': 82}, thHi={'GB': 87}), Theta(thLo={'GB': 82}, thHi={'GB': 88}), Theta(thLo={'GB': 82}, thHi={'GB': 89}), Theta(thLo={'GB': 82}, thHi={'GB': 90}), Theta(thLo={'GB': 82}, thHi={'GB': 91}), Theta(thLo={'GB': 82}, thHi={'GB': 92}), Theta(thLo={'GB': 82}, thHi={'GB': 93}), Theta(thLo={'GB': 82}, thHi={'GB': 94}), Theta(thLo={'GB': 82}, thHi={'GB': 95}), Theta(thLo={'GB': 82}, thHi={'GB': 96}), Theta(thLo={'GB': 82}, thHi={'GB': 97}), Theta(thLo={'GB': 82}, thHi={'GB': 98}), Theta(thLo={'GB': 82}, thHi={'GB': 99}), Theta(thLo={'GB': 83}, thHi={'GB': 10}), Theta(thLo={'GB': 83}, thHi={'GB': 11}), Theta(thLo={'GB': 83}, thHi={'GB': 12}), Theta(thLo={'GB': 83}, thHi={'GB': 13}), Theta(thLo={'GB': 83}, thHi={'GB': 14}), Theta(thLo={'GB': 83}, thHi={'GB': 15}), Theta(thLo={'GB': 83}, thHi={'GB': 16}), Theta(thLo={'GB': 83}, thHi={'GB': 17}), Theta(thLo={'GB': 83}, thHi={'GB': 18}), Theta(thLo={'GB': 83}, thHi={'GB': 19}), Theta(thLo={'GB': 83}, thHi={'GB': 20}), Theta(thLo={'GB': 83}, thHi={'GB': 21}), Theta(thLo={'GB': 83}, thHi={'GB': 22}), Theta(thLo={'GB': 83}, thHi={'GB': 23}), Theta(thLo={'GB': 83}, thHi={'GB': 24}), Theta(thLo={'GB': 83}, thHi={'GB': 25}), Theta(thLo={'GB': 83}, thHi={'GB': 26}), Theta(thLo={'GB': 83}, thHi={'GB': 27}), Theta(thLo={'GB': 83}, thHi={'GB': 28}), Theta(thLo={'GB': 83}, thHi={'GB': 29}), Theta(thLo={'GB': 83}, thHi={'GB': 30}), Theta(thLo={'GB': 83}, thHi={'GB': 31}), Theta(thLo={'GB': 83}, thHi={'GB': 32}), Theta(thLo={'GB': 83}, thHi={'GB': 33}), Theta(thLo={'GB': 83}, thHi={'GB': 34}), Theta(thLo={'GB': 83}, thHi={'GB': 35}), Theta(thLo={'GB': 83}, thHi={'GB': 36}), Theta(thLo={'GB': 83}, thHi={'GB': 37}), Theta(thLo={'GB': 83}, thHi={'GB': 38}), Theta(thLo={'GB': 83}, thHi={'GB': 39}), Theta(thLo={'GB': 83}, thHi={'GB': 40}), Theta(thLo={'GB': 83}, thHi={'GB': 41}), Theta(thLo={'GB': 83}, thHi={'GB': 42}), Theta(thLo={'GB': 83}, thHi={'GB': 43}), Theta(thLo={'GB': 83}, thHi={'GB': 44}), Theta(thLo={'GB': 83}, thHi={'GB': 45}), Theta(thLo={'GB': 83}, thHi={'GB': 46}), Theta(thLo={'GB': 83}, thHi={'GB': 47}), Theta(thLo={'GB': 83}, thHi={'GB': 48}), Theta(thLo={'GB': 83}, thHi={'GB': 49}), Theta(thLo={'GB': 83}, thHi={'GB': 50}), Theta(thLo={'GB': 83}, thHi={'GB': 51}), Theta(thLo={'GB': 83}, thHi={'GB': 52}), Theta(thLo={'GB': 83}, thHi={'GB': 53}), Theta(thLo={'GB': 83}, thHi={'GB': 54}), Theta(thLo={'GB': 83}, thHi={'GB': 55}), Theta(thLo={'GB': 83}, thHi={'GB': 56}), Theta(thLo={'GB': 83}, thHi={'GB': 57}), Theta(thLo={'GB': 83}, thHi={'GB': 58}), Theta(thLo={'GB': 83}, thHi={'GB': 59}), Theta(thLo={'GB': 83}, thHi={'GB': 60}), Theta(thLo={'GB': 83}, thHi={'GB': 61}), Theta(thLo={'GB': 83}, thHi={'GB': 62}), Theta(thLo={'GB': 83}, thHi={'GB': 63}), Theta(thLo={'GB': 83}, thHi={'GB': 64}), Theta(thLo={'GB': 83}, thHi={'GB': 65}), Theta(thLo={'GB': 83}, thHi={'GB': 66}), Theta(thLo={'GB': 83}, thHi={'GB': 67}), Theta(thLo={'GB': 83}, thHi={'GB': 68}), Theta(thLo={'GB': 83}, thHi={'GB': 69}), Theta(thLo={'GB': 83}, thHi={'GB': 70}), Theta(thLo={'GB': 83}, thHi={'GB': 71}), Theta(thLo={'GB': 83}, thHi={'GB': 72}), Theta(thLo={'GB': 83}, thHi={'GB': 73}), Theta(thLo={'GB': 83}, thHi={'GB': 74}), Theta(thLo={'GB': 83}, thHi={'GB': 75}), Theta(thLo={'GB': 83}, thHi={'GB': 76}), Theta(thLo={'GB': 83}, thHi={'GB': 77}), Theta(thLo={'GB': 83}, thHi={'GB': 78}), Theta(thLo={'GB': 83}, thHi={'GB': 79}), Theta(thLo={'GB': 83}, thHi={'GB': 80}), Theta(thLo={'GB': 83}, thHi={'GB': 81}), Theta(thLo={'GB': 83}, thHi={'GB': 82}), Theta(thLo={'GB': 83}, thHi={'GB': 83}), Theta(thLo={'GB': 83}, thHi={'GB': 84}), Theta(thLo={'GB': 83}, thHi={'GB': 85}), Theta(thLo={'GB': 83}, thHi={'GB': 86}), Theta(thLo={'GB': 83}, thHi={'GB': 87}), Theta(thLo={'GB': 83}, thHi={'GB': 88}), Theta(thLo={'GB': 83}, thHi={'GB': 89}), Theta(thLo={'GB': 83}, thHi={'GB': 90}), Theta(thLo={'GB': 83}, thHi={'GB': 91}), Theta(thLo={'GB': 83}, thHi={'GB': 92}), Theta(thLo={'GB': 83}, thHi={'GB': 93}), Theta(thLo={'GB': 83}, thHi={'GB': 94}), Theta(thLo={'GB': 83}, thHi={'GB': 95}), Theta(thLo={'GB': 83}, thHi={'GB': 96}), Theta(thLo={'GB': 83}, thHi={'GB': 97}), Theta(thLo={'GB': 83}, thHi={'GB': 98}), Theta(thLo={'GB': 83}, thHi={'GB': 99}), Theta(thLo={'GB': 84}, thHi={'GB': 10}), Theta(thLo={'GB': 84}, thHi={'GB': 11}), Theta(thLo={'GB': 84}, thHi={'GB': 12}), Theta(thLo={'GB': 84}, thHi={'GB': 13}), Theta(thLo={'GB': 84}, thHi={'GB': 14}), Theta(thLo={'GB': 84}, thHi={'GB': 15}), Theta(thLo={'GB': 84}, thHi={'GB': 16}), Theta(thLo={'GB': 84}, thHi={'GB': 17}), Theta(thLo={'GB': 84}, thHi={'GB': 18}), Theta(thLo={'GB': 84}, thHi={'GB': 19}), Theta(thLo={'GB': 84}, thHi={'GB': 20}), Theta(thLo={'GB': 84}, thHi={'GB': 21}), Theta(thLo={'GB': 84}, thHi={'GB': 22}), Theta(thLo={'GB': 84}, thHi={'GB': 23}), Theta(thLo={'GB': 84}, thHi={'GB': 24}), Theta(thLo={'GB': 84}, thHi={'GB': 25}), Theta(thLo={'GB': 84}, thHi={'GB': 26}), Theta(thLo={'GB': 84}, thHi={'GB': 27}), Theta(thLo={'GB': 84}, thHi={'GB': 28}), Theta(thLo={'GB': 84}, thHi={'GB': 29}), Theta(thLo={'GB': 84}, thHi={'GB': 30}), Theta(thLo={'GB': 84}, thHi={'GB': 31}), Theta(thLo={'GB': 84}, thHi={'GB': 32}), Theta(thLo={'GB': 84}, thHi={'GB': 33}), Theta(thLo={'GB': 84}, thHi={'GB': 34}), Theta(thLo={'GB': 84}, thHi={'GB': 35}), Theta(thLo={'GB': 84}, thHi={'GB': 36}), Theta(thLo={'GB': 84}, thHi={'GB': 37}), Theta(thLo={'GB': 84}, thHi={'GB': 38}), Theta(thLo={'GB': 84}, thHi={'GB': 39}), Theta(thLo={'GB': 84}, thHi={'GB': 40}), Theta(thLo={'GB': 84}, thHi={'GB': 41}), Theta(thLo={'GB': 84}, thHi={'GB': 42}), Theta(thLo={'GB': 84}, thHi={'GB': 43}), Theta(thLo={'GB': 84}, thHi={'GB': 44}), Theta(thLo={'GB': 84}, thHi={'GB': 45}), Theta(thLo={'GB': 84}, thHi={'GB': 46}), Theta(thLo={'GB': 84}, thHi={'GB': 47}), Theta(thLo={'GB': 84}, thHi={'GB': 48}), Theta(thLo={'GB': 84}, thHi={'GB': 49}), Theta(thLo={'GB': 84}, thHi={'GB': 50}), Theta(thLo={'GB': 84}, thHi={'GB': 51}), Theta(thLo={'GB': 84}, thHi={'GB': 52}), Theta(thLo={'GB': 84}, thHi={'GB': 53}), Theta(thLo={'GB': 84}, thHi={'GB': 54}), Theta(thLo={'GB': 84}, thHi={'GB': 55}), Theta(thLo={'GB': 84}, thHi={'GB': 56}), Theta(thLo={'GB': 84}, thHi={'GB': 57}), Theta(thLo={'GB': 84}, thHi={'GB': 58}), Theta(thLo={'GB': 84}, thHi={'GB': 59}), Theta(thLo={'GB': 84}, thHi={'GB': 60}), Theta(thLo={'GB': 84}, thHi={'GB': 61}), Theta(thLo={'GB': 84}, thHi={'GB': 62}), Theta(thLo={'GB': 84}, thHi={'GB': 63}), Theta(thLo={'GB': 84}, thHi={'GB': 64}), Theta(thLo={'GB': 84}, thHi={'GB': 65}), Theta(thLo={'GB': 84}, thHi={'GB': 66}), Theta(thLo={'GB': 84}, thHi={'GB': 67}), Theta(thLo={'GB': 84}, thHi={'GB': 68}), Theta(thLo={'GB': 84}, thHi={'GB': 69}), Theta(thLo={'GB': 84}, thHi={'GB': 70}), Theta(thLo={'GB': 84}, thHi={'GB': 71}), Theta(thLo={'GB': 84}, thHi={'GB': 72}), Theta(thLo={'GB': 84}, thHi={'GB': 73}), Theta(thLo={'GB': 84}, thHi={'GB': 74}), Theta(thLo={'GB': 84}, thHi={'GB': 75}), Theta(thLo={'GB': 84}, thHi={'GB': 76}), Theta(thLo={'GB': 84}, thHi={'GB': 77}), Theta(thLo={'GB': 84}, thHi={'GB': 78}), Theta(thLo={'GB': 84}, thHi={'GB': 79}), Theta(thLo={'GB': 84}, thHi={'GB': 80}), Theta(thLo={'GB': 84}, thHi={'GB': 81}), Theta(thLo={'GB': 84}, thHi={'GB': 82}), Theta(thLo={'GB': 84}, thHi={'GB': 83}), Theta(thLo={'GB': 84}, thHi={'GB': 84}), Theta(thLo={'GB': 84}, thHi={'GB': 85}), Theta(thLo={'GB': 84}, thHi={'GB': 86}), Theta(thLo={'GB': 84}, thHi={'GB': 87}), Theta(thLo={'GB': 84}, thHi={'GB': 88}), Theta(thLo={'GB': 84}, thHi={'GB': 89}), Theta(thLo={'GB': 84}, thHi={'GB': 90}), Theta(thLo={'GB': 84}, thHi={'GB': 91}), Theta(thLo={'GB': 84}, thHi={'GB': 92}), Theta(thLo={'GB': 84}, thHi={'GB': 93}), Theta(thLo={'GB': 84}, thHi={'GB': 94}), Theta(thLo={'GB': 84}, thHi={'GB': 95}), Theta(thLo={'GB': 84}, thHi={'GB': 96}), Theta(thLo={'GB': 84}, thHi={'GB': 97}), Theta(thLo={'GB': 84}, thHi={'GB': 98}), Theta(thLo={'GB': 84}, thHi={'GB': 99}), Theta(thLo={'GB': 85}, thHi={'GB': 10}), Theta(thLo={'GB': 85}, thHi={'GB': 11}), Theta(thLo={'GB': 85}, thHi={'GB': 12}), Theta(thLo={'GB': 85}, thHi={'GB': 13}), Theta(thLo={'GB': 85}, thHi={'GB': 14}), Theta(thLo={'GB': 85}, thHi={'GB': 15}), Theta(thLo={'GB': 85}, thHi={'GB': 16}), Theta(thLo={'GB': 85}, thHi={'GB': 17}), Theta(thLo={'GB': 85}, thHi={'GB': 18}), Theta(thLo={'GB': 85}, thHi={'GB': 19}), Theta(thLo={'GB': 85}, thHi={'GB': 20}), Theta(thLo={'GB': 85}, thHi={'GB': 21}), Theta(thLo={'GB': 85}, thHi={'GB': 22}), Theta(thLo={'GB': 85}, thHi={'GB': 23}), Theta(thLo={'GB': 85}, thHi={'GB': 24}), Theta(thLo={'GB': 85}, thHi={'GB': 25}), Theta(thLo={'GB': 85}, thHi={'GB': 26}), Theta(thLo={'GB': 85}, thHi={'GB': 27}), Theta(thLo={'GB': 85}, thHi={'GB': 28}), Theta(thLo={'GB': 85}, thHi={'GB': 29}), Theta(thLo={'GB': 85}, thHi={'GB': 30}), Theta(thLo={'GB': 85}, thHi={'GB': 31}), Theta(thLo={'GB': 85}, thHi={'GB': 32}), Theta(thLo={'GB': 85}, thHi={'GB': 33}), Theta(thLo={'GB': 85}, thHi={'GB': 34}), Theta(thLo={'GB': 85}, thHi={'GB': 35}), Theta(thLo={'GB': 85}, thHi={'GB': 36}), Theta(thLo={'GB': 85}, thHi={'GB': 37}), Theta(thLo={'GB': 85}, thHi={'GB': 38}), Theta(thLo={'GB': 85}, thHi={'GB': 39}), Theta(thLo={'GB': 85}, thHi={'GB': 40}), Theta(thLo={'GB': 85}, thHi={'GB': 41}), Theta(thLo={'GB': 85}, thHi={'GB': 42}), Theta(thLo={'GB': 85}, thHi={'GB': 43}), Theta(thLo={'GB': 85}, thHi={'GB': 44}), Theta(thLo={'GB': 85}, thHi={'GB': 45}), Theta(thLo={'GB': 85}, thHi={'GB': 46}), Theta(thLo={'GB': 85}, thHi={'GB': 47}), Theta(thLo={'GB': 85}, thHi={'GB': 48}), Theta(thLo={'GB': 85}, thHi={'GB': 49}), Theta(thLo={'GB': 85}, thHi={'GB': 50}), Theta(thLo={'GB': 85}, thHi={'GB': 51}), Theta(thLo={'GB': 85}, thHi={'GB': 52}), Theta(thLo={'GB': 85}, thHi={'GB': 53}), Theta(thLo={'GB': 85}, thHi={'GB': 54}), Theta(thLo={'GB': 85}, thHi={'GB': 55}), Theta(thLo={'GB': 85}, thHi={'GB': 56}), Theta(thLo={'GB': 85}, thHi={'GB': 57}), Theta(thLo={'GB': 85}, thHi={'GB': 58}), Theta(thLo={'GB': 85}, thHi={'GB': 59}), Theta(thLo={'GB': 85}, thHi={'GB': 60}), Theta(thLo={'GB': 85}, thHi={'GB': 61}), Theta(thLo={'GB': 85}, thHi={'GB': 62}), Theta(thLo={'GB': 85}, thHi={'GB': 63}), Theta(thLo={'GB': 85}, thHi={'GB': 64}), Theta(thLo={'GB': 85}, thHi={'GB': 65}), Theta(thLo={'GB': 85}, thHi={'GB': 66}), Theta(thLo={'GB': 85}, thHi={'GB': 67}), Theta(thLo={'GB': 85}, thHi={'GB': 68}), Theta(thLo={'GB': 85}, thHi={'GB': 69}), Theta(thLo={'GB': 85}, thHi={'GB': 70}), Theta(thLo={'GB': 85}, thHi={'GB': 71}), Theta(thLo={'GB': 85}, thHi={'GB': 72}), Theta(thLo={'GB': 85}, thHi={'GB': 73}), Theta(thLo={'GB': 85}, thHi={'GB': 74}), Theta(thLo={'GB': 85}, thHi={'GB': 75}), Theta(thLo={'GB': 85}, thHi={'GB': 76}), Theta(thLo={'GB': 85}, thHi={'GB': 77}), Theta(thLo={'GB': 85}, thHi={'GB': 78}), Theta(thLo={'GB': 85}, thHi={'GB': 79}), Theta(thLo={'GB': 85}, thHi={'GB': 80}), Theta(thLo={'GB': 85}, thHi={'GB': 81}), Theta(thLo={'GB': 85}, thHi={'GB': 82}), Theta(thLo={'GB': 85}, thHi={'GB': 83}), Theta(thLo={'GB': 85}, thHi={'GB': 84}), Theta(thLo={'GB': 85}, thHi={'GB': 85}), Theta(thLo={'GB': 85}, thHi={'GB': 86}), Theta(thLo={'GB': 85}, thHi={'GB': 87}), Theta(thLo={'GB': 85}, thHi={'GB': 88}), Theta(thLo={'GB': 85}, thHi={'GB': 89}), Theta(thLo={'GB': 85}, thHi={'GB': 90}), Theta(thLo={'GB': 85}, thHi={'GB': 91}), Theta(thLo={'GB': 85}, thHi={'GB': 92}), Theta(thLo={'GB': 85}, thHi={'GB': 93}), Theta(thLo={'GB': 85}, thHi={'GB': 94}), Theta(thLo={'GB': 85}, thHi={'GB': 95}), Theta(thLo={'GB': 85}, thHi={'GB': 96}), Theta(thLo={'GB': 85}, thHi={'GB': 97}), Theta(thLo={'GB': 85}, thHi={'GB': 98}), Theta(thLo={'GB': 85}, thHi={'GB': 99}), Theta(thLo={'GB': 86}, thHi={'GB': 10}), Theta(thLo={'GB': 86}, thHi={'GB': 11}), Theta(thLo={'GB': 86}, thHi={'GB': 12}), Theta(thLo={'GB': 86}, thHi={'GB': 13}), Theta(thLo={'GB': 86}, thHi={'GB': 14}), Theta(thLo={'GB': 86}, thHi={'GB': 15}), Theta(thLo={'GB': 86}, thHi={'GB': 16}), Theta(thLo={'GB': 86}, thHi={'GB': 17}), Theta(thLo={'GB': 86}, thHi={'GB': 18}), Theta(thLo={'GB': 86}, thHi={'GB': 19}), Theta(thLo={'GB': 86}, thHi={'GB': 20}), Theta(thLo={'GB': 86}, thHi={'GB': 21}), Theta(thLo={'GB': 86}, thHi={'GB': 22}), Theta(thLo={'GB': 86}, thHi={'GB': 23}), Theta(thLo={'GB': 86}, thHi={'GB': 24}), Theta(thLo={'GB': 86}, thHi={'GB': 25}), Theta(thLo={'GB': 86}, thHi={'GB': 26}), Theta(thLo={'GB': 86}, thHi={'GB': 27}), Theta(thLo={'GB': 86}, thHi={'GB': 28}), Theta(thLo={'GB': 86}, thHi={'GB': 29}), Theta(thLo={'GB': 86}, thHi={'GB': 30}), Theta(thLo={'GB': 86}, thHi={'GB': 31}), Theta(thLo={'GB': 86}, thHi={'GB': 32}), Theta(thLo={'GB': 86}, thHi={'GB': 33}), Theta(thLo={'GB': 86}, thHi={'GB': 34}), Theta(thLo={'GB': 86}, thHi={'GB': 35}), Theta(thLo={'GB': 86}, thHi={'GB': 36}), Theta(thLo={'GB': 86}, thHi={'GB': 37}), Theta(thLo={'GB': 86}, thHi={'GB': 38}), Theta(thLo={'GB': 86}, thHi={'GB': 39}), Theta(thLo={'GB': 86}, thHi={'GB': 40}), Theta(thLo={'GB': 86}, thHi={'GB': 41}), Theta(thLo={'GB': 86}, thHi={'GB': 42}), Theta(thLo={'GB': 86}, thHi={'GB': 43}), Theta(thLo={'GB': 86}, thHi={'GB': 44}), Theta(thLo={'GB': 86}, thHi={'GB': 45}), Theta(thLo={'GB': 86}, thHi={'GB': 46}), Theta(thLo={'GB': 86}, thHi={'GB': 47}), Theta(thLo={'GB': 86}, thHi={'GB': 48}), Theta(thLo={'GB': 86}, thHi={'GB': 49}), Theta(thLo={'GB': 86}, thHi={'GB': 50}), Theta(thLo={'GB': 86}, thHi={'GB': 51}), Theta(thLo={'GB': 86}, thHi={'GB': 52}), Theta(thLo={'GB': 86}, thHi={'GB': 53}), Theta(thLo={'GB': 86}, thHi={'GB': 54}), Theta(thLo={'GB': 86}, thHi={'GB': 55}), Theta(thLo={'GB': 86}, thHi={'GB': 56}), Theta(thLo={'GB': 86}, thHi={'GB': 57}), Theta(thLo={'GB': 86}, thHi={'GB': 58}), Theta(thLo={'GB': 86}, thHi={'GB': 59}), Theta(thLo={'GB': 86}, thHi={'GB': 60}), Theta(thLo={'GB': 86}, thHi={'GB': 61}), Theta(thLo={'GB': 86}, thHi={'GB': 62}), Theta(thLo={'GB': 86}, thHi={'GB': 63}), Theta(thLo={'GB': 86}, thHi={'GB': 64}), Theta(thLo={'GB': 86}, thHi={'GB': 65}), Theta(thLo={'GB': 86}, thHi={'GB': 66}), Theta(thLo={'GB': 86}, thHi={'GB': 67}), Theta(thLo={'GB': 86}, thHi={'GB': 68}), Theta(thLo={'GB': 86}, thHi={'GB': 69}), Theta(thLo={'GB': 86}, thHi={'GB': 70}), Theta(thLo={'GB': 86}, thHi={'GB': 71}), Theta(thLo={'GB': 86}, thHi={'GB': 72}), Theta(thLo={'GB': 86}, thHi={'GB': 73}), Theta(thLo={'GB': 86}, thHi={'GB': 74}), Theta(thLo={'GB': 86}, thHi={'GB': 75}), Theta(thLo={'GB': 86}, thHi={'GB': 76}), Theta(thLo={'GB': 86}, thHi={'GB': 77}), Theta(thLo={'GB': 86}, thHi={'GB': 78}), Theta(thLo={'GB': 86}, thHi={'GB': 79}), Theta(thLo={'GB': 86}, thHi={'GB': 80}), Theta(thLo={'GB': 86}, thHi={'GB': 81}), Theta(thLo={'GB': 86}, thHi={'GB': 82}), Theta(thLo={'GB': 86}, thHi={'GB': 83}), Theta(thLo={'GB': 86}, thHi={'GB': 84}), Theta(thLo={'GB': 86}, thHi={'GB': 85}), Theta(thLo={'GB': 86}, thHi={'GB': 86}), Theta(thLo={'GB': 86}, thHi={'GB': 87}), Theta(thLo={'GB': 86}, thHi={'GB': 88}), Theta(thLo={'GB': 86}, thHi={'GB': 89}), Theta(thLo={'GB': 86}, thHi={'GB': 90}), Theta(thLo={'GB': 86}, thHi={'GB': 91}), Theta(thLo={'GB': 86}, thHi={'GB': 92}), Theta(thLo={'GB': 86}, thHi={'GB': 93}), Theta(thLo={'GB': 86}, thHi={'GB': 94}), Theta(thLo={'GB': 86}, thHi={'GB': 95}), Theta(thLo={'GB': 86}, thHi={'GB': 96}), Theta(thLo={'GB': 86}, thHi={'GB': 97}), Theta(thLo={'GB': 86}, thHi={'GB': 98}), Theta(thLo={'GB': 86}, thHi={'GB': 99}), Theta(thLo={'GB': 87}, thHi={'GB': 10}), Theta(thLo={'GB': 87}, thHi={'GB': 11}), Theta(thLo={'GB': 87}, thHi={'GB': 12}), Theta(thLo={'GB': 87}, thHi={'GB': 13}), Theta(thLo={'GB': 87}, thHi={'GB': 14}), Theta(thLo={'GB': 87}, thHi={'GB': 15}), Theta(thLo={'GB': 87}, thHi={'GB': 16}), Theta(thLo={'GB': 87}, thHi={'GB': 17}), Theta(thLo={'GB': 87}, thHi={'GB': 18}), Theta(thLo={'GB': 87}, thHi={'GB': 19}), Theta(thLo={'GB': 87}, thHi={'GB': 20}), Theta(thLo={'GB': 87}, thHi={'GB': 21}), Theta(thLo={'GB': 87}, thHi={'GB': 22}), Theta(thLo={'GB': 87}, thHi={'GB': 23}), Theta(thLo={'GB': 87}, thHi={'GB': 24}), Theta(thLo={'GB': 87}, thHi={'GB': 25}), Theta(thLo={'GB': 87}, thHi={'GB': 26}), Theta(thLo={'GB': 87}, thHi={'GB': 27}), Theta(thLo={'GB': 87}, thHi={'GB': 28}), Theta(thLo={'GB': 87}, thHi={'GB': 29}), Theta(thLo={'GB': 87}, thHi={'GB': 30}), Theta(thLo={'GB': 87}, thHi={'GB': 31}), Theta(thLo={'GB': 87}, thHi={'GB': 32}), Theta(thLo={'GB': 87}, thHi={'GB': 33}), Theta(thLo={'GB': 87}, thHi={'GB': 34}), Theta(thLo={'GB': 87}, thHi={'GB': 35}), Theta(thLo={'GB': 87}, thHi={'GB': 36}), Theta(thLo={'GB': 87}, thHi={'GB': 37}), Theta(thLo={'GB': 87}, thHi={'GB': 38}), Theta(thLo={'GB': 87}, thHi={'GB': 39}), Theta(thLo={'GB': 87}, thHi={'GB': 40}), Theta(thLo={'GB': 87}, thHi={'GB': 41}), Theta(thLo={'GB': 87}, thHi={'GB': 42}), Theta(thLo={'GB': 87}, thHi={'GB': 43}), Theta(thLo={'GB': 87}, thHi={'GB': 44}), Theta(thLo={'GB': 87}, thHi={'GB': 45}), Theta(thLo={'GB': 87}, thHi={'GB': 46}), Theta(thLo={'GB': 87}, thHi={'GB': 47}), Theta(thLo={'GB': 87}, thHi={'GB': 48}), Theta(thLo={'GB': 87}, thHi={'GB': 49}), Theta(thLo={'GB': 87}, thHi={'GB': 50}), Theta(thLo={'GB': 87}, thHi={'GB': 51}), Theta(thLo={'GB': 87}, thHi={'GB': 52}), Theta(thLo={'GB': 87}, thHi={'GB': 53}), Theta(thLo={'GB': 87}, thHi={'GB': 54}), Theta(thLo={'GB': 87}, thHi={'GB': 55}), Theta(thLo={'GB': 87}, thHi={'GB': 56}), Theta(thLo={'GB': 87}, thHi={'GB': 57}), Theta(thLo={'GB': 87}, thHi={'GB': 58}), Theta(thLo={'GB': 87}, thHi={'GB': 59}), Theta(thLo={'GB': 87}, thHi={'GB': 60}), Theta(thLo={'GB': 87}, thHi={'GB': 61}), Theta(thLo={'GB': 87}, thHi={'GB': 62}), Theta(thLo={'GB': 87}, thHi={'GB': 63}), Theta(thLo={'GB': 87}, thHi={'GB': 64}), Theta(thLo={'GB': 87}, thHi={'GB': 65}), Theta(thLo={'GB': 87}, thHi={'GB': 66}), Theta(thLo={'GB': 87}, thHi={'GB': 67}), Theta(thLo={'GB': 87}, thHi={'GB': 68}), Theta(thLo={'GB': 87}, thHi={'GB': 69}), Theta(thLo={'GB': 87}, thHi={'GB': 70}), Theta(thLo={'GB': 87}, thHi={'GB': 71}), Theta(thLo={'GB': 87}, thHi={'GB': 72}), Theta(thLo={'GB': 87}, thHi={'GB': 73}), Theta(thLo={'GB': 87}, thHi={'GB': 74}), Theta(thLo={'GB': 87}, thHi={'GB': 75}), Theta(thLo={'GB': 87}, thHi={'GB': 76}), Theta(thLo={'GB': 87}, thHi={'GB': 77}), Theta(thLo={'GB': 87}, thHi={'GB': 78}), Theta(thLo={'GB': 87}, thHi={'GB': 79}), Theta(thLo={'GB': 87}, thHi={'GB': 80}), Theta(thLo={'GB': 87}, thHi={'GB': 81}), Theta(thLo={'GB': 87}, thHi={'GB': 82}), Theta(thLo={'GB': 87}, thHi={'GB': 83}), Theta(thLo={'GB': 87}, thHi={'GB': 84}), Theta(thLo={'GB': 87}, thHi={'GB': 85}), Theta(thLo={'GB': 87}, thHi={'GB': 86}), Theta(thLo={'GB': 87}, thHi={'GB': 87}), Theta(thLo={'GB': 87}, thHi={'GB': 88}), Theta(thLo={'GB': 87}, thHi={'GB': 89}), Theta(thLo={'GB': 87}, thHi={'GB': 90}), Theta(thLo={'GB': 87}, thHi={'GB': 91}), Theta(thLo={'GB': 87}, thHi={'GB': 92}), Theta(thLo={'GB': 87}, thHi={'GB': 93}), Theta(thLo={'GB': 87}, thHi={'GB': 94}), Theta(thLo={'GB': 87}, thHi={'GB': 95}), Theta(thLo={'GB': 87}, thHi={'GB': 96}), Theta(thLo={'GB': 87}, thHi={'GB': 97}), Theta(thLo={'GB': 87}, thHi={'GB': 98}), Theta(thLo={'GB': 87}, thHi={'GB': 99}), Theta(thLo={'GB': 88}, thHi={'GB': 10}), Theta(thLo={'GB': 88}, thHi={'GB': 11}), Theta(thLo={'GB': 88}, thHi={'GB': 12}), Theta(thLo={'GB': 88}, thHi={'GB': 13}), Theta(thLo={'GB': 88}, thHi={'GB': 14}), Theta(thLo={'GB': 88}, thHi={'GB': 15}), Theta(thLo={'GB': 88}, thHi={'GB': 16}), Theta(thLo={'GB': 88}, thHi={'GB': 17}), Theta(thLo={'GB': 88}, thHi={'GB': 18}), Theta(thLo={'GB': 88}, thHi={'GB': 19}), Theta(thLo={'GB': 88}, thHi={'GB': 20}), Theta(thLo={'GB': 88}, thHi={'GB': 21}), Theta(thLo={'GB': 88}, thHi={'GB': 22}), Theta(thLo={'GB': 88}, thHi={'GB': 23}), Theta(thLo={'GB': 88}, thHi={'GB': 24}), Theta(thLo={'GB': 88}, thHi={'GB': 25}), Theta(thLo={'GB': 88}, thHi={'GB': 26}), Theta(thLo={'GB': 88}, thHi={'GB': 27}), Theta(thLo={'GB': 88}, thHi={'GB': 28}), Theta(thLo={'GB': 88}, thHi={'GB': 29}), Theta(thLo={'GB': 88}, thHi={'GB': 30}), Theta(thLo={'GB': 88}, thHi={'GB': 31}), Theta(thLo={'GB': 88}, thHi={'GB': 32}), Theta(thLo={'GB': 88}, thHi={'GB': 33}), Theta(thLo={'GB': 88}, thHi={'GB': 34}), Theta(thLo={'GB': 88}, thHi={'GB': 35}), Theta(thLo={'GB': 88}, thHi={'GB': 36}), Theta(thLo={'GB': 88}, thHi={'GB': 37}), Theta(thLo={'GB': 88}, thHi={'GB': 38}), Theta(thLo={'GB': 88}, thHi={'GB': 39}), Theta(thLo={'GB': 88}, thHi={'GB': 40}), Theta(thLo={'GB': 88}, thHi={'GB': 41}), Theta(thLo={'GB': 88}, thHi={'GB': 42}), Theta(thLo={'GB': 88}, thHi={'GB': 43}), Theta(thLo={'GB': 88}, thHi={'GB': 44}), Theta(thLo={'GB': 88}, thHi={'GB': 45}), Theta(thLo={'GB': 88}, thHi={'GB': 46}), Theta(thLo={'GB': 88}, thHi={'GB': 47}), Theta(thLo={'GB': 88}, thHi={'GB': 48}), Theta(thLo={'GB': 88}, thHi={'GB': 49}), Theta(thLo={'GB': 88}, thHi={'GB': 50}), Theta(thLo={'GB': 88}, thHi={'GB': 51}), Theta(thLo={'GB': 88}, thHi={'GB': 52}), Theta(thLo={'GB': 88}, thHi={'GB': 53}), Theta(thLo={'GB': 88}, thHi={'GB': 54}), Theta(thLo={'GB': 88}, thHi={'GB': 55}), Theta(thLo={'GB': 88}, thHi={'GB': 56}), Theta(thLo={'GB': 88}, thHi={'GB': 57}), Theta(thLo={'GB': 88}, thHi={'GB': 58}), Theta(thLo={'GB': 88}, thHi={'GB': 59}), Theta(thLo={'GB': 88}, thHi={'GB': 60}), Theta(thLo={'GB': 88}, thHi={'GB': 61}), Theta(thLo={'GB': 88}, thHi={'GB': 62}), Theta(thLo={'GB': 88}, thHi={'GB': 63}), Theta(thLo={'GB': 88}, thHi={'GB': 64}), Theta(thLo={'GB': 88}, thHi={'GB': 65}), Theta(thLo={'GB': 88}, thHi={'GB': 66}), Theta(thLo={'GB': 88}, thHi={'GB': 67}), Theta(thLo={'GB': 88}, thHi={'GB': 68}), Theta(thLo={'GB': 88}, thHi={'GB': 69}), Theta(thLo={'GB': 88}, thHi={'GB': 70}), Theta(thLo={'GB': 88}, thHi={'GB': 71}), Theta(thLo={'GB': 88}, thHi={'GB': 72}), Theta(thLo={'GB': 88}, thHi={'GB': 73}), Theta(thLo={'GB': 88}, thHi={'GB': 74}), Theta(thLo={'GB': 88}, thHi={'GB': 75}), Theta(thLo={'GB': 88}, thHi={'GB': 76}), Theta(thLo={'GB': 88}, thHi={'GB': 77}), Theta(thLo={'GB': 88}, thHi={'GB': 78}), Theta(thLo={'GB': 88}, thHi={'GB': 79}), Theta(thLo={'GB': 88}, thHi={'GB': 80}), Theta(thLo={'GB': 88}, thHi={'GB': 81}), Theta(thLo={'GB': 88}, thHi={'GB': 82}), Theta(thLo={'GB': 88}, thHi={'GB': 83}), Theta(thLo={'GB': 88}, thHi={'GB': 84}), Theta(thLo={'GB': 88}, thHi={'GB': 85}), Theta(thLo={'GB': 88}, thHi={'GB': 86}), Theta(thLo={'GB': 88}, thHi={'GB': 87}), Theta(thLo={'GB': 88}, thHi={'GB': 88}), Theta(thLo={'GB': 88}, thHi={'GB': 89}), Theta(thLo={'GB': 88}, thHi={'GB': 90}), Theta(thLo={'GB': 88}, thHi={'GB': 91}), Theta(thLo={'GB': 88}, thHi={'GB': 92}), Theta(thLo={'GB': 88}, thHi={'GB': 93}), Theta(thLo={'GB': 88}, thHi={'GB': 94}), Theta(thLo={'GB': 88}, thHi={'GB': 95}), Theta(thLo={'GB': 88}, thHi={'GB': 96}), Theta(thLo={'GB': 88}, thHi={'GB': 97}), Theta(thLo={'GB': 88}, thHi={'GB': 98}), Theta(thLo={'GB': 88}, thHi={'GB': 99}), Theta(thLo={'GB': 89}, thHi={'GB': 10}), Theta(thLo={'GB': 89}, thHi={'GB': 11}), Theta(thLo={'GB': 89}, thHi={'GB': 12}), Theta(thLo={'GB': 89}, thHi={'GB': 13}), Theta(thLo={'GB': 89}, thHi={'GB': 14}), Theta(thLo={'GB': 89}, thHi={'GB': 15}), Theta(thLo={'GB': 89}, thHi={'GB': 16}), Theta(thLo={'GB': 89}, thHi={'GB': 17}), Theta(thLo={'GB': 89}, thHi={'GB': 18}), Theta(thLo={'GB': 89}, thHi={'GB': 19}), Theta(thLo={'GB': 89}, thHi={'GB': 20}), Theta(thLo={'GB': 89}, thHi={'GB': 21}), Theta(thLo={'GB': 89}, thHi={'GB': 22}), Theta(thLo={'GB': 89}, thHi={'GB': 23}), Theta(thLo={'GB': 89}, thHi={'GB': 24}), Theta(thLo={'GB': 89}, thHi={'GB': 25}), Theta(thLo={'GB': 89}, thHi={'GB': 26}), Theta(thLo={'GB': 89}, thHi={'GB': 27}), Theta(thLo={'GB': 89}, thHi={'GB': 28}), Theta(thLo={'GB': 89}, thHi={'GB': 29}), Theta(thLo={'GB': 89}, thHi={'GB': 30}), Theta(thLo={'GB': 89}, thHi={'GB': 31}), Theta(thLo={'GB': 89}, thHi={'GB': 32}), Theta(thLo={'GB': 89}, thHi={'GB': 33}), Theta(thLo={'GB': 89}, thHi={'GB': 34}), Theta(thLo={'GB': 89}, thHi={'GB': 35}), Theta(thLo={'GB': 89}, thHi={'GB': 36}), Theta(thLo={'GB': 89}, thHi={'GB': 37}), Theta(thLo={'GB': 89}, thHi={'GB': 38}), Theta(thLo={'GB': 89}, thHi={'GB': 39}), Theta(thLo={'GB': 89}, thHi={'GB': 40}), Theta(thLo={'GB': 89}, thHi={'GB': 41}), Theta(thLo={'GB': 89}, thHi={'GB': 42}), Theta(thLo={'GB': 89}, thHi={'GB': 43}), Theta(thLo={'GB': 89}, thHi={'GB': 44}), Theta(thLo={'GB': 89}, thHi={'GB': 45}), Theta(thLo={'GB': 89}, thHi={'GB': 46}), Theta(thLo={'GB': 89}, thHi={'GB': 47}), Theta(thLo={'GB': 89}, thHi={'GB': 48}), Theta(thLo={'GB': 89}, thHi={'GB': 49}), Theta(thLo={'GB': 89}, thHi={'GB': 50}), Theta(thLo={'GB': 89}, thHi={'GB': 51}), Theta(thLo={'GB': 89}, thHi={'GB': 52}), Theta(thLo={'GB': 89}, thHi={'GB': 53}), Theta(thLo={'GB': 89}, thHi={'GB': 54}), Theta(thLo={'GB': 89}, thHi={'GB': 55}), Theta(thLo={'GB': 89}, thHi={'GB': 56}), Theta(thLo={'GB': 89}, thHi={'GB': 57}), Theta(thLo={'GB': 89}, thHi={'GB': 58}), Theta(thLo={'GB': 89}, thHi={'GB': 59}), Theta(thLo={'GB': 89}, thHi={'GB': 60}), Theta(thLo={'GB': 89}, thHi={'GB': 61}), Theta(thLo={'GB': 89}, thHi={'GB': 62}), Theta(thLo={'GB': 89}, thHi={'GB': 63}), Theta(thLo={'GB': 89}, thHi={'GB': 64}), Theta(thLo={'GB': 89}, thHi={'GB': 65}), Theta(thLo={'GB': 89}, thHi={'GB': 66}), Theta(thLo={'GB': 89}, thHi={'GB': 67}), Theta(thLo={'GB': 89}, thHi={'GB': 68}), Theta(thLo={'GB': 89}, thHi={'GB': 69}), Theta(thLo={'GB': 89}, thHi={'GB': 70}), Theta(thLo={'GB': 89}, thHi={'GB': 71}), Theta(thLo={'GB': 89}, thHi={'GB': 72}), Theta(thLo={'GB': 89}, thHi={'GB': 73}), Theta(thLo={'GB': 89}, thHi={'GB': 74}), Theta(thLo={'GB': 89}, thHi={'GB': 75}), Theta(thLo={'GB': 89}, thHi={'GB': 76}), Theta(thLo={'GB': 89}, thHi={'GB': 77}), Theta(thLo={'GB': 89}, thHi={'GB': 78}), Theta(thLo={'GB': 89}, thHi={'GB': 79}), Theta(thLo={'GB': 89}, thHi={'GB': 80}), Theta(thLo={'GB': 89}, thHi={'GB': 81}), Theta(thLo={'GB': 89}, thHi={'GB': 82}), Theta(thLo={'GB': 89}, thHi={'GB': 83}), Theta(thLo={'GB': 89}, thHi={'GB': 84}), Theta(thLo={'GB': 89}, thHi={'GB': 85}), Theta(thLo={'GB': 89}, thHi={'GB': 86}), Theta(thLo={'GB': 89}, thHi={'GB': 87}), Theta(thLo={'GB': 89}, thHi={'GB': 88}), Theta(thLo={'GB': 89}, thHi={'GB': 89}), Theta(thLo={'GB': 89}, thHi={'GB': 90}), Theta(thLo={'GB': 89}, thHi={'GB': 91}), Theta(thLo={'GB': 89}, thHi={'GB': 92}), Theta(thLo={'GB': 89}, thHi={'GB': 93}), Theta(thLo={'GB': 89}, thHi={'GB': 94}), Theta(thLo={'GB': 89}, thHi={'GB': 95}), Theta(thLo={'GB': 89}, thHi={'GB': 96}), Theta(thLo={'GB': 89}, thHi={'GB': 97}), Theta(thLo={'GB': 89}, thHi={'GB': 98}), Theta(thLo={'GB': 89}, thHi={'GB': 99}), Theta(thLo={'GB': 90}, thHi={'GB': 10}), Theta(thLo={'GB': 90}, thHi={'GB': 11}), Theta(thLo={'GB': 90}, thHi={'GB': 12}), Theta(thLo={'GB': 90}, thHi={'GB': 13}), Theta(thLo={'GB': 90}, thHi={'GB': 14}), Theta(thLo={'GB': 90}, thHi={'GB': 15}), Theta(thLo={'GB': 90}, thHi={'GB': 16}), Theta(thLo={'GB': 90}, thHi={'GB': 17}), Theta(thLo={'GB': 90}, thHi={'GB': 18}), Theta(thLo={'GB': 90}, thHi={'GB': 19}), Theta(thLo={'GB': 90}, thHi={'GB': 20}), Theta(thLo={'GB': 90}, thHi={'GB': 21}), Theta(thLo={'GB': 90}, thHi={'GB': 22}), Theta(thLo={'GB': 90}, thHi={'GB': 23}), Theta(thLo={'GB': 90}, thHi={'GB': 24}), Theta(thLo={'GB': 90}, thHi={'GB': 25}), Theta(thLo={'GB': 90}, thHi={'GB': 26}), Theta(thLo={'GB': 90}, thHi={'GB': 27}), Theta(thLo={'GB': 90}, thHi={'GB': 28}), Theta(thLo={'GB': 90}, thHi={'GB': 29}), Theta(thLo={'GB': 90}, thHi={'GB': 30}), Theta(thLo={'GB': 90}, thHi={'GB': 31}), Theta(thLo={'GB': 90}, thHi={'GB': 32}), Theta(thLo={'GB': 90}, thHi={'GB': 33}), Theta(thLo={'GB': 90}, thHi={'GB': 34}), Theta(thLo={'GB': 90}, thHi={'GB': 35}), Theta(thLo={'GB': 90}, thHi={'GB': 36}), Theta(thLo={'GB': 90}, thHi={'GB': 37}), Theta(thLo={'GB': 90}, thHi={'GB': 38}), Theta(thLo={'GB': 90}, thHi={'GB': 39}), Theta(thLo={'GB': 90}, thHi={'GB': 40}), Theta(thLo={'GB': 90}, thHi={'GB': 41}), Theta(thLo={'GB': 90}, thHi={'GB': 42}), Theta(thLo={'GB': 90}, thHi={'GB': 43}), Theta(thLo={'GB': 90}, thHi={'GB': 44}), Theta(thLo={'GB': 90}, thHi={'GB': 45}), Theta(thLo={'GB': 90}, thHi={'GB': 46}), Theta(thLo={'GB': 90}, thHi={'GB': 47}), Theta(thLo={'GB': 90}, thHi={'GB': 48}), Theta(thLo={'GB': 90}, thHi={'GB': 49}), Theta(thLo={'GB': 90}, thHi={'GB': 50}), Theta(thLo={'GB': 90}, thHi={'GB': 51}), Theta(thLo={'GB': 90}, thHi={'GB': 52}), Theta(thLo={'GB': 90}, thHi={'GB': 53}), Theta(thLo={'GB': 90}, thHi={'GB': 54}), Theta(thLo={'GB': 90}, thHi={'GB': 55}), Theta(thLo={'GB': 90}, thHi={'GB': 56}), Theta(thLo={'GB': 90}, thHi={'GB': 57}), Theta(thLo={'GB': 90}, thHi={'GB': 58}), Theta(thLo={'GB': 90}, thHi={'GB': 59}), Theta(thLo={'GB': 90}, thHi={'GB': 60}), Theta(thLo={'GB': 90}, thHi={'GB': 61}), Theta(thLo={'GB': 90}, thHi={'GB': 62}), Theta(thLo={'GB': 90}, thHi={'GB': 63}), Theta(thLo={'GB': 90}, thHi={'GB': 64}), Theta(thLo={'GB': 90}, thHi={'GB': 65}), Theta(thLo={'GB': 90}, thHi={'GB': 66}), Theta(thLo={'GB': 90}, thHi={'GB': 67}), Theta(thLo={'GB': 90}, thHi={'GB': 68}), Theta(thLo={'GB': 90}, thHi={'GB': 69}), Theta(thLo={'GB': 90}, thHi={'GB': 70}), Theta(thLo={'GB': 90}, thHi={'GB': 71}), Theta(thLo={'GB': 90}, thHi={'GB': 72}), Theta(thLo={'GB': 90}, thHi={'GB': 73}), Theta(thLo={'GB': 90}, thHi={'GB': 74}), Theta(thLo={'GB': 90}, thHi={'GB': 75}), Theta(thLo={'GB': 90}, thHi={'GB': 76}), Theta(thLo={'GB': 90}, thHi={'GB': 77}), Theta(thLo={'GB': 90}, thHi={'GB': 78}), Theta(thLo={'GB': 90}, thHi={'GB': 79}), Theta(thLo={'GB': 90}, thHi={'GB': 80}), Theta(thLo={'GB': 90}, thHi={'GB': 81}), Theta(thLo={'GB': 90}, thHi={'GB': 82}), Theta(thLo={'GB': 90}, thHi={'GB': 83}), Theta(thLo={'GB': 90}, thHi={'GB': 84}), Theta(thLo={'GB': 90}, thHi={'GB': 85}), Theta(thLo={'GB': 90}, thHi={'GB': 86}), Theta(thLo={'GB': 90}, thHi={'GB': 87}), Theta(thLo={'GB': 90}, thHi={'GB': 88}), Theta(thLo={'GB': 90}, thHi={'GB': 89}), Theta(thLo={'GB': 90}, thHi={'GB': 90}), Theta(thLo={'GB': 90}, thHi={'GB': 91}), Theta(thLo={'GB': 90}, thHi={'GB': 92}), Theta(thLo={'GB': 90}, thHi={'GB': 93}), Theta(thLo={'GB': 90}, thHi={'GB': 94}), Theta(thLo={'GB': 90}, thHi={'GB': 95}), Theta(thLo={'GB': 90}, thHi={'GB': 96}), Theta(thLo={'GB': 90}, thHi={'GB': 97}), Theta(thLo={'GB': 90}, thHi={'GB': 98}), Theta(thLo={'GB': 90}, thHi={'GB': 99}), Theta(thLo={'GB': 91}, thHi={'GB': 10}), Theta(thLo={'GB': 91}, thHi={'GB': 11}), Theta(thLo={'GB': 91}, thHi={'GB': 12}), Theta(thLo={'GB': 91}, thHi={'GB': 13}), Theta(thLo={'GB': 91}, thHi={'GB': 14}), Theta(thLo={'GB': 91}, thHi={'GB': 15}), Theta(thLo={'GB': 91}, thHi={'GB': 16}), Theta(thLo={'GB': 91}, thHi={'GB': 17}), Theta(thLo={'GB': 91}, thHi={'GB': 18}), Theta(thLo={'GB': 91}, thHi={'GB': 19}), Theta(thLo={'GB': 91}, thHi={'GB': 20}), Theta(thLo={'GB': 91}, thHi={'GB': 21}), Theta(thLo={'GB': 91}, thHi={'GB': 22}), Theta(thLo={'GB': 91}, thHi={'GB': 23}), Theta(thLo={'GB': 91}, thHi={'GB': 24}), Theta(thLo={'GB': 91}, thHi={'GB': 25}), Theta(thLo={'GB': 91}, thHi={'GB': 26}), Theta(thLo={'GB': 91}, thHi={'GB': 27}), Theta(thLo={'GB': 91}, thHi={'GB': 28}), Theta(thLo={'GB': 91}, thHi={'GB': 29}), Theta(thLo={'GB': 91}, thHi={'GB': 30}), Theta(thLo={'GB': 91}, thHi={'GB': 31}), Theta(thLo={'GB': 91}, thHi={'GB': 32}), Theta(thLo={'GB': 91}, thHi={'GB': 33}), Theta(thLo={'GB': 91}, thHi={'GB': 34}), Theta(thLo={'GB': 91}, thHi={'GB': 35}), Theta(thLo={'GB': 91}, thHi={'GB': 36}), Theta(thLo={'GB': 91}, thHi={'GB': 37}), Theta(thLo={'GB': 91}, thHi={'GB': 38}), Theta(thLo={'GB': 91}, thHi={'GB': 39}), Theta(thLo={'GB': 91}, thHi={'GB': 40}), Theta(thLo={'GB': 91}, thHi={'GB': 41}), Theta(thLo={'GB': 91}, thHi={'GB': 42}), Theta(thLo={'GB': 91}, thHi={'GB': 43}), Theta(thLo={'GB': 91}, thHi={'GB': 44}), Theta(thLo={'GB': 91}, thHi={'GB': 45}), Theta(thLo={'GB': 91}, thHi={'GB': 46}), Theta(thLo={'GB': 91}, thHi={'GB': 47}), Theta(thLo={'GB': 91}, thHi={'GB': 48}), Theta(thLo={'GB': 91}, thHi={'GB': 49}), Theta(thLo={'GB': 91}, thHi={'GB': 50}), Theta(thLo={'GB': 91}, thHi={'GB': 51}), Theta(thLo={'GB': 91}, thHi={'GB': 52}), Theta(thLo={'GB': 91}, thHi={'GB': 53}), Theta(thLo={'GB': 91}, thHi={'GB': 54}), Theta(thLo={'GB': 91}, thHi={'GB': 55}), Theta(thLo={'GB': 91}, thHi={'GB': 56}), Theta(thLo={'GB': 91}, thHi={'GB': 57}), Theta(thLo={'GB': 91}, thHi={'GB': 58}), Theta(thLo={'GB': 91}, thHi={'GB': 59}), Theta(thLo={'GB': 91}, thHi={'GB': 60}), Theta(thLo={'GB': 91}, thHi={'GB': 61}), Theta(thLo={'GB': 91}, thHi={'GB': 62}), Theta(thLo={'GB': 91}, thHi={'GB': 63}), Theta(thLo={'GB': 91}, thHi={'GB': 64}), Theta(thLo={'GB': 91}, thHi={'GB': 65}), Theta(thLo={'GB': 91}, thHi={'GB': 66}), Theta(thLo={'GB': 91}, thHi={'GB': 67}), Theta(thLo={'GB': 91}, thHi={'GB': 68}), Theta(thLo={'GB': 91}, thHi={'GB': 69}), Theta(thLo={'GB': 91}, thHi={'GB': 70}), Theta(thLo={'GB': 91}, thHi={'GB': 71}), Theta(thLo={'GB': 91}, thHi={'GB': 72}), Theta(thLo={'GB': 91}, thHi={'GB': 73}), Theta(thLo={'GB': 91}, thHi={'GB': 74}), Theta(thLo={'GB': 91}, thHi={'GB': 75}), Theta(thLo={'GB': 91}, thHi={'GB': 76}), Theta(thLo={'GB': 91}, thHi={'GB': 77}), Theta(thLo={'GB': 91}, thHi={'GB': 78}), Theta(thLo={'GB': 91}, thHi={'GB': 79}), Theta(thLo={'GB': 91}, thHi={'GB': 80}), Theta(thLo={'GB': 91}, thHi={'GB': 81}), Theta(thLo={'GB': 91}, thHi={'GB': 82}), Theta(thLo={'GB': 91}, thHi={'GB': 83}), Theta(thLo={'GB': 91}, thHi={'GB': 84}), Theta(thLo={'GB': 91}, thHi={'GB': 85}), Theta(thLo={'GB': 91}, thHi={'GB': 86}), Theta(thLo={'GB': 91}, thHi={'GB': 87}), Theta(thLo={'GB': 91}, thHi={'GB': 88}), Theta(thLo={'GB': 91}, thHi={'GB': 89}), Theta(thLo={'GB': 91}, thHi={'GB': 90}), Theta(thLo={'GB': 91}, thHi={'GB': 91}), Theta(thLo={'GB': 91}, thHi={'GB': 92}), Theta(thLo={'GB': 91}, thHi={'GB': 93}), Theta(thLo={'GB': 91}, thHi={'GB': 94}), Theta(thLo={'GB': 91}, thHi={'GB': 95}), Theta(thLo={'GB': 91}, thHi={'GB': 96}), Theta(thLo={'GB': 91}, thHi={'GB': 97}), Theta(thLo={'GB': 91}, thHi={'GB': 98}), Theta(thLo={'GB': 91}, thHi={'GB': 99}), Theta(thLo={'GB': 92}, thHi={'GB': 10}), Theta(thLo={'GB': 92}, thHi={'GB': 11}), Theta(thLo={'GB': 92}, thHi={'GB': 12}), Theta(thLo={'GB': 92}, thHi={'GB': 13}), Theta(thLo={'GB': 92}, thHi={'GB': 14}), Theta(thLo={'GB': 92}, thHi={'GB': 15}), Theta(thLo={'GB': 92}, thHi={'GB': 16}), Theta(thLo={'GB': 92}, thHi={'GB': 17}), Theta(thLo={'GB': 92}, thHi={'GB': 18}), Theta(thLo={'GB': 92}, thHi={'GB': 19}), Theta(thLo={'GB': 92}, thHi={'GB': 20}), Theta(thLo={'GB': 92}, thHi={'GB': 21}), Theta(thLo={'GB': 92}, thHi={'GB': 22}), Theta(thLo={'GB': 92}, thHi={'GB': 23}), Theta(thLo={'GB': 92}, thHi={'GB': 24}), Theta(thLo={'GB': 92}, thHi={'GB': 25}), Theta(thLo={'GB': 92}, thHi={'GB': 26}), Theta(thLo={'GB': 92}, thHi={'GB': 27}), Theta(thLo={'GB': 92}, thHi={'GB': 28}), Theta(thLo={'GB': 92}, thHi={'GB': 29}), Theta(thLo={'GB': 92}, thHi={'GB': 30}), Theta(thLo={'GB': 92}, thHi={'GB': 31}), Theta(thLo={'GB': 92}, thHi={'GB': 32}), Theta(thLo={'GB': 92}, thHi={'GB': 33}), Theta(thLo={'GB': 92}, thHi={'GB': 34}), Theta(thLo={'GB': 92}, thHi={'GB': 35}), Theta(thLo={'GB': 92}, thHi={'GB': 36}), Theta(thLo={'GB': 92}, thHi={'GB': 37}), Theta(thLo={'GB': 92}, thHi={'GB': 38}), Theta(thLo={'GB': 92}, thHi={'GB': 39}), Theta(thLo={'GB': 92}, thHi={'GB': 40}), Theta(thLo={'GB': 92}, thHi={'GB': 41}), Theta(thLo={'GB': 92}, thHi={'GB': 42}), Theta(thLo={'GB': 92}, thHi={'GB': 43}), Theta(thLo={'GB': 92}, thHi={'GB': 44}), Theta(thLo={'GB': 92}, thHi={'GB': 45}), Theta(thLo={'GB': 92}, thHi={'GB': 46}), Theta(thLo={'GB': 92}, thHi={'GB': 47}), Theta(thLo={'GB': 92}, thHi={'GB': 48}), Theta(thLo={'GB': 92}, thHi={'GB': 49}), Theta(thLo={'GB': 92}, thHi={'GB': 50}), Theta(thLo={'GB': 92}, thHi={'GB': 51}), Theta(thLo={'GB': 92}, thHi={'GB': 52}), Theta(thLo={'GB': 92}, thHi={'GB': 53}), Theta(thLo={'GB': 92}, thHi={'GB': 54}), Theta(thLo={'GB': 92}, thHi={'GB': 55}), Theta(thLo={'GB': 92}, thHi={'GB': 56}), Theta(thLo={'GB': 92}, thHi={'GB': 57}), Theta(thLo={'GB': 92}, thHi={'GB': 58}), Theta(thLo={'GB': 92}, thHi={'GB': 59}), Theta(thLo={'GB': 92}, thHi={'GB': 60}), Theta(thLo={'GB': 92}, thHi={'GB': 61}), Theta(thLo={'GB': 92}, thHi={'GB': 62}), Theta(thLo={'GB': 92}, thHi={'GB': 63}), Theta(thLo={'GB': 92}, thHi={'GB': 64}), Theta(thLo={'GB': 92}, thHi={'GB': 65}), Theta(thLo={'GB': 92}, thHi={'GB': 66}), Theta(thLo={'GB': 92}, thHi={'GB': 67}), Theta(thLo={'GB': 92}, thHi={'GB': 68}), Theta(thLo={'GB': 92}, thHi={'GB': 69}), Theta(thLo={'GB': 92}, thHi={'GB': 70}), Theta(thLo={'GB': 92}, thHi={'GB': 71}), Theta(thLo={'GB': 92}, thHi={'GB': 72}), Theta(thLo={'GB': 92}, thHi={'GB': 73}), Theta(thLo={'GB': 92}, thHi={'GB': 74}), Theta(thLo={'GB': 92}, thHi={'GB': 75}), Theta(thLo={'GB': 92}, thHi={'GB': 76}), Theta(thLo={'GB': 92}, thHi={'GB': 77}), Theta(thLo={'GB': 92}, thHi={'GB': 78}), Theta(thLo={'GB': 92}, thHi={'GB': 79}), Theta(thLo={'GB': 92}, thHi={'GB': 80}), Theta(thLo={'GB': 92}, thHi={'GB': 81}), Theta(thLo={'GB': 92}, thHi={'GB': 82}), Theta(thLo={'GB': 92}, thHi={'GB': 83}), Theta(thLo={'GB': 92}, thHi={'GB': 84}), Theta(thLo={'GB': 92}, thHi={'GB': 85}), Theta(thLo={'GB': 92}, thHi={'GB': 86}), Theta(thLo={'GB': 92}, thHi={'GB': 87}), Theta(thLo={'GB': 92}, thHi={'GB': 88}), Theta(thLo={'GB': 92}, thHi={'GB': 89}), Theta(thLo={'GB': 92}, thHi={'GB': 90}), Theta(thLo={'GB': 92}, thHi={'GB': 91}), Theta(thLo={'GB': 92}, thHi={'GB': 92}), Theta(thLo={'GB': 92}, thHi={'GB': 93}), Theta(thLo={'GB': 92}, thHi={'GB': 94}), Theta(thLo={'GB': 92}, thHi={'GB': 95}), Theta(thLo={'GB': 92}, thHi={'GB': 96}), Theta(thLo={'GB': 92}, thHi={'GB': 97}), Theta(thLo={'GB': 92}, thHi={'GB': 98}), Theta(thLo={'GB': 92}, thHi={'GB': 99}), Theta(thLo={'GB': 93}, thHi={'GB': 10}), Theta(thLo={'GB': 93}, thHi={'GB': 11}), Theta(thLo={'GB': 93}, thHi={'GB': 12}), Theta(thLo={'GB': 93}, thHi={'GB': 13}), Theta(thLo={'GB': 93}, thHi={'GB': 14}), Theta(thLo={'GB': 93}, thHi={'GB': 15}), Theta(thLo={'GB': 93}, thHi={'GB': 16}), Theta(thLo={'GB': 93}, thHi={'GB': 17}), Theta(thLo={'GB': 93}, thHi={'GB': 18}), Theta(thLo={'GB': 93}, thHi={'GB': 19}), Theta(thLo={'GB': 93}, thHi={'GB': 20}), Theta(thLo={'GB': 93}, thHi={'GB': 21}), Theta(thLo={'GB': 93}, thHi={'GB': 22}), Theta(thLo={'GB': 93}, thHi={'GB': 23}), Theta(thLo={'GB': 93}, thHi={'GB': 24}), Theta(thLo={'GB': 93}, thHi={'GB': 25}), Theta(thLo={'GB': 93}, thHi={'GB': 26}), Theta(thLo={'GB': 93}, thHi={'GB': 27}), Theta(thLo={'GB': 93}, thHi={'GB': 28}), Theta(thLo={'GB': 93}, thHi={'GB': 29}), Theta(thLo={'GB': 93}, thHi={'GB': 30}), Theta(thLo={'GB': 93}, thHi={'GB': 31}), Theta(thLo={'GB': 93}, thHi={'GB': 32}), Theta(thLo={'GB': 93}, thHi={'GB': 33}), Theta(thLo={'GB': 93}, thHi={'GB': 34}), Theta(thLo={'GB': 93}, thHi={'GB': 35}), Theta(thLo={'GB': 93}, thHi={'GB': 36}), Theta(thLo={'GB': 93}, thHi={'GB': 37}), Theta(thLo={'GB': 93}, thHi={'GB': 38}), Theta(thLo={'GB': 93}, thHi={'GB': 39}), Theta(thLo={'GB': 93}, thHi={'GB': 40}), Theta(thLo={'GB': 93}, thHi={'GB': 41}), Theta(thLo={'GB': 93}, thHi={'GB': 42}), Theta(thLo={'GB': 93}, thHi={'GB': 43}), Theta(thLo={'GB': 93}, thHi={'GB': 44}), Theta(thLo={'GB': 93}, thHi={'GB': 45}), Theta(thLo={'GB': 93}, thHi={'GB': 46}), Theta(thLo={'GB': 93}, thHi={'GB': 47}), Theta(thLo={'GB': 93}, thHi={'GB': 48}), Theta(thLo={'GB': 93}, thHi={'GB': 49}), Theta(thLo={'GB': 93}, thHi={'GB': 50}), Theta(thLo={'GB': 93}, thHi={'GB': 51}), Theta(thLo={'GB': 93}, thHi={'GB': 52}), Theta(thLo={'GB': 93}, thHi={'GB': 53}), Theta(thLo={'GB': 93}, thHi={'GB': 54}), Theta(thLo={'GB': 93}, thHi={'GB': 55}), Theta(thLo={'GB': 93}, thHi={'GB': 56}), Theta(thLo={'GB': 93}, thHi={'GB': 57}), Theta(thLo={'GB': 93}, thHi={'GB': 58}), Theta(thLo={'GB': 93}, thHi={'GB': 59}), Theta(thLo={'GB': 93}, thHi={'GB': 60}), Theta(thLo={'GB': 93}, thHi={'GB': 61}), Theta(thLo={'GB': 93}, thHi={'GB': 62}), Theta(thLo={'GB': 93}, thHi={'GB': 63}), Theta(thLo={'GB': 93}, thHi={'GB': 64}), Theta(thLo={'GB': 93}, thHi={'GB': 65}), Theta(thLo={'GB': 93}, thHi={'GB': 66}), Theta(thLo={'GB': 93}, thHi={'GB': 67}), Theta(thLo={'GB': 93}, thHi={'GB': 68}), Theta(thLo={'GB': 93}, thHi={'GB': 69}), Theta(thLo={'GB': 93}, thHi={'GB': 70}), Theta(thLo={'GB': 93}, thHi={'GB': 71}), Theta(thLo={'GB': 93}, thHi={'GB': 72}), Theta(thLo={'GB': 93}, thHi={'GB': 73}), Theta(thLo={'GB': 93}, thHi={'GB': 74}), Theta(thLo={'GB': 93}, thHi={'GB': 75}), Theta(thLo={'GB': 93}, thHi={'GB': 76}), Theta(thLo={'GB': 93}, thHi={'GB': 77}), Theta(thLo={'GB': 93}, thHi={'GB': 78}), Theta(thLo={'GB': 93}, thHi={'GB': 79}), Theta(thLo={'GB': 93}, thHi={'GB': 80}), Theta(thLo={'GB': 93}, thHi={'GB': 81}), Theta(thLo={'GB': 93}, thHi={'GB': 82}), Theta(thLo={'GB': 93}, thHi={'GB': 83}), Theta(thLo={'GB': 93}, thHi={'GB': 84}), Theta(thLo={'GB': 93}, thHi={'GB': 85}), Theta(thLo={'GB': 93}, thHi={'GB': 86}), Theta(thLo={'GB': 93}, thHi={'GB': 87}), Theta(thLo={'GB': 93}, thHi={'GB': 88}), Theta(thLo={'GB': 93}, thHi={'GB': 89}), Theta(thLo={'GB': 93}, thHi={'GB': 90}), Theta(thLo={'GB': 93}, thHi={'GB': 91}), Theta(thLo={'GB': 93}, thHi={'GB': 92}), Theta(thLo={'GB': 93}, thHi={'GB': 93}), Theta(thLo={'GB': 93}, thHi={'GB': 94}), Theta(thLo={'GB': 93}, thHi={'GB': 95}), Theta(thLo={'GB': 93}, thHi={'GB': 96}), Theta(thLo={'GB': 93}, thHi={'GB': 97}), Theta(thLo={'GB': 93}, thHi={'GB': 98}), Theta(thLo={'GB': 93}, thHi={'GB': 99}), Theta(thLo={'GB': 94}, thHi={'GB': 10}), Theta(thLo={'GB': 94}, thHi={'GB': 11}), Theta(thLo={'GB': 94}, thHi={'GB': 12}), Theta(thLo={'GB': 94}, thHi={'GB': 13}), Theta(thLo={'GB': 94}, thHi={'GB': 14}), Theta(thLo={'GB': 94}, thHi={'GB': 15}), Theta(thLo={'GB': 94}, thHi={'GB': 16}), Theta(thLo={'GB': 94}, thHi={'GB': 17}), Theta(thLo={'GB': 94}, thHi={'GB': 18}), Theta(thLo={'GB': 94}, thHi={'GB': 19}), Theta(thLo={'GB': 94}, thHi={'GB': 20}), Theta(thLo={'GB': 94}, thHi={'GB': 21}), Theta(thLo={'GB': 94}, thHi={'GB': 22}), Theta(thLo={'GB': 94}, thHi={'GB': 23}), Theta(thLo={'GB': 94}, thHi={'GB': 24}), Theta(thLo={'GB': 94}, thHi={'GB': 25}), Theta(thLo={'GB': 94}, thHi={'GB': 26}), Theta(thLo={'GB': 94}, thHi={'GB': 27}), Theta(thLo={'GB': 94}, thHi={'GB': 28}), Theta(thLo={'GB': 94}, thHi={'GB': 29}), Theta(thLo={'GB': 94}, thHi={'GB': 30}), Theta(thLo={'GB': 94}, thHi={'GB': 31}), Theta(thLo={'GB': 94}, thHi={'GB': 32}), Theta(thLo={'GB': 94}, thHi={'GB': 33}), Theta(thLo={'GB': 94}, thHi={'GB': 34}), Theta(thLo={'GB': 94}, thHi={'GB': 35}), Theta(thLo={'GB': 94}, thHi={'GB': 36}), Theta(thLo={'GB': 94}, thHi={'GB': 37}), Theta(thLo={'GB': 94}, thHi={'GB': 38}), Theta(thLo={'GB': 94}, thHi={'GB': 39}), Theta(thLo={'GB': 94}, thHi={'GB': 40}), Theta(thLo={'GB': 94}, thHi={'GB': 41}), Theta(thLo={'GB': 94}, thHi={'GB': 42}), Theta(thLo={'GB': 94}, thHi={'GB': 43}), Theta(thLo={'GB': 94}, thHi={'GB': 44}), Theta(thLo={'GB': 94}, thHi={'GB': 45}), Theta(thLo={'GB': 94}, thHi={'GB': 46}), Theta(thLo={'GB': 94}, thHi={'GB': 47}), Theta(thLo={'GB': 94}, thHi={'GB': 48}), Theta(thLo={'GB': 94}, thHi={'GB': 49}), Theta(thLo={'GB': 94}, thHi={'GB': 50}), Theta(thLo={'GB': 94}, thHi={'GB': 51}), Theta(thLo={'GB': 94}, thHi={'GB': 52}), Theta(thLo={'GB': 94}, thHi={'GB': 53}), Theta(thLo={'GB': 94}, thHi={'GB': 54}), Theta(thLo={'GB': 94}, thHi={'GB': 55}), Theta(thLo={'GB': 94}, thHi={'GB': 56}), Theta(thLo={'GB': 94}, thHi={'GB': 57}), Theta(thLo={'GB': 94}, thHi={'GB': 58}), Theta(thLo={'GB': 94}, thHi={'GB': 59}), Theta(thLo={'GB': 94}, thHi={'GB': 60}), Theta(thLo={'GB': 94}, thHi={'GB': 61}), Theta(thLo={'GB': 94}, thHi={'GB': 62}), Theta(thLo={'GB': 94}, thHi={'GB': 63}), Theta(thLo={'GB': 94}, thHi={'GB': 64}), Theta(thLo={'GB': 94}, thHi={'GB': 65}), Theta(thLo={'GB': 94}, thHi={'GB': 66}), Theta(thLo={'GB': 94}, thHi={'GB': 67}), Theta(thLo={'GB': 94}, thHi={'GB': 68}), Theta(thLo={'GB': 94}, thHi={'GB': 69}), Theta(thLo={'GB': 94}, thHi={'GB': 70}), Theta(thLo={'GB': 94}, thHi={'GB': 71}), Theta(thLo={'GB': 94}, thHi={'GB': 72}), Theta(thLo={'GB': 94}, thHi={'GB': 73}), Theta(thLo={'GB': 94}, thHi={'GB': 74}), Theta(thLo={'GB': 94}, thHi={'GB': 75}), Theta(thLo={'GB': 94}, thHi={'GB': 76}), Theta(thLo={'GB': 94}, thHi={'GB': 77}), Theta(thLo={'GB': 94}, thHi={'GB': 78}), Theta(thLo={'GB': 94}, thHi={'GB': 79}), Theta(thLo={'GB': 94}, thHi={'GB': 80}), Theta(thLo={'GB': 94}, thHi={'GB': 81}), Theta(thLo={'GB': 94}, thHi={'GB': 82}), Theta(thLo={'GB': 94}, thHi={'GB': 83}), Theta(thLo={'GB': 94}, thHi={'GB': 84}), Theta(thLo={'GB': 94}, thHi={'GB': 85}), Theta(thLo={'GB': 94}, thHi={'GB': 86}), Theta(thLo={'GB': 94}, thHi={'GB': 87}), Theta(thLo={'GB': 94}, thHi={'GB': 88}), Theta(thLo={'GB': 94}, thHi={'GB': 89}), Theta(thLo={'GB': 94}, thHi={'GB': 90}), Theta(thLo={'GB': 94}, thHi={'GB': 91}), Theta(thLo={'GB': 94}, thHi={'GB': 92}), Theta(thLo={'GB': 94}, thHi={'GB': 93}), Theta(thLo={'GB': 94}, thHi={'GB': 94}), Theta(thLo={'GB': 94}, thHi={'GB': 95}), Theta(thLo={'GB': 94}, thHi={'GB': 96}), Theta(thLo={'GB': 94}, thHi={'GB': 97}), Theta(thLo={'GB': 94}, thHi={'GB': 98}), Theta(thLo={'GB': 94}, thHi={'GB': 99}), Theta(thLo={'GB': 95}, thHi={'GB': 10}), Theta(thLo={'GB': 95}, thHi={'GB': 11}), Theta(thLo={'GB': 95}, thHi={'GB': 12}), Theta(thLo={'GB': 95}, thHi={'GB': 13}), Theta(thLo={'GB': 95}, thHi={'GB': 14}), Theta(thLo={'GB': 95}, thHi={'GB': 15}), Theta(thLo={'GB': 95}, thHi={'GB': 16}), Theta(thLo={'GB': 95}, thHi={'GB': 17}), Theta(thLo={'GB': 95}, thHi={'GB': 18}), Theta(thLo={'GB': 95}, thHi={'GB': 19}), Theta(thLo={'GB': 95}, thHi={'GB': 20}), Theta(thLo={'GB': 95}, thHi={'GB': 21}), Theta(thLo={'GB': 95}, thHi={'GB': 22}), Theta(thLo={'GB': 95}, thHi={'GB': 23}), Theta(thLo={'GB': 95}, thHi={'GB': 24}), Theta(thLo={'GB': 95}, thHi={'GB': 25}), Theta(thLo={'GB': 95}, thHi={'GB': 26}), Theta(thLo={'GB': 95}, thHi={'GB': 27}), Theta(thLo={'GB': 95}, thHi={'GB': 28}), Theta(thLo={'GB': 95}, thHi={'GB': 29}), Theta(thLo={'GB': 95}, thHi={'GB': 30}), Theta(thLo={'GB': 95}, thHi={'GB': 31}), Theta(thLo={'GB': 95}, thHi={'GB': 32}), Theta(thLo={'GB': 95}, thHi={'GB': 33}), Theta(thLo={'GB': 95}, thHi={'GB': 34}), Theta(thLo={'GB': 95}, thHi={'GB': 35}), Theta(thLo={'GB': 95}, thHi={'GB': 36}), Theta(thLo={'GB': 95}, thHi={'GB': 37}), Theta(thLo={'GB': 95}, thHi={'GB': 38}), Theta(thLo={'GB': 95}, thHi={'GB': 39}), Theta(thLo={'GB': 95}, thHi={'GB': 40}), Theta(thLo={'GB': 95}, thHi={'GB': 41}), Theta(thLo={'GB': 95}, thHi={'GB': 42}), Theta(thLo={'GB': 95}, thHi={'GB': 43}), Theta(thLo={'GB': 95}, thHi={'GB': 44}), Theta(thLo={'GB': 95}, thHi={'GB': 45}), Theta(thLo={'GB': 95}, thHi={'GB': 46}), Theta(thLo={'GB': 95}, thHi={'GB': 47}), Theta(thLo={'GB': 95}, thHi={'GB': 48}), Theta(thLo={'GB': 95}, thHi={'GB': 49}), Theta(thLo={'GB': 95}, thHi={'GB': 50}), Theta(thLo={'GB': 95}, thHi={'GB': 51}), Theta(thLo={'GB': 95}, thHi={'GB': 52}), Theta(thLo={'GB': 95}, thHi={'GB': 53}), Theta(thLo={'GB': 95}, thHi={'GB': 54}), Theta(thLo={'GB': 95}, thHi={'GB': 55}), Theta(thLo={'GB': 95}, thHi={'GB': 56}), Theta(thLo={'GB': 95}, thHi={'GB': 57}), Theta(thLo={'GB': 95}, thHi={'GB': 58}), Theta(thLo={'GB': 95}, thHi={'GB': 59}), Theta(thLo={'GB': 95}, thHi={'GB': 60}), Theta(thLo={'GB': 95}, thHi={'GB': 61}), Theta(thLo={'GB': 95}, thHi={'GB': 62}), Theta(thLo={'GB': 95}, thHi={'GB': 63}), Theta(thLo={'GB': 95}, thHi={'GB': 64}), Theta(thLo={'GB': 95}, thHi={'GB': 65}), Theta(thLo={'GB': 95}, thHi={'GB': 66}), Theta(thLo={'GB': 95}, thHi={'GB': 67}), Theta(thLo={'GB': 95}, thHi={'GB': 68}), Theta(thLo={'GB': 95}, thHi={'GB': 69}), Theta(thLo={'GB': 95}, thHi={'GB': 70}), Theta(thLo={'GB': 95}, thHi={'GB': 71}), Theta(thLo={'GB': 95}, thHi={'GB': 72}), Theta(thLo={'GB': 95}, thHi={'GB': 73}), Theta(thLo={'GB': 95}, thHi={'GB': 74}), Theta(thLo={'GB': 95}, thHi={'GB': 75}), Theta(thLo={'GB': 95}, thHi={'GB': 76}), Theta(thLo={'GB': 95}, thHi={'GB': 77}), Theta(thLo={'GB': 95}, thHi={'GB': 78}), Theta(thLo={'GB': 95}, thHi={'GB': 79}), Theta(thLo={'GB': 95}, thHi={'GB': 80}), Theta(thLo={'GB': 95}, thHi={'GB': 81}), Theta(thLo={'GB': 95}, thHi={'GB': 82}), Theta(thLo={'GB': 95}, thHi={'GB': 83}), Theta(thLo={'GB': 95}, thHi={'GB': 84}), Theta(thLo={'GB': 95}, thHi={'GB': 85}), Theta(thLo={'GB': 95}, thHi={'GB': 86}), Theta(thLo={'GB': 95}, thHi={'GB': 87}), Theta(thLo={'GB': 95}, thHi={'GB': 88}), Theta(thLo={'GB': 95}, thHi={'GB': 89}), Theta(thLo={'GB': 95}, thHi={'GB': 90}), Theta(thLo={'GB': 95}, thHi={'GB': 91}), Theta(thLo={'GB': 95}, thHi={'GB': 92}), Theta(thLo={'GB': 95}, thHi={'GB': 93}), Theta(thLo={'GB': 95}, thHi={'GB': 94}), Theta(thLo={'GB': 95}, thHi={'GB': 95}), Theta(thLo={'GB': 95}, thHi={'GB': 96}), Theta(thLo={'GB': 95}, thHi={'GB': 97}), Theta(thLo={'GB': 95}, thHi={'GB': 98}), Theta(thLo={'GB': 95}, thHi={'GB': 99}), Theta(thLo={'GB': 96}, thHi={'GB': 10}), Theta(thLo={'GB': 96}, thHi={'GB': 11}), Theta(thLo={'GB': 96}, thHi={'GB': 12}), Theta(thLo={'GB': 96}, thHi={'GB': 13}), Theta(thLo={'GB': 96}, thHi={'GB': 14}), Theta(thLo={'GB': 96}, thHi={'GB': 15}), Theta(thLo={'GB': 96}, thHi={'GB': 16}), Theta(thLo={'GB': 96}, thHi={'GB': 17}), Theta(thLo={'GB': 96}, thHi={'GB': 18}), Theta(thLo={'GB': 96}, thHi={'GB': 19}), Theta(thLo={'GB': 96}, thHi={'GB': 20}), Theta(thLo={'GB': 96}, thHi={'GB': 21}), Theta(thLo={'GB': 96}, thHi={'GB': 22}), Theta(thLo={'GB': 96}, thHi={'GB': 23}), Theta(thLo={'GB': 96}, thHi={'GB': 24}), Theta(thLo={'GB': 96}, thHi={'GB': 25}), Theta(thLo={'GB': 96}, thHi={'GB': 26}), Theta(thLo={'GB': 96}, thHi={'GB': 27}), Theta(thLo={'GB': 96}, thHi={'GB': 28}), Theta(thLo={'GB': 96}, thHi={'GB': 29}), Theta(thLo={'GB': 96}, thHi={'GB': 30}), Theta(thLo={'GB': 96}, thHi={'GB': 31}), Theta(thLo={'GB': 96}, thHi={'GB': 32}), Theta(thLo={'GB': 96}, thHi={'GB': 33}), Theta(thLo={'GB': 96}, thHi={'GB': 34}), Theta(thLo={'GB': 96}, thHi={'GB': 35}), Theta(thLo={'GB': 96}, thHi={'GB': 36}), Theta(thLo={'GB': 96}, thHi={'GB': 37}), Theta(thLo={'GB': 96}, thHi={'GB': 38}), Theta(thLo={'GB': 96}, thHi={'GB': 39}), Theta(thLo={'GB': 96}, thHi={'GB': 40}), Theta(thLo={'GB': 96}, thHi={'GB': 41}), Theta(thLo={'GB': 96}, thHi={'GB': 42}), Theta(thLo={'GB': 96}, thHi={'GB': 43}), Theta(thLo={'GB': 96}, thHi={'GB': 44}), Theta(thLo={'GB': 96}, thHi={'GB': 45}), Theta(thLo={'GB': 96}, thHi={'GB': 46}), Theta(thLo={'GB': 96}, thHi={'GB': 47}), Theta(thLo={'GB': 96}, thHi={'GB': 48}), Theta(thLo={'GB': 96}, thHi={'GB': 49}), Theta(thLo={'GB': 96}, thHi={'GB': 50}), Theta(thLo={'GB': 96}, thHi={'GB': 51}), Theta(thLo={'GB': 96}, thHi={'GB': 52}), Theta(thLo={'GB': 96}, thHi={'GB': 53}), Theta(thLo={'GB': 96}, thHi={'GB': 54}), Theta(thLo={'GB': 96}, thHi={'GB': 55}), Theta(thLo={'GB': 96}, thHi={'GB': 56}), Theta(thLo={'GB': 96}, thHi={'GB': 57}), Theta(thLo={'GB': 96}, thHi={'GB': 58}), Theta(thLo={'GB': 96}, thHi={'GB': 59}), Theta(thLo={'GB': 96}, thHi={'GB': 60}), Theta(thLo={'GB': 96}, thHi={'GB': 61}), Theta(thLo={'GB': 96}, thHi={'GB': 62}), Theta(thLo={'GB': 96}, thHi={'GB': 63}), Theta(thLo={'GB': 96}, thHi={'GB': 64}), Theta(thLo={'GB': 96}, thHi={'GB': 65}), Theta(thLo={'GB': 96}, thHi={'GB': 66}), Theta(thLo={'GB': 96}, thHi={'GB': 67}), Theta(thLo={'GB': 96}, thHi={'GB': 68}), Theta(thLo={'GB': 96}, thHi={'GB': 69}), Theta(thLo={'GB': 96}, thHi={'GB': 70}), Theta(thLo={'GB': 96}, thHi={'GB': 71}), Theta(thLo={'GB': 96}, thHi={'GB': 72}), Theta(thLo={'GB': 96}, thHi={'GB': 73}), Theta(thLo={'GB': 96}, thHi={'GB': 74}), Theta(thLo={'GB': 96}, thHi={'GB': 75}), Theta(thLo={'GB': 96}, thHi={'GB': 76}), Theta(thLo={'GB': 96}, thHi={'GB': 77}), Theta(thLo={'GB': 96}, thHi={'GB': 78}), Theta(thLo={'GB': 96}, thHi={'GB': 79}), Theta(thLo={'GB': 96}, thHi={'GB': 80}), Theta(thLo={'GB': 96}, thHi={'GB': 81}), Theta(thLo={'GB': 96}, thHi={'GB': 82}), Theta(thLo={'GB': 96}, thHi={'GB': 83}), Theta(thLo={'GB': 96}, thHi={'GB': 84}), Theta(thLo={'GB': 96}, thHi={'GB': 85}), Theta(thLo={'GB': 96}, thHi={'GB': 86}), Theta(thLo={'GB': 96}, thHi={'GB': 87}), Theta(thLo={'GB': 96}, thHi={'GB': 88}), Theta(thLo={'GB': 96}, thHi={'GB': 89}), Theta(thLo={'GB': 96}, thHi={'GB': 90}), Theta(thLo={'GB': 96}, thHi={'GB': 91}), Theta(thLo={'GB': 96}, thHi={'GB': 92}), Theta(thLo={'GB': 96}, thHi={'GB': 93}), Theta(thLo={'GB': 96}, thHi={'GB': 94}), Theta(thLo={'GB': 96}, thHi={'GB': 95}), Theta(thLo={'GB': 96}, thHi={'GB': 96}), Theta(thLo={'GB': 96}, thHi={'GB': 97}), Theta(thLo={'GB': 96}, thHi={'GB': 98}), Theta(thLo={'GB': 96}, thHi={'GB': 99}), Theta(thLo={'GB': 97}, thHi={'GB': 10}), Theta(thLo={'GB': 97}, thHi={'GB': 11}), Theta(thLo={'GB': 97}, thHi={'GB': 12}), Theta(thLo={'GB': 97}, thHi={'GB': 13}), Theta(thLo={'GB': 97}, thHi={'GB': 14}), Theta(thLo={'GB': 97}, thHi={'GB': 15}), Theta(thLo={'GB': 97}, thHi={'GB': 16}), Theta(thLo={'GB': 97}, thHi={'GB': 17}), Theta(thLo={'GB': 97}, thHi={'GB': 18}), Theta(thLo={'GB': 97}, thHi={'GB': 19}), Theta(thLo={'GB': 97}, thHi={'GB': 20}), Theta(thLo={'GB': 97}, thHi={'GB': 21}), Theta(thLo={'GB': 97}, thHi={'GB': 22}), Theta(thLo={'GB': 97}, thHi={'GB': 23}), Theta(thLo={'GB': 97}, thHi={'GB': 24}), Theta(thLo={'GB': 97}, thHi={'GB': 25}), Theta(thLo={'GB': 97}, thHi={'GB': 26}), Theta(thLo={'GB': 97}, thHi={'GB': 27}), Theta(thLo={'GB': 97}, thHi={'GB': 28}), Theta(thLo={'GB': 97}, thHi={'GB': 29}), Theta(thLo={'GB': 97}, thHi={'GB': 30}), Theta(thLo={'GB': 97}, thHi={'GB': 31}), Theta(thLo={'GB': 97}, thHi={'GB': 32}), Theta(thLo={'GB': 97}, thHi={'GB': 33}), Theta(thLo={'GB': 97}, thHi={'GB': 34}), Theta(thLo={'GB': 97}, thHi={'GB': 35}), Theta(thLo={'GB': 97}, thHi={'GB': 36}), Theta(thLo={'GB': 97}, thHi={'GB': 37}), Theta(thLo={'GB': 97}, thHi={'GB': 38}), Theta(thLo={'GB': 97}, thHi={'GB': 39}), Theta(thLo={'GB': 97}, thHi={'GB': 40}), Theta(thLo={'GB': 97}, thHi={'GB': 41}), Theta(thLo={'GB': 97}, thHi={'GB': 42}), Theta(thLo={'GB': 97}, thHi={'GB': 43}), Theta(thLo={'GB': 97}, thHi={'GB': 44}), Theta(thLo={'GB': 97}, thHi={'GB': 45}), Theta(thLo={'GB': 97}, thHi={'GB': 46}), Theta(thLo={'GB': 97}, thHi={'GB': 47}), Theta(thLo={'GB': 97}, thHi={'GB': 48}), Theta(thLo={'GB': 97}, thHi={'GB': 49}), Theta(thLo={'GB': 97}, thHi={'GB': 50}), Theta(thLo={'GB': 97}, thHi={'GB': 51}), Theta(thLo={'GB': 97}, thHi={'GB': 52}), Theta(thLo={'GB': 97}, thHi={'GB': 53}), Theta(thLo={'GB': 97}, thHi={'GB': 54}), Theta(thLo={'GB': 97}, thHi={'GB': 55}), Theta(thLo={'GB': 97}, thHi={'GB': 56}), Theta(thLo={'GB': 97}, thHi={'GB': 57}), Theta(thLo={'GB': 97}, thHi={'GB': 58}), Theta(thLo={'GB': 97}, thHi={'GB': 59}), Theta(thLo={'GB': 97}, thHi={'GB': 60}), Theta(thLo={'GB': 97}, thHi={'GB': 61}), Theta(thLo={'GB': 97}, thHi={'GB': 62}), Theta(thLo={'GB': 97}, thHi={'GB': 63}), Theta(thLo={'GB': 97}, thHi={'GB': 64}), Theta(thLo={'GB': 97}, thHi={'GB': 65}), Theta(thLo={'GB': 97}, thHi={'GB': 66}), Theta(thLo={'GB': 97}, thHi={'GB': 67}), Theta(thLo={'GB': 97}, thHi={'GB': 68}), Theta(thLo={'GB': 97}, thHi={'GB': 69}), Theta(thLo={'GB': 97}, thHi={'GB': 70}), Theta(thLo={'GB': 97}, thHi={'GB': 71}), Theta(thLo={'GB': 97}, thHi={'GB': 72}), Theta(thLo={'GB': 97}, thHi={'GB': 73}), Theta(thLo={'GB': 97}, thHi={'GB': 74}), Theta(thLo={'GB': 97}, thHi={'GB': 75}), Theta(thLo={'GB': 97}, thHi={'GB': 76}), Theta(thLo={'GB': 97}, thHi={'GB': 77}), Theta(thLo={'GB': 97}, thHi={'GB': 78}), Theta(thLo={'GB': 97}, thHi={'GB': 79}), Theta(thLo={'GB': 97}, thHi={'GB': 80}), Theta(thLo={'GB': 97}, thHi={'GB': 81}), Theta(thLo={'GB': 97}, thHi={'GB': 82}), Theta(thLo={'GB': 97}, thHi={'GB': 83}), Theta(thLo={'GB': 97}, thHi={'GB': 84}), Theta(thLo={'GB': 97}, thHi={'GB': 85}), Theta(thLo={'GB': 97}, thHi={'GB': 86}), Theta(thLo={'GB': 97}, thHi={'GB': 87}), Theta(thLo={'GB': 97}, thHi={'GB': 88}), Theta(thLo={'GB': 97}, thHi={'GB': 89}), Theta(thLo={'GB': 97}, thHi={'GB': 90}), Theta(thLo={'GB': 97}, thHi={'GB': 91}), Theta(thLo={'GB': 97}, thHi={'GB': 92}), Theta(thLo={'GB': 97}, thHi={'GB': 93}), Theta(thLo={'GB': 97}, thHi={'GB': 94}), Theta(thLo={'GB': 97}, thHi={'GB': 95}), Theta(thLo={'GB': 97}, thHi={'GB': 96}), Theta(thLo={'GB': 97}, thHi={'GB': 97}), Theta(thLo={'GB': 97}, thHi={'GB': 98}), Theta(thLo={'GB': 97}, thHi={'GB': 99}), Theta(thLo={'GB': 98}, thHi={'GB': 10}), Theta(thLo={'GB': 98}, thHi={'GB': 11}), Theta(thLo={'GB': 98}, thHi={'GB': 12}), Theta(thLo={'GB': 98}, thHi={'GB': 13}), Theta(thLo={'GB': 98}, thHi={'GB': 14}), Theta(thLo={'GB': 98}, thHi={'GB': 15}), Theta(thLo={'GB': 98}, thHi={'GB': 16}), Theta(thLo={'GB': 98}, thHi={'GB': 17}), Theta(thLo={'GB': 98}, thHi={'GB': 18}), Theta(thLo={'GB': 98}, thHi={'GB': 19}), Theta(thLo={'GB': 98}, thHi={'GB': 20}), Theta(thLo={'GB': 98}, thHi={'GB': 21}), Theta(thLo={'GB': 98}, thHi={'GB': 22}), Theta(thLo={'GB': 98}, thHi={'GB': 23}), Theta(thLo={'GB': 98}, thHi={'GB': 24}), Theta(thLo={'GB': 98}, thHi={'GB': 25}), Theta(thLo={'GB': 98}, thHi={'GB': 26}), Theta(thLo={'GB': 98}, thHi={'GB': 27}), Theta(thLo={'GB': 98}, thHi={'GB': 28}), Theta(thLo={'GB': 98}, thHi={'GB': 29}), Theta(thLo={'GB': 98}, thHi={'GB': 30}), Theta(thLo={'GB': 98}, thHi={'GB': 31}), Theta(thLo={'GB': 98}, thHi={'GB': 32}), Theta(thLo={'GB': 98}, thHi={'GB': 33}), Theta(thLo={'GB': 98}, thHi={'GB': 34}), Theta(thLo={'GB': 98}, thHi={'GB': 35}), Theta(thLo={'GB': 98}, thHi={'GB': 36}), Theta(thLo={'GB': 98}, thHi={'GB': 37}), Theta(thLo={'GB': 98}, thHi={'GB': 38}), Theta(thLo={'GB': 98}, thHi={'GB': 39}), Theta(thLo={'GB': 98}, thHi={'GB': 40}), Theta(thLo={'GB': 98}, thHi={'GB': 41}), Theta(thLo={'GB': 98}, thHi={'GB': 42}), Theta(thLo={'GB': 98}, thHi={'GB': 43}), Theta(thLo={'GB': 98}, thHi={'GB': 44}), Theta(thLo={'GB': 98}, thHi={'GB': 45}), Theta(thLo={'GB': 98}, thHi={'GB': 46}), Theta(thLo={'GB': 98}, thHi={'GB': 47}), Theta(thLo={'GB': 98}, thHi={'GB': 48}), Theta(thLo={'GB': 98}, thHi={'GB': 49}), Theta(thLo={'GB': 98}, thHi={'GB': 50}), Theta(thLo={'GB': 98}, thHi={'GB': 51}), Theta(thLo={'GB': 98}, thHi={'GB': 52}), Theta(thLo={'GB': 98}, thHi={'GB': 53}), Theta(thLo={'GB': 98}, thHi={'GB': 54}), Theta(thLo={'GB': 98}, thHi={'GB': 55}), Theta(thLo={'GB': 98}, thHi={'GB': 56}), Theta(thLo={'GB': 98}, thHi={'GB': 57}), Theta(thLo={'GB': 98}, thHi={'GB': 58}), Theta(thLo={'GB': 98}, thHi={'GB': 59}), Theta(thLo={'GB': 98}, thHi={'GB': 60}), Theta(thLo={'GB': 98}, thHi={'GB': 61}), Theta(thLo={'GB': 98}, thHi={'GB': 62}), Theta(thLo={'GB': 98}, thHi={'GB': 63}), Theta(thLo={'GB': 98}, thHi={'GB': 64}), Theta(thLo={'GB': 98}, thHi={'GB': 65}), Theta(thLo={'GB': 98}, thHi={'GB': 66}), Theta(thLo={'GB': 98}, thHi={'GB': 67}), Theta(thLo={'GB': 98}, thHi={'GB': 68}), Theta(thLo={'GB': 98}, thHi={'GB': 69}), Theta(thLo={'GB': 98}, thHi={'GB': 70}), Theta(thLo={'GB': 98}, thHi={'GB': 71}), Theta(thLo={'GB': 98}, thHi={'GB': 72}), Theta(thLo={'GB': 98}, thHi={'GB': 73}), Theta(thLo={'GB': 98}, thHi={'GB': 74}), Theta(thLo={'GB': 98}, thHi={'GB': 75}), Theta(thLo={'GB': 98}, thHi={'GB': 76}), Theta(thLo={'GB': 98}, thHi={'GB': 77}), Theta(thLo={'GB': 98}, thHi={'GB': 78}), Theta(thLo={'GB': 98}, thHi={'GB': 79}), Theta(thLo={'GB': 98}, thHi={'GB': 80}), Theta(thLo={'GB': 98}, thHi={'GB': 81}), Theta(thLo={'GB': 98}, thHi={'GB': 82}), Theta(thLo={'GB': 98}, thHi={'GB': 83}), Theta(thLo={'GB': 98}, thHi={'GB': 84}), Theta(thLo={'GB': 98}, thHi={'GB': 85}), Theta(thLo={'GB': 98}, thHi={'GB': 86}), Theta(thLo={'GB': 98}, thHi={'GB': 87}), Theta(thLo={'GB': 98}, thHi={'GB': 88}), Theta(thLo={'GB': 98}, thHi={'GB': 89}), Theta(thLo={'GB': 98}, thHi={'GB': 90}), Theta(thLo={'GB': 98}, thHi={'GB': 91}), Theta(thLo={'GB': 98}, thHi={'GB': 92}), Theta(thLo={'GB': 98}, thHi={'GB': 93}), Theta(thLo={'GB': 98}, thHi={'GB': 94}), Theta(thLo={'GB': 98}, thHi={'GB': 95}), Theta(thLo={'GB': 98}, thHi={'GB': 96}), Theta(thLo={'GB': 98}, thHi={'GB': 97}), Theta(thLo={'GB': 98}, thHi={'GB': 98}), Theta(thLo={'GB': 98}, thHi={'GB': 99}), Theta(thLo={'GB': 99}, thHi={'GB': 10}), Theta(thLo={'GB': 99}, thHi={'GB': 11}), Theta(thLo={'GB': 99}, thHi={'GB': 12}), Theta(thLo={'GB': 99}, thHi={'GB': 13}), Theta(thLo={'GB': 99}, thHi={'GB': 14}), Theta(thLo={'GB': 99}, thHi={'GB': 15}), Theta(thLo={'GB': 99}, thHi={'GB': 16}), Theta(thLo={'GB': 99}, thHi={'GB': 17}), Theta(thLo={'GB': 99}, thHi={'GB': 18}), Theta(thLo={'GB': 99}, thHi={'GB': 19}), Theta(thLo={'GB': 99}, thHi={'GB': 20}), Theta(thLo={'GB': 99}, thHi={'GB': 21}), Theta(thLo={'GB': 99}, thHi={'GB': 22}), Theta(thLo={'GB': 99}, thHi={'GB': 23}), Theta(thLo={'GB': 99}, thHi={'GB': 24}), Theta(thLo={'GB': 99}, thHi={'GB': 25}), Theta(thLo={'GB': 99}, thHi={'GB': 26}), Theta(thLo={'GB': 99}, thHi={'GB': 27}), Theta(thLo={'GB': 99}, thHi={'GB': 28}), Theta(thLo={'GB': 99}, thHi={'GB': 29}), Theta(thLo={'GB': 99}, thHi={'GB': 30}), Theta(thLo={'GB': 99}, thHi={'GB': 31}), Theta(thLo={'GB': 99}, thHi={'GB': 32}), Theta(thLo={'GB': 99}, thHi={'GB': 33}), Theta(thLo={'GB': 99}, thHi={'GB': 34}), Theta(thLo={'GB': 99}, thHi={'GB': 35}), Theta(thLo={'GB': 99}, thHi={'GB': 36}), Theta(thLo={'GB': 99}, thHi={'GB': 37}), Theta(thLo={'GB': 99}, thHi={'GB': 38}), Theta(thLo={'GB': 99}, thHi={'GB': 39}), Theta(thLo={'GB': 99}, thHi={'GB': 40}), Theta(thLo={'GB': 99}, thHi={'GB': 41}), Theta(thLo={'GB': 99}, thHi={'GB': 42}), Theta(thLo={'GB': 99}, thHi={'GB': 43}), Theta(thLo={'GB': 99}, thHi={'GB': 44}), Theta(thLo={'GB': 99}, thHi={'GB': 45}), Theta(thLo={'GB': 99}, thHi={'GB': 46}), Theta(thLo={'GB': 99}, thHi={'GB': 47}), Theta(thLo={'GB': 99}, thHi={'GB': 48}), Theta(thLo={'GB': 99}, thHi={'GB': 49}), Theta(thLo={'GB': 99}, thHi={'GB': 50}), Theta(thLo={'GB': 99}, thHi={'GB': 51}), Theta(thLo={'GB': 99}, thHi={'GB': 52}), Theta(thLo={'GB': 99}, thHi={'GB': 53}), Theta(thLo={'GB': 99}, thHi={'GB': 54}), Theta(thLo={'GB': 99}, thHi={'GB': 55}), Theta(thLo={'GB': 99}, thHi={'GB': 56}), Theta(thLo={'GB': 99}, thHi={'GB': 57}), Theta(thLo={'GB': 99}, thHi={'GB': 58}), Theta(thLo={'GB': 99}, thHi={'GB': 59}), Theta(thLo={'GB': 99}, thHi={'GB': 60}), Theta(thLo={'GB': 99}, thHi={'GB': 61}), Theta(thLo={'GB': 99}, thHi={'GB': 62}), Theta(thLo={'GB': 99}, thHi={'GB': 63}), Theta(thLo={'GB': 99}, thHi={'GB': 64}), Theta(thLo={'GB': 99}, thHi={'GB': 65}), Theta(thLo={'GB': 99}, thHi={'GB': 66}), Theta(thLo={'GB': 99}, thHi={'GB': 67}), Theta(thLo={'GB': 99}, thHi={'GB': 68}), Theta(thLo={'GB': 99}, thHi={'GB': 69}), Theta(thLo={'GB': 99}, thHi={'GB': 70}), Theta(thLo={'GB': 99}, thHi={'GB': 71}), Theta(thLo={'GB': 99}, thHi={'GB': 72}), Theta(thLo={'GB': 99}, thHi={'GB': 73}), Theta(thLo={'GB': 99}, thHi={'GB': 74}), Theta(thLo={'GB': 99}, thHi={'GB': 75}), Theta(thLo={'GB': 99}, thHi={'GB': 76}), Theta(thLo={'GB': 99}, thHi={'GB': 77}), Theta(thLo={'GB': 99}, thHi={'GB': 78}), Theta(thLo={'GB': 99}, thHi={'GB': 79}), Theta(thLo={'GB': 99}, thHi={'GB': 80}), Theta(thLo={'GB': 99}, thHi={'GB': 81}), Theta(thLo={'GB': 99}, thHi={'GB': 82}), Theta(thLo={'GB': 99}, thHi={'GB': 83}), Theta(thLo={'GB': 99}, thHi={'GB': 84}), Theta(thLo={'GB': 99}, thHi={'GB': 85}), Theta(thLo={'GB': 99}, thHi={'GB': 86}), Theta(thLo={'GB': 99}, thHi={'GB': 87}), Theta(thLo={'GB': 99}, thHi={'GB': 88}), Theta(thLo={'GB': 99}, thHi={'GB': 89}), Theta(thLo={'GB': 99}, thHi={'GB': 90}), Theta(thLo={'GB': 99}, thHi={'GB': 91}), Theta(thLo={'GB': 99}, thHi={'GB': 92}), Theta(thLo={'GB': 99}, thHi={'GB': 93}), Theta(thLo={'GB': 99}, thHi={'GB': 94}), Theta(thLo={'GB': 99}, thHi={'GB': 95}), Theta(thLo={'GB': 99}, thHi={'GB': 96}), Theta(thLo={'GB': 99}, thHi={'GB': 97}), Theta(thLo={'GB': 99}, thHi={'GB': 98}), Theta(thLo={'GB': 99}, thHi={'GB': 99})]
... printing every 500th theta ...
=== (0 / 8,100), theta=Theta(thLo={'GB': 10}, thHi={'GB': 11}) ===
=== (500 / 8,100), theta=Theta(thLo={'GB': 15}, thHi={'GB': 81}) ===
=== (1,000 / 8,100), theta=Theta(thLo={'GB': 21}, thHi={'GB': 98}) ===
=== (1,500 / 8,100), theta=Theta(thLo={'GB': 28}, thHi={'GB': 80}) ===
=== (2,000 / 8,100), theta=Theta(thLo={'GB': 36}, thHi={'GB': 48}) ===
=== (2,500 / 8,100), theta=Theta(thLo={'GB': 44}, thHi={'GB': 80}) ===
=== (3,000 / 8,100), theta=Theta(thLo={'GB': 54}, thHi={'GB': 85}) ===
=== (3,500 / 8,100), theta=Theta(thLo={'GB': 67}, thHi={'GB': 91}) ===
=== (4,000 / 8,100), theta=Theta(thLo={'GB': 96}, thHi={'GB': 98}) ===
best_theta_en:
Theta(thLo={'GB': 11}, thHi={'GB': 38})
best_Cbarcum=168.47
best_Ctilcum=0.00
worst_theta_en:
Theta(thLo={'GB': 10}, thHi={'GB': 10})
worst_Cbarcum=0.00
worst_Ctilcum=0.00
CPU times: user 3min 10s, sys: 5.93 s, total: 3min 16s
Wall time: 3min 23s

best_theta_BuyLowSellHigh

Theta(thLo={'GB': 11}, thHi={'GB': 38})

P.plot_Fhat_map_2(
    FhatI_theta_I=Cbarcum_BuyLowSellHigh,
    thetasX=th_lo[eNAMES[0]],
    thetasY=th_hi[eNAMES[0]],
    labelX=r'$\theta^{buy}$',
    labelY=r'$\theta^{sell}$',
    title="Sample mean of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
      r"$\theta^* =$"+ P.round_theta(best_theta_BuyLowSellHigh)+", " \
      r"$\bar{C}^{cum}(\theta^*) =$"+f"{best_Cbarcum_BuyLowSellHigh:.2f}",
)
print()
P.plot_Fhat_map_2(
    FhatI_theta_I=Ctilcum_BuyLowSellHigh,
    thetasX=th_lo[eNAMES[0]],
    thetasY=th_hi[eNAMES[0]],
    labelX=r'$\theta^{buy}$',
    labelY=r'$\theta^{sell}$',
    title="Standard error of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
      r"$\theta^* =$"+ P.round_theta(best_theta_BuyLowSellHigh)+", " \
      r"$\tilde{C}^{cum}(\theta^*) =$"+f"{best_Ctilcum_BuyLowSellHigh:.2f}",
);

P.plot_expFhat_chart(
  thetaStar_expCbarcum_BuyLowSellHigh,
  r'$\ell$',
  r"$exp\bar{C}^{cum}(\theta^*)$"+"\n(Profit)\n[$]",
  "Expanding sample mean of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
    r"$\theta^* =$"+ P.round_theta(best_theta_BuyLowSellHigh)+", " \
    r"$\bar{C}^{cum}(\theta^*) =$"+f"{best_Cbarcum_BuyLowSellHigh:.2f}",
  'b-'
)
print()
P.plot_expFhat_chart(
  thetaStar_expCtilcum_BuyLowSellHigh,
  r'$\ell$',
  r"$exp\tilde{C}^{cum}(\theta^*)$"+"\n(Profit)\n[$]",
  "Expanding standard error of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
    r"$\theta^* =$"+ P.round_theta(best_theta_BuyLowSellHigh)+", " \
    r"$\tilde{C}^{cum}(\theta^*) =$"+f"{best_Ctilcum_BuyLowSellHigh:.2f}",
  'b--'
);

f'{len(record_BuyLowSellHigh):,}', L, T

('20,025,000', 50, 100)

best_theta_BuyLowSellHigh

Theta(thLo={'GB': 11}, thHi={'GB': 38})

P.plot_records(
  df=df_first_n_t,
  df_non=None,
  pars=defaultdict(str, {
    'thetaLo': {en: best_theta_BuyLowSellHigh.thLo[en] for en in eNAMES},
    'thetaHi': {en: best_theta_BuyLowSellHigh.thHi[en] for en in eNAMES},
    'suptitle': f'TRAINING OF X__BuyLowSellHigh POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$\theta^*=$'+f'{P.round_theta(best_theta_BuyLowSellHigh)}',
  }),
)

P.plot_records(
  df=df_last_n_t,
  df_non=None,
  pars=defaultdict(str, {
    'thetaLo': {en: best_theta_BuyLowSellHigh.thLo[en] for en in eNAMES},
    'thetaHi': {en: best_theta_BuyLowSellHigh.thHi[en] for en in eNAMES},
    'suptitle': f'TRAINING OF X__BuyLowSellHigh POLICY'+'\n'+f'(last {last_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$\theta^*=$'+f'{P.round_theta(best_theta_BuyLowSellHigh)}',
  }),
)

4.6.1.2 X__Bellman

# setup labels to plot info
R_t_labels = ['R_t_'+en for en in eNAMES]
p_t_labels = ['p_t_'+en for en in eNAMES]
x_t_labels = ['x_t_'+en for en in eNAMES]
labels = ['piName', 'inc', 'l'] + \
  ['t'] + R_t_labels + p_t_labels + \
  ['Ccum'] + x_t_labels
labels

['piName', 'inc', 'l', 't', 'R_t_GB', 'p_t_GB', 'Ccum', 'x_t_GB']

N_SAMPLEPATHS, N_TRANSITIONS

(3, 192)

%%time
L = 5 #N_SAMPLEPATHS
T = 100 #N_TRANSITIONS
first_n_t = int(2*T)
last_n_t = int(2*T)

M = Model(S_0_INFO)
P = Policy(M)

#Constructing the state space

#discrete energy
# R__disc = np.array([0., 1.]) #USE TO DEBUG (fast)
R__disc = np.array([0., .5, 1.]) #USE TO PUBLISH
# R__disc = np.array([0., 1., 2.])
# R__disc = np.array([0., 1.])
# R__disc = np.array([0., .2, .4, .6, .8, 1.])
# R__disc = np.array([0., .5, 1.])

minPrice = np.min(EXOG_PARAMS['hist_price'])
maxPrice = np.max(EXOG_PARAMS['hist_price'])

# incs = [.1, .2, .5, 1.0, 2.0, 5.0] #2.5 hours
incs = [0.5, 1.0, 2.0, 5.0, 10.0] #3 mins #USE TO PUBLISH
# incs = [2.0, 5.0, 10.0] #USE TO DEBUG (fast)
incStar_expCbarcum_Bellman, incStar_expCtilcum_Bellman, \
Cbarcum_Bellman, Ctilcum_Bellman, \
best_inc_Bellman, worst_inc_Bellman, \
best_Cbarcum_Bellman, worst_Cbarcum_Bellman, \
best_Ctilcum_Bellman, worst_Ctilcum_Bellman, \
bdp_Bellman, \
best_bdp_Bellman, \
record_Bellman = \
  P.perform_bellman_search_sample_paths(
    "X__Bellman", R__disc, minPrice, maxPrice, incs)
df_first_n_t = pd.DataFrame.from_records(record_Bellman[:first_n_t], columns=labels)
df_last_n_t = pd.DataFrame.from_records(record_Bellman[-last_n_t:], columns=labels)

# SUMMARY
# P.perform_bellman_search_sample_paths()
#     for inc in incs: #for each discretization
#         /////// additional ////////
#         test_2D_bdp = BDP()
#         test_2D_bdp.compute_value_function()
#             while t != -1: #. for each t
#                 for S_t in self.possible_states: #. for each S_t
#                     for d in self.model.possible_decisions: #. for each x_t
#                         for w in self.discrete_price_changes: #. for each w
#         \\\\\\\
#         P.run_bellman_sample_paths(inc, test_2D_bdp, piName, record)
#             for l in list(range(L)): #for each sample-path
#                 for t in range(T): #for each transition/step
#                     x_t = getattr(self, piName)(t, M.S_t, piInfo, T) #. piInfo is bdp
#                     S_t, Ccum, x_t = M.step(t, x_t)
#     return \
#         incStar_expCbarcum, incStar_expCtilcum, \
#         Cbarcum, Ctilcum, \
#         best_inc, worst_inc, \
#         best_Cbarcum, worst_Cbarcum, \
#         best_Ctilcum, worst_Ctilcum, \
#         bdp, \
#         best_bdp, \
#         record

..... P.perform_bellman_search_sample_paths() .....
numIncs=5
incs=[0.5, 1.0, 2.0, 5.0, 10.0]
printing every 1th inc
=== (0 / 4), inc=0.5 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 648.           Exogenous info size: 50
    self.p__disc=array([  0. ,   0.5,   1. ,   1.5,   2. ,   2.5,   3. ,   3.5,   4. ,
         4.5,   5. ,   5.5,   6. ,   6.5,   7. ,   7.5,   8. ,   8.5,
         9. ,   9.5,  10. ,  10.5,  11. ,  11.5,  12. ,  12.5,  13. ,
        13.5,  14. ,  14.5,  15. ,  15.5,  16. ,  16.5,  17. ,  17.5,
        18. ,  18.5,  19. ,  19.5,  20. ,  20.5,  21. ,  21.5,  22. ,
        22.5,  23. ,  23.5,  24. ,  24.5,  25. ,  25.5,  26. ,  26.5,
        27. ,  27.5,  28. ,  28.5,  29. ,  29.5,  30. ,  30.5,  31. ,
        31.5,  32. ,  32.5,  33. ,  33.5,  34. ,  34.5,  35. ,  35.5,
        36. ,  36.5,  37. ,  37.5,  38. ,  38.5,  39. ,  39.5,  40. ,
        40.5,  41. ,  41.5,  42. ,  42.5,  43. ,  43.5,  44. ,  44.5,
        45. ,  45.5,  46. ,  46.5,  47. ,  47.5,  48. ,  48.5,  49. ,
        49.5,  50. ,  50.5,  51. ,  51.5,  52. ,  52.5,  53. ,  53.5,
        54. ,  54.5,  55. ,  55.5,  56. ,  56.5,  57. ,  57.5,  58. ,
        58.5,  59. ,  59.5,  60. ,  60.5,  61. ,  61.5,  62. ,  62.5,
        63. ,  63.5,  64. ,  64.5,  65. ,  65.5,  66. ,  66.5,  67. ,
        67.5,  68. ,  68.5,  69. ,  69.5,  70. ,  70.5,  71. ,  71.5,
        72. ,  72.5,  73. ,  73.5,  74. ,  74.5,  75. ,  75.5,  76. ,
        76.5,  77. ,  77.5,  78. ,  78.5,  79. ,  79.5,  80. ,  80.5,
        81. ,  81.5,  82. ,  82.5,  83. ,  83.5,  84. ,  84.5,  85. ,
        85.5,  86. ,  86.5,  87. ,  87.5,  88. ,  88.5,  89. ,  89.5,
        90. ,  90.5,  91. ,  91.5,  92. ,  92.5,  93. ,  93.5,  94. ,
        94.5,  95. ,  95.5,  96. ,  96.5,  97. ,  97.5,  98. ,  98.5,
        99. ,  99.5, 100. , 100.5, 101. , 101.5, 102. , 102.5, 103. ,
       103.5, 104. , 104.5, 105. , 105.5, 106. , 106.5, 107. , 107.5])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=0.5), State(R_t=0.5, p_t=0.5), State(R_t=1.0, p_t=0.5), State(R_t=0.0, p_t=1.0), State(R_t=0.5, p_t=1.0), State(R_t=1.0, p_t=1.0), State(R_t=0.0, p_t=1.5), State(R_t=0.5, p_t=1.5), State(R_t=1.0, p_t=1.5), State(R_t=0.0, p_t=2.0), State(R_t=0.5, p_t=2.0), State(R_t=1.0, p_t=2.0), State(R_t=0.0, p_t=2.5), State(R_t=0.5, p_t=2.5), State(R_t=1.0, p_t=2.5), State(R_t=0.0, p_t=3.0), State(R_t=0.5, p_t=3.0), State(R_t=1.0, p_t=3.0), State(R_t=0.0, p_t=3.5), State(R_t=0.5, p_t=3.5), State(R_t=1.0, p_t=3.5), State(R_t=0.0, p_t=4.0), State(R_t=0.5, p_t=4.0), State(R_t=1.0, p_t=4.0), State(R_t=0.0, p_t=4.5), State(R_t=0.5, p_t=4.5), State(R_t=1.0, p_t=4.5), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=5.5), State(R_t=0.5, p_t=5.5), State(R_t=1.0, p_t=5.5), State(R_t=0.0, p_t=6.0), State(R_t=0.5, p_t=6.0), State(R_t=1.0, p_t=6.0), State(R_t=0.0, p_t=6.5), State(R_t=0.5, p_t=6.5), State(R_t=1.0, p_t=6.5), State(R_t=0.0, p_t=7.0), State(R_t=0.5, p_t=7.0), State(R_t=1.0, p_t=7.0), State(R_t=0.0, p_t=7.5), State(R_t=0.5, p_t=7.5), State(R_t=1.0, p_t=7.5), State(R_t=0.0, p_t=8.0), State(R_t=0.5, p_t=8.0), State(R_t=1.0, p_t=8.0), State(R_t=0.0, p_t=8.5), State(R_t=0.5, p_t=8.5), State(R_t=1.0, p_t=8.5), State(R_t=0.0, p_t=9.0), State(R_t=0.5, p_t=9.0), State(R_t=1.0, p_t=9.0), State(R_t=0.0, p_t=9.5), State(R_t=0.5, p_t=9.5), State(R_t=1.0, p_t=9.5), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=10.5), State(R_t=0.5, p_t=10.5), State(R_t=1.0, p_t=10.5), State(R_t=0.0, p_t=11.0), State(R_t=0.5, p_t=11.0), State(R_t=1.0, p_t=11.0), State(R_t=0.0, p_t=11.5), State(R_t=0.5, p_t=11.5), State(R_t=1.0, p_t=11.5), State(R_t=0.0, p_t=12.0), State(R_t=0.5, p_t=12.0), State(R_t=1.0, p_t=12.0), State(R_t=0.0, p_t=12.5), State(R_t=0.5, p_t=12.5), State(R_t=1.0, p_t=12.5), State(R_t=0.0, p_t=13.0), State(R_t=0.5, p_t=13.0), State(R_t=1.0, p_t=13.0), State(R_t=0.0, p_t=13.5), State(R_t=0.5, p_t=13.5), State(R_t=1.0, p_t=13.5), State(R_t=0.0, p_t=14.0), State(R_t=0.5, p_t=14.0), State(R_t=1.0, p_t=14.0), State(R_t=0.0, p_t=14.5), State(R_t=0.5, p_t=14.5), State(R_t=1.0, p_t=14.5), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=15.5), State(R_t=0.5, p_t=15.5), State(R_t=1.0, p_t=15.5), State(R_t=0.0, p_t=16.0), State(R_t=0.5, p_t=16.0), State(R_t=1.0, p_t=16.0), State(R_t=0.0, p_t=16.5), State(R_t=0.5, p_t=16.5), State(R_t=1.0, p_t=16.5), State(R_t=0.0, p_t=17.0), State(R_t=0.5, p_t=17.0), State(R_t=1.0, p_t=17.0), State(R_t=0.0, p_t=17.5), State(R_t=0.5, p_t=17.5), State(R_t=1.0, p_t=17.5), State(R_t=0.0, p_t=18.0), State(R_t=0.5, p_t=18.0), State(R_t=1.0, p_t=18.0), State(R_t=0.0, p_t=18.5), State(R_t=0.5, p_t=18.5), State(R_t=1.0, p_t=18.5), State(R_t=0.0, p_t=19.0), State(R_t=0.5, p_t=19.0), State(R_t=1.0, p_t=19.0), State(R_t=0.0, p_t=19.5), State(R_t=0.5, p_t=19.5), State(R_t=1.0, p_t=19.5), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=20.5), State(R_t=0.5, p_t=20.5), State(R_t=1.0, p_t=20.5), State(R_t=0.0, p_t=21.0), State(R_t=0.5, p_t=21.0), State(R_t=1.0, p_t=21.0), State(R_t=0.0, p_t=21.5), State(R_t=0.5, p_t=21.5), State(R_t=1.0, p_t=21.5), State(R_t=0.0, p_t=22.0), State(R_t=0.5, p_t=22.0), State(R_t=1.0, p_t=22.0), State(R_t=0.0, p_t=22.5), State(R_t=0.5, p_t=22.5), State(R_t=1.0, p_t=22.5), State(R_t=0.0, p_t=23.0), State(R_t=0.5, p_t=23.0), State(R_t=1.0, p_t=23.0), State(R_t=0.0, p_t=23.5), State(R_t=0.5, p_t=23.5), State(R_t=1.0, p_t=23.5), State(R_t=0.0, p_t=24.0), State(R_t=0.5, p_t=24.0), State(R_t=1.0, p_t=24.0), State(R_t=0.0, p_t=24.5), State(R_t=0.5, p_t=24.5), State(R_t=1.0, p_t=24.5), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=25.5), State(R_t=0.5, p_t=25.5), State(R_t=1.0, p_t=25.5), State(R_t=0.0, p_t=26.0), State(R_t=0.5, p_t=26.0), State(R_t=1.0, p_t=26.0), State(R_t=0.0, p_t=26.5), State(R_t=0.5, p_t=26.5), State(R_t=1.0, p_t=26.5), State(R_t=0.0, p_t=27.0), State(R_t=0.5, p_t=27.0), State(R_t=1.0, p_t=27.0), State(R_t=0.0, p_t=27.5), State(R_t=0.5, p_t=27.5), State(R_t=1.0, p_t=27.5), State(R_t=0.0, p_t=28.0), State(R_t=0.5, p_t=28.0), State(R_t=1.0, p_t=28.0), State(R_t=0.0, p_t=28.5), State(R_t=0.5, p_t=28.5), State(R_t=1.0, p_t=28.5), State(R_t=0.0, p_t=29.0), State(R_t=0.5, p_t=29.0), State(R_t=1.0, p_t=29.0), State(R_t=0.0, p_t=29.5), State(R_t=0.5, p_t=29.5), State(R_t=1.0, p_t=29.5), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=30.5), State(R_t=0.5, p_t=30.5), State(R_t=1.0, p_t=30.5), State(R_t=0.0, p_t=31.0), State(R_t=0.5, p_t=31.0), State(R_t=1.0, p_t=31.0), State(R_t=0.0, p_t=31.5), State(R_t=0.5, p_t=31.5), State(R_t=1.0, p_t=31.5), State(R_t=0.0, p_t=32.0), State(R_t=0.5, p_t=32.0), State(R_t=1.0, p_t=32.0), State(R_t=0.0, p_t=32.5), State(R_t=0.5, p_t=32.5), State(R_t=1.0, p_t=32.5), State(R_t=0.0, p_t=33.0), State(R_t=0.5, p_t=33.0), State(R_t=1.0, p_t=33.0), State(R_t=0.0, p_t=33.5), State(R_t=0.5, p_t=33.5), State(R_t=1.0, p_t=33.5), State(R_t=0.0, p_t=34.0), State(R_t=0.5, p_t=34.0), State(R_t=1.0, p_t=34.0), State(R_t=0.0, p_t=34.5), State(R_t=0.5, p_t=34.5), State(R_t=1.0, p_t=34.5), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=35.5), State(R_t=0.5, p_t=35.5), State(R_t=1.0, p_t=35.5), State(R_t=0.0, p_t=36.0), State(R_t=0.5, p_t=36.0), State(R_t=1.0, p_t=36.0), State(R_t=0.0, p_t=36.5), State(R_t=0.5, p_t=36.5), State(R_t=1.0, p_t=36.5), State(R_t=0.0, p_t=37.0), State(R_t=0.5, p_t=37.0), State(R_t=1.0, p_t=37.0), State(R_t=0.0, p_t=37.5), State(R_t=0.5, p_t=37.5), State(R_t=1.0, p_t=37.5), State(R_t=0.0, p_t=38.0), State(R_t=0.5, p_t=38.0), State(R_t=1.0, p_t=38.0), State(R_t=0.0, p_t=38.5), State(R_t=0.5, p_t=38.5), State(R_t=1.0, p_t=38.5), State(R_t=0.0, p_t=39.0), State(R_t=0.5, p_t=39.0), State(R_t=1.0, p_t=39.0), State(R_t=0.0, p_t=39.5), State(R_t=0.5, p_t=39.5), State(R_t=1.0, p_t=39.5), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=40.5), State(R_t=0.5, p_t=40.5), State(R_t=1.0, p_t=40.5), State(R_t=0.0, p_t=41.0), State(R_t=0.5, p_t=41.0), State(R_t=1.0, p_t=41.0), State(R_t=0.0, p_t=41.5), State(R_t=0.5, p_t=41.5), State(R_t=1.0, p_t=41.5), State(R_t=0.0, p_t=42.0), State(R_t=0.5, p_t=42.0), State(R_t=1.0, p_t=42.0), State(R_t=0.0, p_t=42.5), State(R_t=0.5, p_t=42.5), State(R_t=1.0, p_t=42.5), State(R_t=0.0, p_t=43.0), State(R_t=0.5, p_t=43.0), State(R_t=1.0, p_t=43.0), State(R_t=0.0, p_t=43.5), State(R_t=0.5, p_t=43.5), State(R_t=1.0, p_t=43.5), State(R_t=0.0, p_t=44.0), State(R_t=0.5, p_t=44.0), State(R_t=1.0, p_t=44.0), State(R_t=0.0, p_t=44.5), State(R_t=0.5, p_t=44.5), State(R_t=1.0, p_t=44.5), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=45.5), State(R_t=0.5, p_t=45.5), State(R_t=1.0, p_t=45.5), State(R_t=0.0, p_t=46.0), State(R_t=0.5, p_t=46.0), State(R_t=1.0, p_t=46.0), State(R_t=0.0, p_t=46.5), State(R_t=0.5, p_t=46.5), State(R_t=1.0, p_t=46.5), State(R_t=0.0, p_t=47.0), State(R_t=0.5, p_t=47.0), State(R_t=1.0, p_t=47.0), State(R_t=0.0, p_t=47.5), State(R_t=0.5, p_t=47.5), State(R_t=1.0, p_t=47.5), State(R_t=0.0, p_t=48.0), State(R_t=0.5, p_t=48.0), State(R_t=1.0, p_t=48.0), State(R_t=0.0, p_t=48.5), State(R_t=0.5, p_t=48.5), State(R_t=1.0, p_t=48.5), State(R_t=0.0, p_t=49.0), State(R_t=0.5, p_t=49.0), State(R_t=1.0, p_t=49.0), State(R_t=0.0, p_t=49.5), State(R_t=0.5, p_t=49.5), State(R_t=1.0, p_t=49.5), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=50.5), State(R_t=0.5, p_t=50.5), State(R_t=1.0, p_t=50.5), State(R_t=0.0, p_t=51.0), State(R_t=0.5, p_t=51.0), State(R_t=1.0, p_t=51.0), State(R_t=0.0, p_t=51.5), State(R_t=0.5, p_t=51.5), State(R_t=1.0, p_t=51.5), State(R_t=0.0, p_t=52.0), State(R_t=0.5, p_t=52.0), State(R_t=1.0, p_t=52.0), State(R_t=0.0, p_t=52.5), State(R_t=0.5, p_t=52.5), State(R_t=1.0, p_t=52.5), State(R_t=0.0, p_t=53.0), State(R_t=0.5, p_t=53.0), State(R_t=1.0, p_t=53.0), State(R_t=0.0, p_t=53.5), State(R_t=0.5, p_t=53.5), State(R_t=1.0, p_t=53.5), State(R_t=0.0, p_t=54.0), State(R_t=0.5, p_t=54.0), State(R_t=1.0, p_t=54.0), State(R_t=0.0, p_t=54.5), State(R_t=0.5, p_t=54.5), State(R_t=1.0, p_t=54.5), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=55.5), State(R_t=0.5, p_t=55.5), State(R_t=1.0, p_t=55.5), State(R_t=0.0, p_t=56.0), State(R_t=0.5, p_t=56.0), State(R_t=1.0, p_t=56.0), State(R_t=0.0, p_t=56.5), State(R_t=0.5, p_t=56.5), State(R_t=1.0, p_t=56.5), State(R_t=0.0, p_t=57.0), State(R_t=0.5, p_t=57.0), State(R_t=1.0, p_t=57.0), State(R_t=0.0, p_t=57.5), State(R_t=0.5, p_t=57.5), State(R_t=1.0, p_t=57.5), State(R_t=0.0, p_t=58.0), State(R_t=0.5, p_t=58.0), State(R_t=1.0, p_t=58.0), State(R_t=0.0, p_t=58.5), State(R_t=0.5, p_t=58.5), State(R_t=1.0, p_t=58.5), State(R_t=0.0, p_t=59.0), State(R_t=0.5, p_t=59.0), State(R_t=1.0, p_t=59.0), State(R_t=0.0, p_t=59.5), State(R_t=0.5, p_t=59.5), State(R_t=1.0, p_t=59.5), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=60.5), State(R_t=0.5, p_t=60.5), State(R_t=1.0, p_t=60.5), State(R_t=0.0, p_t=61.0), State(R_t=0.5, p_t=61.0), State(R_t=1.0, p_t=61.0), State(R_t=0.0, p_t=61.5), State(R_t=0.5, p_t=61.5), State(R_t=1.0, p_t=61.5), State(R_t=0.0, p_t=62.0), State(R_t=0.5, p_t=62.0), State(R_t=1.0, p_t=62.0), State(R_t=0.0, p_t=62.5), State(R_t=0.5, p_t=62.5), State(R_t=1.0, p_t=62.5), State(R_t=0.0, p_t=63.0), State(R_t=0.5, p_t=63.0), State(R_t=1.0, p_t=63.0), State(R_t=0.0, p_t=63.5), State(R_t=0.5, p_t=63.5), State(R_t=1.0, p_t=63.5), State(R_t=0.0, p_t=64.0), State(R_t=0.5, p_t=64.0), State(R_t=1.0, p_t=64.0), State(R_t=0.0, p_t=64.5), State(R_t=0.5, p_t=64.5), State(R_t=1.0, p_t=64.5), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=65.5), State(R_t=0.5, p_t=65.5), State(R_t=1.0, p_t=65.5), State(R_t=0.0, p_t=66.0), State(R_t=0.5, p_t=66.0), State(R_t=1.0, p_t=66.0), State(R_t=0.0, p_t=66.5), State(R_t=0.5, p_t=66.5), State(R_t=1.0, p_t=66.5), State(R_t=0.0, p_t=67.0), State(R_t=0.5, p_t=67.0), State(R_t=1.0, p_t=67.0), State(R_t=0.0, p_t=67.5), State(R_t=0.5, p_t=67.5), State(R_t=1.0, p_t=67.5), State(R_t=0.0, p_t=68.0), State(R_t=0.5, p_t=68.0), State(R_t=1.0, p_t=68.0), State(R_t=0.0, p_t=68.5), State(R_t=0.5, p_t=68.5), State(R_t=1.0, p_t=68.5), State(R_t=0.0, p_t=69.0), State(R_t=0.5, p_t=69.0), State(R_t=1.0, p_t=69.0), State(R_t=0.0, p_t=69.5), State(R_t=0.5, p_t=69.5), State(R_t=1.0, p_t=69.5), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=70.5), State(R_t=0.5, p_t=70.5), State(R_t=1.0, p_t=70.5), State(R_t=0.0, p_t=71.0), State(R_t=0.5, p_t=71.0), State(R_t=1.0, p_t=71.0), State(R_t=0.0, p_t=71.5), State(R_t=0.5, p_t=71.5), State(R_t=1.0, p_t=71.5), State(R_t=0.0, p_t=72.0), State(R_t=0.5, p_t=72.0), State(R_t=1.0, p_t=72.0), State(R_t=0.0, p_t=72.5), State(R_t=0.5, p_t=72.5), State(R_t=1.0, p_t=72.5), State(R_t=0.0, p_t=73.0), State(R_t=0.5, p_t=73.0), State(R_t=1.0, p_t=73.0), State(R_t=0.0, p_t=73.5), State(R_t=0.5, p_t=73.5), State(R_t=1.0, p_t=73.5), State(R_t=0.0, p_t=74.0), State(R_t=0.5, p_t=74.0), State(R_t=1.0, p_t=74.0), State(R_t=0.0, p_t=74.5), State(R_t=0.5, p_t=74.5), State(R_t=1.0, p_t=74.5), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=75.5), State(R_t=0.5, p_t=75.5), State(R_t=1.0, p_t=75.5), State(R_t=0.0, p_t=76.0), State(R_t=0.5, p_t=76.0), State(R_t=1.0, p_t=76.0), State(R_t=0.0, p_t=76.5), State(R_t=0.5, p_t=76.5), State(R_t=1.0, p_t=76.5), State(R_t=0.0, p_t=77.0), State(R_t=0.5, p_t=77.0), State(R_t=1.0, p_t=77.0), State(R_t=0.0, p_t=77.5), State(R_t=0.5, p_t=77.5), State(R_t=1.0, p_t=77.5), State(R_t=0.0, p_t=78.0), State(R_t=0.5, p_t=78.0), State(R_t=1.0, p_t=78.0), State(R_t=0.0, p_t=78.5), State(R_t=0.5, p_t=78.5), State(R_t=1.0, p_t=78.5), State(R_t=0.0, p_t=79.0), State(R_t=0.5, p_t=79.0), State(R_t=1.0, p_t=79.0), State(R_t=0.0, p_t=79.5), State(R_t=0.5, p_t=79.5), State(R_t=1.0, p_t=79.5), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=80.5), State(R_t=0.5, p_t=80.5), State(R_t=1.0, p_t=80.5), State(R_t=0.0, p_t=81.0), State(R_t=0.5, p_t=81.0), State(R_t=1.0, p_t=81.0), State(R_t=0.0, p_t=81.5), State(R_t=0.5, p_t=81.5), State(R_t=1.0, p_t=81.5), State(R_t=0.0, p_t=82.0), State(R_t=0.5, p_t=82.0), State(R_t=1.0, p_t=82.0), State(R_t=0.0, p_t=82.5), State(R_t=0.5, p_t=82.5), State(R_t=1.0, p_t=82.5), State(R_t=0.0, p_t=83.0), State(R_t=0.5, p_t=83.0), State(R_t=1.0, p_t=83.0), State(R_t=0.0, p_t=83.5), State(R_t=0.5, p_t=83.5), State(R_t=1.0, p_t=83.5), State(R_t=0.0, p_t=84.0), State(R_t=0.5, p_t=84.0), State(R_t=1.0, p_t=84.0), State(R_t=0.0, p_t=84.5), State(R_t=0.5, p_t=84.5), State(R_t=1.0, p_t=84.5), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=85.5), State(R_t=0.5, p_t=85.5), State(R_t=1.0, p_t=85.5), State(R_t=0.0, p_t=86.0), State(R_t=0.5, p_t=86.0), State(R_t=1.0, p_t=86.0), State(R_t=0.0, p_t=86.5), State(R_t=0.5, p_t=86.5), State(R_t=1.0, p_t=86.5), State(R_t=0.0, p_t=87.0), State(R_t=0.5, p_t=87.0), State(R_t=1.0, p_t=87.0), State(R_t=0.0, p_t=87.5), State(R_t=0.5, p_t=87.5), State(R_t=1.0, p_t=87.5), State(R_t=0.0, p_t=88.0), State(R_t=0.5, p_t=88.0), State(R_t=1.0, p_t=88.0), State(R_t=0.0, p_t=88.5), State(R_t=0.5, p_t=88.5), State(R_t=1.0, p_t=88.5), State(R_t=0.0, p_t=89.0), State(R_t=0.5, p_t=89.0), State(R_t=1.0, p_t=89.0), State(R_t=0.0, p_t=89.5), State(R_t=0.5, p_t=89.5), State(R_t=1.0, p_t=89.5), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=90.5), State(R_t=0.5, p_t=90.5), State(R_t=1.0, p_t=90.5), State(R_t=0.0, p_t=91.0), State(R_t=0.5, p_t=91.0), State(R_t=1.0, p_t=91.0), State(R_t=0.0, p_t=91.5), State(R_t=0.5, p_t=91.5), State(R_t=1.0, p_t=91.5), State(R_t=0.0, p_t=92.0), State(R_t=0.5, p_t=92.0), State(R_t=1.0, p_t=92.0), State(R_t=0.0, p_t=92.5), State(R_t=0.5, p_t=92.5), State(R_t=1.0, p_t=92.5), State(R_t=0.0, p_t=93.0), State(R_t=0.5, p_t=93.0), State(R_t=1.0, p_t=93.0), State(R_t=0.0, p_t=93.5), State(R_t=0.5, p_t=93.5), State(R_t=1.0, p_t=93.5), State(R_t=0.0, p_t=94.0), State(R_t=0.5, p_t=94.0), State(R_t=1.0, p_t=94.0), State(R_t=0.0, p_t=94.5), State(R_t=0.5, p_t=94.5), State(R_t=1.0, p_t=94.5), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=95.5), State(R_t=0.5, p_t=95.5), State(R_t=1.0, p_t=95.5), State(R_t=0.0, p_t=96.0), State(R_t=0.5, p_t=96.0), State(R_t=1.0, p_t=96.0), State(R_t=0.0, p_t=96.5), State(R_t=0.5, p_t=96.5), State(R_t=1.0, p_t=96.5), State(R_t=0.0, p_t=97.0), State(R_t=0.5, p_t=97.0), State(R_t=1.0, p_t=97.0), State(R_t=0.0, p_t=97.5), State(R_t=0.5, p_t=97.5), State(R_t=1.0, p_t=97.5), State(R_t=0.0, p_t=98.0), State(R_t=0.5, p_t=98.0), State(R_t=1.0, p_t=98.0), State(R_t=0.0, p_t=98.5), State(R_t=0.5, p_t=98.5), State(R_t=1.0, p_t=98.5), State(R_t=0.0, p_t=99.0), State(R_t=0.5, p_t=99.0), State(R_t=1.0, p_t=99.0), State(R_t=0.0, p_t=99.5), State(R_t=0.5, p_t=99.5), State(R_t=1.0, p_t=99.5), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=100.5), State(R_t=0.5, p_t=100.5), State(R_t=1.0, p_t=100.5), State(R_t=0.0, p_t=101.0), State(R_t=0.5, p_t=101.0), State(R_t=1.0, p_t=101.0), State(R_t=0.0, p_t=101.5), State(R_t=0.5, p_t=101.5), State(R_t=1.0, p_t=101.5), State(R_t=0.0, p_t=102.0), State(R_t=0.5, p_t=102.0), State(R_t=1.0, p_t=102.0), State(R_t=0.0, p_t=102.5), State(R_t=0.5, p_t=102.5), State(R_t=1.0, p_t=102.5), State(R_t=0.0, p_t=103.0), State(R_t=0.5, p_t=103.0), State(R_t=1.0, p_t=103.0), State(R_t=0.0, p_t=103.5), State(R_t=0.5, p_t=103.5), State(R_t=1.0, p_t=103.5), State(R_t=0.0, p_t=104.0), State(R_t=0.5, p_t=104.0), State(R_t=1.0, p_t=104.0), State(R_t=0.0, p_t=104.5), State(R_t=0.5, p_t=104.5), State(R_t=1.0, p_t=104.5), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=105.5), State(R_t=0.5, p_t=105.5), State(R_t=1.0, p_t=105.5), State(R_t=0.0, p_t=106.0), State(R_t=0.5, p_t=106.0), State(R_t=1.0, p_t=106.0), State(R_t=0.0, p_t=106.5), State(R_t=0.5, p_t=106.5), State(R_t=1.0, p_t=106.5), State(R_t=0.0, p_t=107.0), State(R_t=0.5, p_t=107.0), State(R_t=1.0, p_t=107.0), State(R_t=0.0, p_t=107.5), State(R_t=0.5, p_t=107.5), State(R_t=1.0, p_t=107.5)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
Finishing inc 0.5 with best_inc_evolving=0.5, best_Cbarcum_evolving=23.355
=== (1 / 4), inc=1.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 327.           Exogenous info size: 50
    self.p__disc=array([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,
        11.,  12.,  13.,  14.,  15.,  16.,  17.,  18.,  19.,  20.,  21.,
        22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,  30.,  31.,  32.,
        33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,  42.,  43.,
        44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,  54.,
        55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
        66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,
        77.,  78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,
        88.,  89.,  90.,  91.,  92.,  93.,  94.,  95.,  96.,  97.,  98.,
        99., 100., 101., 102., 103., 104., 105., 106., 107., 108.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=1.0), State(R_t=0.5, p_t=1.0), State(R_t=1.0, p_t=1.0), State(R_t=0.0, p_t=2.0), State(R_t=0.5, p_t=2.0), State(R_t=1.0, p_t=2.0), State(R_t=0.0, p_t=3.0), State(R_t=0.5, p_t=3.0), State(R_t=1.0, p_t=3.0), State(R_t=0.0, p_t=4.0), State(R_t=0.5, p_t=4.0), State(R_t=1.0, p_t=4.0), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=6.0), State(R_t=0.5, p_t=6.0), State(R_t=1.0, p_t=6.0), State(R_t=0.0, p_t=7.0), State(R_t=0.5, p_t=7.0), State(R_t=1.0, p_t=7.0), State(R_t=0.0, p_t=8.0), State(R_t=0.5, p_t=8.0), State(R_t=1.0, p_t=8.0), State(R_t=0.0, p_t=9.0), State(R_t=0.5, p_t=9.0), State(R_t=1.0, p_t=9.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=11.0), State(R_t=0.5, p_t=11.0), State(R_t=1.0, p_t=11.0), State(R_t=0.0, p_t=12.0), State(R_t=0.5, p_t=12.0), State(R_t=1.0, p_t=12.0), State(R_t=0.0, p_t=13.0), State(R_t=0.5, p_t=13.0), State(R_t=1.0, p_t=13.0), State(R_t=0.0, p_t=14.0), State(R_t=0.5, p_t=14.0), State(R_t=1.0, p_t=14.0), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=16.0), State(R_t=0.5, p_t=16.0), State(R_t=1.0, p_t=16.0), State(R_t=0.0, p_t=17.0), State(R_t=0.5, p_t=17.0), State(R_t=1.0, p_t=17.0), State(R_t=0.0, p_t=18.0), State(R_t=0.5, p_t=18.0), State(R_t=1.0, p_t=18.0), State(R_t=0.0, p_t=19.0), State(R_t=0.5, p_t=19.0), State(R_t=1.0, p_t=19.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=21.0), State(R_t=0.5, p_t=21.0), State(R_t=1.0, p_t=21.0), State(R_t=0.0, p_t=22.0), State(R_t=0.5, p_t=22.0), State(R_t=1.0, p_t=22.0), State(R_t=0.0, p_t=23.0), State(R_t=0.5, p_t=23.0), State(R_t=1.0, p_t=23.0), State(R_t=0.0, p_t=24.0), State(R_t=0.5, p_t=24.0), State(R_t=1.0, p_t=24.0), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=26.0), State(R_t=0.5, p_t=26.0), State(R_t=1.0, p_t=26.0), State(R_t=0.0, p_t=27.0), State(R_t=0.5, p_t=27.0), State(R_t=1.0, p_t=27.0), State(R_t=0.0, p_t=28.0), State(R_t=0.5, p_t=28.0), State(R_t=1.0, p_t=28.0), State(R_t=0.0, p_t=29.0), State(R_t=0.5, p_t=29.0), State(R_t=1.0, p_t=29.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=31.0), State(R_t=0.5, p_t=31.0), State(R_t=1.0, p_t=31.0), State(R_t=0.0, p_t=32.0), State(R_t=0.5, p_t=32.0), State(R_t=1.0, p_t=32.0), State(R_t=0.0, p_t=33.0), State(R_t=0.5, p_t=33.0), State(R_t=1.0, p_t=33.0), State(R_t=0.0, p_t=34.0), State(R_t=0.5, p_t=34.0), State(R_t=1.0, p_t=34.0), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=36.0), State(R_t=0.5, p_t=36.0), State(R_t=1.0, p_t=36.0), State(R_t=0.0, p_t=37.0), State(R_t=0.5, p_t=37.0), State(R_t=1.0, p_t=37.0), State(R_t=0.0, p_t=38.0), State(R_t=0.5, p_t=38.0), State(R_t=1.0, p_t=38.0), State(R_t=0.0, p_t=39.0), State(R_t=0.5, p_t=39.0), State(R_t=1.0, p_t=39.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=41.0), State(R_t=0.5, p_t=41.0), State(R_t=1.0, p_t=41.0), State(R_t=0.0, p_t=42.0), State(R_t=0.5, p_t=42.0), State(R_t=1.0, p_t=42.0), State(R_t=0.0, p_t=43.0), State(R_t=0.5, p_t=43.0), State(R_t=1.0, p_t=43.0), State(R_t=0.0, p_t=44.0), State(R_t=0.5, p_t=44.0), State(R_t=1.0, p_t=44.0), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=46.0), State(R_t=0.5, p_t=46.0), State(R_t=1.0, p_t=46.0), State(R_t=0.0, p_t=47.0), State(R_t=0.5, p_t=47.0), State(R_t=1.0, p_t=47.0), State(R_t=0.0, p_t=48.0), State(R_t=0.5, p_t=48.0), State(R_t=1.0, p_t=48.0), State(R_t=0.0, p_t=49.0), State(R_t=0.5, p_t=49.0), State(R_t=1.0, p_t=49.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=51.0), State(R_t=0.5, p_t=51.0), State(R_t=1.0, p_t=51.0), State(R_t=0.0, p_t=52.0), State(R_t=0.5, p_t=52.0), State(R_t=1.0, p_t=52.0), State(R_t=0.0, p_t=53.0), State(R_t=0.5, p_t=53.0), State(R_t=1.0, p_t=53.0), State(R_t=0.0, p_t=54.0), State(R_t=0.5, p_t=54.0), State(R_t=1.0, p_t=54.0), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=56.0), State(R_t=0.5, p_t=56.0), State(R_t=1.0, p_t=56.0), State(R_t=0.0, p_t=57.0), State(R_t=0.5, p_t=57.0), State(R_t=1.0, p_t=57.0), State(R_t=0.0, p_t=58.0), State(R_t=0.5, p_t=58.0), State(R_t=1.0, p_t=58.0), State(R_t=0.0, p_t=59.0), State(R_t=0.5, p_t=59.0), State(R_t=1.0, p_t=59.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=61.0), State(R_t=0.5, p_t=61.0), State(R_t=1.0, p_t=61.0), State(R_t=0.0, p_t=62.0), State(R_t=0.5, p_t=62.0), State(R_t=1.0, p_t=62.0), State(R_t=0.0, p_t=63.0), State(R_t=0.5, p_t=63.0), State(R_t=1.0, p_t=63.0), State(R_t=0.0, p_t=64.0), State(R_t=0.5, p_t=64.0), State(R_t=1.0, p_t=64.0), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=66.0), State(R_t=0.5, p_t=66.0), State(R_t=1.0, p_t=66.0), State(R_t=0.0, p_t=67.0), State(R_t=0.5, p_t=67.0), State(R_t=1.0, p_t=67.0), State(R_t=0.0, p_t=68.0), State(R_t=0.5, p_t=68.0), State(R_t=1.0, p_t=68.0), State(R_t=0.0, p_t=69.0), State(R_t=0.5, p_t=69.0), State(R_t=1.0, p_t=69.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=71.0), State(R_t=0.5, p_t=71.0), State(R_t=1.0, p_t=71.0), State(R_t=0.0, p_t=72.0), State(R_t=0.5, p_t=72.0), State(R_t=1.0, p_t=72.0), State(R_t=0.0, p_t=73.0), State(R_t=0.5, p_t=73.0), State(R_t=1.0, p_t=73.0), State(R_t=0.0, p_t=74.0), State(R_t=0.5, p_t=74.0), State(R_t=1.0, p_t=74.0), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=76.0), State(R_t=0.5, p_t=76.0), State(R_t=1.0, p_t=76.0), State(R_t=0.0, p_t=77.0), State(R_t=0.5, p_t=77.0), State(R_t=1.0, p_t=77.0), State(R_t=0.0, p_t=78.0), State(R_t=0.5, p_t=78.0), State(R_t=1.0, p_t=78.0), State(R_t=0.0, p_t=79.0), State(R_t=0.5, p_t=79.0), State(R_t=1.0, p_t=79.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=81.0), State(R_t=0.5, p_t=81.0), State(R_t=1.0, p_t=81.0), State(R_t=0.0, p_t=82.0), State(R_t=0.5, p_t=82.0), State(R_t=1.0, p_t=82.0), State(R_t=0.0, p_t=83.0), State(R_t=0.5, p_t=83.0), State(R_t=1.0, p_t=83.0), State(R_t=0.0, p_t=84.0), State(R_t=0.5, p_t=84.0), State(R_t=1.0, p_t=84.0), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=86.0), State(R_t=0.5, p_t=86.0), State(R_t=1.0, p_t=86.0), State(R_t=0.0, p_t=87.0), State(R_t=0.5, p_t=87.0), State(R_t=1.0, p_t=87.0), State(R_t=0.0, p_t=88.0), State(R_t=0.5, p_t=88.0), State(R_t=1.0, p_t=88.0), State(R_t=0.0, p_t=89.0), State(R_t=0.5, p_t=89.0), State(R_t=1.0, p_t=89.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=91.0), State(R_t=0.5, p_t=91.0), State(R_t=1.0, p_t=91.0), State(R_t=0.0, p_t=92.0), State(R_t=0.5, p_t=92.0), State(R_t=1.0, p_t=92.0), State(R_t=0.0, p_t=93.0), State(R_t=0.5, p_t=93.0), State(R_t=1.0, p_t=93.0), State(R_t=0.0, p_t=94.0), State(R_t=0.5, p_t=94.0), State(R_t=1.0, p_t=94.0), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=96.0), State(R_t=0.5, p_t=96.0), State(R_t=1.0, p_t=96.0), State(R_t=0.0, p_t=97.0), State(R_t=0.5, p_t=97.0), State(R_t=1.0, p_t=97.0), State(R_t=0.0, p_t=98.0), State(R_t=0.5, p_t=98.0), State(R_t=1.0, p_t=98.0), State(R_t=0.0, p_t=99.0), State(R_t=0.5, p_t=99.0), State(R_t=1.0, p_t=99.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=101.0), State(R_t=0.5, p_t=101.0), State(R_t=1.0, p_t=101.0), State(R_t=0.0, p_t=102.0), State(R_t=0.5, p_t=102.0), State(R_t=1.0, p_t=102.0), State(R_t=0.0, p_t=103.0), State(R_t=0.5, p_t=103.0), State(R_t=1.0, p_t=103.0), State(R_t=0.0, p_t=104.0), State(R_t=0.5, p_t=104.0), State(R_t=1.0, p_t=104.0), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=106.0), State(R_t=0.5, p_t=106.0), State(R_t=1.0, p_t=106.0), State(R_t=0.0, p_t=107.0), State(R_t=0.5, p_t=107.0), State(R_t=1.0, p_t=107.0), State(R_t=0.0, p_t=108.0), State(R_t=0.5, p_t=108.0), State(R_t=1.0, p_t=108.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
Finishing inc 1.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999997
=== (2 / 4), inc=2.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 165.           Exogenous info size: 50
    self.p__disc=array([  0.,   2.,   4.,   6.,   8.,  10.,  12.,  14.,  16.,  18.,  20.,
        22.,  24.,  26.,  28.,  30.,  32.,  34.,  36.,  38.,  40.,  42.,
        44.,  46.,  48.,  50.,  52.,  54.,  56.,  58.,  60.,  62.,  64.,
        66.,  68.,  70.,  72.,  74.,  76.,  78.,  80.,  82.,  84.,  86.,
        88.,  90.,  92.,  94.,  96.,  98., 100., 102., 104., 106., 108.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=2.0), State(R_t=0.5, p_t=2.0), State(R_t=1.0, p_t=2.0), State(R_t=0.0, p_t=4.0), State(R_t=0.5, p_t=4.0), State(R_t=1.0, p_t=4.0), State(R_t=0.0, p_t=6.0), State(R_t=0.5, p_t=6.0), State(R_t=1.0, p_t=6.0), State(R_t=0.0, p_t=8.0), State(R_t=0.5, p_t=8.0), State(R_t=1.0, p_t=8.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=12.0), State(R_t=0.5, p_t=12.0), State(R_t=1.0, p_t=12.0), State(R_t=0.0, p_t=14.0), State(R_t=0.5, p_t=14.0), State(R_t=1.0, p_t=14.0), State(R_t=0.0, p_t=16.0), State(R_t=0.5, p_t=16.0), State(R_t=1.0, p_t=16.0), State(R_t=0.0, p_t=18.0), State(R_t=0.5, p_t=18.0), State(R_t=1.0, p_t=18.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=22.0), State(R_t=0.5, p_t=22.0), State(R_t=1.0, p_t=22.0), State(R_t=0.0, p_t=24.0), State(R_t=0.5, p_t=24.0), State(R_t=1.0, p_t=24.0), State(R_t=0.0, p_t=26.0), State(R_t=0.5, p_t=26.0), State(R_t=1.0, p_t=26.0), State(R_t=0.0, p_t=28.0), State(R_t=0.5, p_t=28.0), State(R_t=1.0, p_t=28.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=32.0), State(R_t=0.5, p_t=32.0), State(R_t=1.0, p_t=32.0), State(R_t=0.0, p_t=34.0), State(R_t=0.5, p_t=34.0), State(R_t=1.0, p_t=34.0), State(R_t=0.0, p_t=36.0), State(R_t=0.5, p_t=36.0), State(R_t=1.0, p_t=36.0), State(R_t=0.0, p_t=38.0), State(R_t=0.5, p_t=38.0), State(R_t=1.0, p_t=38.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=42.0), State(R_t=0.5, p_t=42.0), State(R_t=1.0, p_t=42.0), State(R_t=0.0, p_t=44.0), State(R_t=0.5, p_t=44.0), State(R_t=1.0, p_t=44.0), State(R_t=0.0, p_t=46.0), State(R_t=0.5, p_t=46.0), State(R_t=1.0, p_t=46.0), State(R_t=0.0, p_t=48.0), State(R_t=0.5, p_t=48.0), State(R_t=1.0, p_t=48.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=52.0), State(R_t=0.5, p_t=52.0), State(R_t=1.0, p_t=52.0), State(R_t=0.0, p_t=54.0), State(R_t=0.5, p_t=54.0), State(R_t=1.0, p_t=54.0), State(R_t=0.0, p_t=56.0), State(R_t=0.5, p_t=56.0), State(R_t=1.0, p_t=56.0), State(R_t=0.0, p_t=58.0), State(R_t=0.5, p_t=58.0), State(R_t=1.0, p_t=58.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=62.0), State(R_t=0.5, p_t=62.0), State(R_t=1.0, p_t=62.0), State(R_t=0.0, p_t=64.0), State(R_t=0.5, p_t=64.0), State(R_t=1.0, p_t=64.0), State(R_t=0.0, p_t=66.0), State(R_t=0.5, p_t=66.0), State(R_t=1.0, p_t=66.0), State(R_t=0.0, p_t=68.0), State(R_t=0.5, p_t=68.0), State(R_t=1.0, p_t=68.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=72.0), State(R_t=0.5, p_t=72.0), State(R_t=1.0, p_t=72.0), State(R_t=0.0, p_t=74.0), State(R_t=0.5, p_t=74.0), State(R_t=1.0, p_t=74.0), State(R_t=0.0, p_t=76.0), State(R_t=0.5, p_t=76.0), State(R_t=1.0, p_t=76.0), State(R_t=0.0, p_t=78.0), State(R_t=0.5, p_t=78.0), State(R_t=1.0, p_t=78.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=82.0), State(R_t=0.5, p_t=82.0), State(R_t=1.0, p_t=82.0), State(R_t=0.0, p_t=84.0), State(R_t=0.5, p_t=84.0), State(R_t=1.0, p_t=84.0), State(R_t=0.0, p_t=86.0), State(R_t=0.5, p_t=86.0), State(R_t=1.0, p_t=86.0), State(R_t=0.0, p_t=88.0), State(R_t=0.5, p_t=88.0), State(R_t=1.0, p_t=88.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=92.0), State(R_t=0.5, p_t=92.0), State(R_t=1.0, p_t=92.0), State(R_t=0.0, p_t=94.0), State(R_t=0.5, p_t=94.0), State(R_t=1.0, p_t=94.0), State(R_t=0.0, p_t=96.0), State(R_t=0.5, p_t=96.0), State(R_t=1.0, p_t=96.0), State(R_t=0.0, p_t=98.0), State(R_t=0.5, p_t=98.0), State(R_t=1.0, p_t=98.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=102.0), State(R_t=0.5, p_t=102.0), State(R_t=1.0, p_t=102.0), State(R_t=0.0, p_t=104.0), State(R_t=0.5, p_t=104.0), State(R_t=1.0, p_t=104.0), State(R_t=0.0, p_t=106.0), State(R_t=0.5, p_t=106.0), State(R_t=1.0, p_t=106.0), State(R_t=0.0, p_t=108.0), State(R_t=0.5, p_t=108.0), State(R_t=1.0, p_t=108.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
Finishing inc 2.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999997
=== (3 / 4), inc=5.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 69.           Exogenous info size: 50
    self.p__disc=array([  0.,   5.,  10.,  15.,  20.,  25.,  30.,  35.,  40.,  45.,  50.,
        55.,  60.,  65.,  70.,  75.,  80.,  85.,  90.,  95., 100., 105.,
       110.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=110.0), State(R_t=0.5, p_t=110.0), State(R_t=1.0, p_t=110.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
Finishing inc 5.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999997
=== (4 / 4), inc=10.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 36.           Exogenous info size: 50
    self.p__disc=array([  0.,  10.,  20.,  30.,  40.,  50.,  60.,  70.,  80.,  90., 100.,
       110.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=110.0), State(R_t=0.5, p_t=110.0), State(R_t=1.0, p_t=110.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
Finishing inc 10.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999997
FOR COMPARISON (final evolving values): 
best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999997
CPU times: user 10min 31s, sys: 1.57 s, total: 10min 33s
Wall time: 10min 39s

P.plot_Fhat_chart(
    Cbarcum_Bellman,
    incs,
    r'$inc$',
    r"$\bar{C}^{cum}(inc)$"+"\n(Profit)\n[$]",
    "Sample mean of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
      r"$inc^* =$"+ str(best_inc_Bellman)+", " \
      r"$\bar{C}^{cum}(inc^*) =$"+f"{best_Cbarcum_Bellman:.2f}",
    'ro-',
    best_inc_Bellman
)
print()
P.plot_Fhat_chart(
    Ctilcum_Bellman,
    incs,
    r'$inc$',
    r"$\tilde{C}^{cum}(inc)$"+"\n(Profit)\n[$]",
    "Standard error of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
      r"$inc^* =$"+ str(best_inc_Bellman)+", " \
      r"$\bar{C}^{cum}(inc^*) =$"+f"{best_Ctilcum_Bellman:.2f}",
    'bo-',
    best_inc_Bellman
)

P.plot_expFhat_chart(
  incStar_expCbarcum_Bellman,
  r'$\ell$',
  r"$exp\bar{C}^{cum}(\theta^*)$"+"\n(Profit)\n[$]",
  "Expanding sample mean of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
    r"$inc^* =$"+ str(best_inc_Bellman)+", " \
    r"$\bar{C}^{cum}(inc^*) =$"+f"{best_Cbarcum_Bellman:.2f}",
  'b-'
)
print()
P.plot_expFhat_chart(
  incStar_expCtilcum_Bellman,
  r'$\ell$',
  r"$exp\tilde{C}^{cum}(\theta^*)$"+"\n(Profit)\n[$]",
  "Expanding standard error of the cumulative reward"+f"\n $L={L}, T={T}$, "+ \
    r"$inc^* =$"+ str(best_inc_Bellman)+", " \
    r"$\bar{C}^{cum}(inc^*) =$"+f"{best_Ctilcum_Bellman:.2f}",
  'b--'
);

f'{len(record_Bellman):,}', L, T

('4,800', 5, 100)

P.plot_records(
  df=df_first_n_t,
  df_non=None,
  pars=defaultdict(str, {
    'suptitle': f'TRAINING OF X__Bellman POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, ' + \
    r'$inc^*=$'+f'{best_inc_Bellman}',
  }),
)

P.plot_records(
  df=df_last_n_t,
  df_non=None,
  pars=defaultdict(str, {
    'suptitle': f'TRAINING OF X__Bellman POLICY'+'\n'+f'(last {last_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, ' + \
    r'$inc^*=$'+f'{best_inc_Bellman}',
  }),
)

4.6.2 Evaluation

4.6.2.1 X__BuyLowSellHigh

best_theta_BuyLowSellHigh

Theta(thLo={'GB': 11}, thHi={'GB': 38})

%%time
#GridSearch #. SDAM-9.4.1
L = 50 #N_SAMPLEPATHS
T = 100 #N_TRANSITIONS
first_n_t = int(.1*L*T)

M = Model(S_0_INFO)
P = Policy(M)
thetasOpt = []; thetasOpt.append(best_theta_BuyLowSellHigh)
thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt, thetaStar_expCtilcum_BuyLowSellHigh_evalu_opt, \
_, _, \
best_theta_BuyLowSellHigh_evalu_opt, worst_theta_BuyLowSellHigh_evalu_opt, \
_, _, \
_, _, \
record_BuyLowSellHigh_evalu_opt = \
  P.perform_grid_search_sample_paths("X__BuyLowSellHigh", thetasOpt, exploitSym=False)
df_BuyLowSellHigh_evalu_opt = pd.DataFrame.from_records(record_BuyLowSellHigh_evalu_opt[:first_n_t], columns=labels)

M = Model(S_0_INFO)
P = Policy(M)
# thetasNon = []; thetasNon.append(worst_theta_BuyLowSellHigh)
thetasNon = []; thetasNon.append(
    P.build_theta(
        {'thLo': {'GB': 5}, 'thHi': {'GB': 15}}
))
thetaStar_expCbarcum_BuyLowSellHigh_evalu_non, thetaStar_expCtilcum_BuyLowSellHigh_evalu_non, \
_, _, \
best_theta_BuyLowSellHigh_evalu_non, worst_theta_BuyLowSellHigh_evalu_non, \
_, _, \
_, _, \
record_BuyLowSellHigh_evalu_non = \
  P.perform_grid_search_sample_paths("X__BuyLowSellHigh", thetasNon, exploitSym=False)
df_BuyLowSellHigh_evalu_non = pd.DataFrame.from_records(record_BuyLowSellHigh_evalu_non[:first_n_t], columns=labels)

print(
  f'{thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=:.2f}, \
    {thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=:.2f}')

numThetas=1
thetas=[Theta(thLo={'GB': 11}, thHi={'GB': 38})]
... printing every 500th theta ...
=== (0 / 1), theta=Theta(thLo={'GB': 11}, thHi={'GB': 38}) ===
best_theta_en:
Theta(thLo={'GB': 11}, thHi={'GB': 38})
best_Cbarcum=168.47
best_Ctilcum=0.00
worst_theta_en:
Theta(thLo={'GB': 11}, thHi={'GB': 38})
worst_Cbarcum=168.47
worst_Ctilcum=0.00
numThetas=1
thetas=[Theta(thLo={'GB': 5}, thHi={'GB': 15})]
... printing every 500th theta ...
=== (0 / 1), theta=Theta(thLo={'GB': 5}, thHi={'GB': 15}) ===
best_theta_en:
Theta(thLo={'GB': 5}, thHi={'GB': 15})
best_Cbarcum=47.44
best_Ctilcum=0.00
worst_theta_en:
Theta(thLo={'GB': 5}, thHi={'GB': 15})
worst_Cbarcum=47.44
worst_Ctilcum=0.00
thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=168.47,     thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=47.44
CPU times: user 102 ms, sys: 990 µs, total: 103 ms
Wall time: 113 ms

P.plot_records(
  df=df_BuyLowSellHigh_evalu_opt,
  df_non=df_BuyLowSellHigh_evalu_non,
  pars=defaultdict(str, {
    'thetaLo': {en: thetasOpt[0].thLo[en] for en in eNAMES},
    'thetaHi': {en: thetasOpt[0].thHi[en] for en in eNAMES},
    'thetaLoNon': {en: thetasNon[0].thLo[en] for en in eNAMES},
    'thetaHiNon': {en: thetasNon[0].thHi[en] for en in eNAMES},
    'suptitle': f'EVALUATION OF X__BuyLowSellHigh POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$\theta^*=$'+f'{P.round_theta(best_theta_BuyLowSellHigh_evalu_opt)}',
  }),
)

last_n_l = int(.95*L)
P.plot_expFhat_charts(
  means={
      'HighLow optimal': thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt[-last_n_l:],
      'HighLow non-optimal': thetaStar_expCbarcum_BuyLowSellHigh_evalu_non[-last_n_l:],
  },
  stdvs={
      'HighLow optimal': thetaStar_expCtilcum_BuyLowSellHigh_evalu_opt[-last_n_l:],
      'HighLow non-optimal': thetaStar_expCtilcum_BuyLowSellHigh_evalu_non[-last_n_l:],
  },
  labelX='Sample paths, ' + r'$\ell$',
  labelY='Profit\n[$]',
  suptitle=f"Comparison of Optimal/Non-optimal Policies after Evaluation\n \
    L = {L}, T = {T}\n \
    last {last_n_l} records\n \
    ('exp' refers to expanding)",
  pars=defaultdict(str, {
    'colors': ['m', 'c']
  }),
)

Next, we evaluate with a single, very long sample-path:

%%time
#GridSearch #. SDAM-9.4.1
L = 1 #N_SAMPLEPATHS
T = 192 #N_TRANSITIONS
first_n_t = int(1*L*T)

M = Model(S_0_INFO)
P = Policy(M)
thetasOpt = []; thetasOpt.append(best_theta_BuyLowSellHigh)
thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt, thetaStar_expCtilcum_BuyLowSellHigh_evalu_opt, \
_, _, \
best_theta_BuyLowSellHigh_evalu_opt, worst_theta_BuyLowSellHigh_evalu_opt, \
_, _, \
_, _, \
record_BuyLowSellHigh_evalu_opt = \
  P.perform_grid_search_sample_paths("X__BuyLowSellHigh", thetasOpt, exploitSym=False)
df_BuyLowSellHigh_evalu_opt = pd.DataFrame.from_records(record_BuyLowSellHigh_evalu_opt[:first_n_t], columns=labels)

M = Model(S_0_INFO)
P = Policy(M)
# thetasNon = []; thetasNon.append(worst_theta_BuyLowSellHigh)
thetasNon = []; thetasNon.append(
    P.build_theta(
        {'thLo': {'GB': 5}, 'thHi': {'GB': 15}}
))
thetaStar_expCbarcum_BuyLowSellHigh_evalu_non, thetaStar_expCtilcum_BuyLowSellHigh_evalu_non, \
_, _, \
best_theta_BuyLowSellHigh_evalu_non, worst_theta_BuyLowSellHigh_evalu_non, \
_, _, \
_, _, \
record_BuyLowSellHigh_evalu_non = \
  P.perform_grid_search_sample_paths("X__BuyLowSellHigh", thetasNon, exploitSym=False)
df_BuyLowSellHigh_evalu_non = pd.DataFrame.from_records(record_BuyLowSellHigh_evalu_non[:first_n_t], columns=labels)

print(
  f'{thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=:.2f}, \
    {thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=:.2f}')

numThetas=1
thetas=[Theta(thLo={'GB': 11}, thHi={'GB': 38})]
... printing every 500th theta ...
=== (0 / 1), theta=Theta(thLo={'GB': 11}, thHi={'GB': 38}) ===
best_theta_en:
Theta(thLo={'GB': 11}, thHi={'GB': 38})
best_Cbarcum=207.35
best_Ctilcum=nan
worst_theta_en:
Theta(thLo={'GB': 11}, thHi={'GB': 38})
worst_Cbarcum=207.35
worst_Ctilcum=nan
numThetas=1
thetas=[Theta(thLo={'GB': 5}, thHi={'GB': 15})]
... printing every 500th theta ...
=== (0 / 1), theta=Theta(thLo={'GB': 5}, thHi={'GB': 15}) ===
best_theta_en:
Theta(thLo={'GB': 5}, thHi={'GB': 15})
best_Cbarcum=47.44
best_Ctilcum=nan
worst_theta_en:
Theta(thLo={'GB': 5}, thHi={'GB': 15})
worst_Cbarcum=47.44
worst_Ctilcum=nan
thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=207.35,     thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=47.44
CPU times: user 22 ms, sys: 997 µs, total: 23 ms
Wall time: 28.8 ms

RuntimeWarning: invalid value encountered in double_scalars
  Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)
<ipython-input-303-7a5f2761a525>:264: RuntimeWarning: invalid value encountered in double_scalars
  Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)

P.plot_records(
  df=df_BuyLowSellHigh_evalu_opt,
  df_non=df_BuyLowSellHigh_evalu_non,
  pars=defaultdict(str, {
    'thetaLo': {en: thetasOpt[0].thLo[en] for en in eNAMES},
    'thetaHi': {en: thetasOpt[0].thHi[en] for en in eNAMES},
    'thetaLoNon': {en: thetasNon[0].thLo[en] for en in eNAMES},
    'thetaHiNon': {en: thetasNon[0].thHi[en] for en in eNAMES},
    'suptitle': f'EVALUATION OF X__BuyLowSellHigh POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$\theta^*=$'+f'{P.round_theta(best_theta_BuyLowSellHigh_evalu_opt)}',
  }),
)

df_BuyLowSellHigh_evalu_opt[df_BuyLowSellHigh_evalu_opt['t']==T-1][['Ccum']]

	Ccum
191	207.3490

df_BuyLowSellHigh_evalu_non[df_BuyLowSellHigh_evalu_non['t']==T-1][['Ccum']]

	Ccum
191	47.4390

4.6.2.2 X__Bellman

best_inc_Bellman

1.0

%%time
L = 50 #N_SAMPLEPATHS
T = 100 #N_TRANSITIONS
first_n_t = int(.1*L*T)

M = Model(S_0_INFO)
P = Policy(M)
incsOpt = []; incsOpt.append(best_inc_Bellman)
incStar_expCbarcum_Bellman_evalu_opt, incStar_expCtilcum_Bellman_evalu_opt, \
_, _, \
best_inc_Bellman_evalu_opt, worst_inc_Bellman_evalu_opt, \
_, _, \
_, _, \
_, _, \
record_Bellman_evalu_opt = \
  P.perform_bellman_search_sample_paths("X__Bellman", R__disc, minPrice, maxPrice, incsOpt)
df_Bellman_evalu_opt = pd.DataFrame.from_records(record_Bellman_evalu_opt[:first_n_t], columns=labels)

M = Model(S_0_INFO)
P = Policy(M)
# thetasNon = []; thetasNon.append(worst_theta_BuyLowSellHigh)
incsNon = []; incsNon.append(5.0) #3, 2
incStar_expCbarcum_Bellman_evalu_non, incStar_expCtilcum_Bellman_evalu_non, \
_, _, \
best_inc_Bellman_evalu_non, worst_inc_Bellman_evalu_non, \
_, _, \
_, _, \
_, _, \
record_Bellman_evalu_non = \
  P.perform_bellman_search_sample_paths("X__Bellman", R__disc, minPrice, maxPrice, incsNon)
df_Bellman_evalu_non = pd.DataFrame.from_records(record_Bellman_evalu_non[:first_n_t], columns=labels)

# print(
#   f'{thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=:.2f}, \
#     {thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=:.2f}')

..... P.perform_bellman_search_sample_paths() .....
numIncs=1
incs=[1.0]
printing every 1th inc
=== (0 / 0), inc=1.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 327.           Exogenous info size: 50
    self.p__disc=array([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,
        11.,  12.,  13.,  14.,  15.,  16.,  17.,  18.,  19.,  20.,  21.,
        22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,  30.,  31.,  32.,
        33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,  42.,  43.,
        44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,  54.,
        55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
        66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,
        77.,  78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,
        88.,  89.,  90.,  91.,  92.,  93.,  94.,  95.,  96.,  97.,  98.,
        99., 100., 101., 102., 103., 104., 105., 106., 107., 108.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=1.0), State(R_t=0.5, p_t=1.0), State(R_t=1.0, p_t=1.0), State(R_t=0.0, p_t=2.0), State(R_t=0.5, p_t=2.0), State(R_t=1.0, p_t=2.0), State(R_t=0.0, p_t=3.0), State(R_t=0.5, p_t=3.0), State(R_t=1.0, p_t=3.0), State(R_t=0.0, p_t=4.0), State(R_t=0.5, p_t=4.0), State(R_t=1.0, p_t=4.0), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=6.0), State(R_t=0.5, p_t=6.0), State(R_t=1.0, p_t=6.0), State(R_t=0.0, p_t=7.0), State(R_t=0.5, p_t=7.0), State(R_t=1.0, p_t=7.0), State(R_t=0.0, p_t=8.0), State(R_t=0.5, p_t=8.0), State(R_t=1.0, p_t=8.0), State(R_t=0.0, p_t=9.0), State(R_t=0.5, p_t=9.0), State(R_t=1.0, p_t=9.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=11.0), State(R_t=0.5, p_t=11.0), State(R_t=1.0, p_t=11.0), State(R_t=0.0, p_t=12.0), State(R_t=0.5, p_t=12.0), State(R_t=1.0, p_t=12.0), State(R_t=0.0, p_t=13.0), State(R_t=0.5, p_t=13.0), State(R_t=1.0, p_t=13.0), State(R_t=0.0, p_t=14.0), State(R_t=0.5, p_t=14.0), State(R_t=1.0, p_t=14.0), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=16.0), State(R_t=0.5, p_t=16.0), State(R_t=1.0, p_t=16.0), State(R_t=0.0, p_t=17.0), State(R_t=0.5, p_t=17.0), State(R_t=1.0, p_t=17.0), State(R_t=0.0, p_t=18.0), State(R_t=0.5, p_t=18.0), State(R_t=1.0, p_t=18.0), State(R_t=0.0, p_t=19.0), State(R_t=0.5, p_t=19.0), State(R_t=1.0, p_t=19.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=21.0), State(R_t=0.5, p_t=21.0), State(R_t=1.0, p_t=21.0), State(R_t=0.0, p_t=22.0), State(R_t=0.5, p_t=22.0), State(R_t=1.0, p_t=22.0), State(R_t=0.0, p_t=23.0), State(R_t=0.5, p_t=23.0), State(R_t=1.0, p_t=23.0), State(R_t=0.0, p_t=24.0), State(R_t=0.5, p_t=24.0), State(R_t=1.0, p_t=24.0), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=26.0), State(R_t=0.5, p_t=26.0), State(R_t=1.0, p_t=26.0), State(R_t=0.0, p_t=27.0), State(R_t=0.5, p_t=27.0), State(R_t=1.0, p_t=27.0), State(R_t=0.0, p_t=28.0), State(R_t=0.5, p_t=28.0), State(R_t=1.0, p_t=28.0), State(R_t=0.0, p_t=29.0), State(R_t=0.5, p_t=29.0), State(R_t=1.0, p_t=29.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=31.0), State(R_t=0.5, p_t=31.0), State(R_t=1.0, p_t=31.0), State(R_t=0.0, p_t=32.0), State(R_t=0.5, p_t=32.0), State(R_t=1.0, p_t=32.0), State(R_t=0.0, p_t=33.0), State(R_t=0.5, p_t=33.0), State(R_t=1.0, p_t=33.0), State(R_t=0.0, p_t=34.0), State(R_t=0.5, p_t=34.0), State(R_t=1.0, p_t=34.0), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=36.0), State(R_t=0.5, p_t=36.0), State(R_t=1.0, p_t=36.0), State(R_t=0.0, p_t=37.0), State(R_t=0.5, p_t=37.0), State(R_t=1.0, p_t=37.0), State(R_t=0.0, p_t=38.0), State(R_t=0.5, p_t=38.0), State(R_t=1.0, p_t=38.0), State(R_t=0.0, p_t=39.0), State(R_t=0.5, p_t=39.0), State(R_t=1.0, p_t=39.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=41.0), State(R_t=0.5, p_t=41.0), State(R_t=1.0, p_t=41.0), State(R_t=0.0, p_t=42.0), State(R_t=0.5, p_t=42.0), State(R_t=1.0, p_t=42.0), State(R_t=0.0, p_t=43.0), State(R_t=0.5, p_t=43.0), State(R_t=1.0, p_t=43.0), State(R_t=0.0, p_t=44.0), State(R_t=0.5, p_t=44.0), State(R_t=1.0, p_t=44.0), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=46.0), State(R_t=0.5, p_t=46.0), State(R_t=1.0, p_t=46.0), State(R_t=0.0, p_t=47.0), State(R_t=0.5, p_t=47.0), State(R_t=1.0, p_t=47.0), State(R_t=0.0, p_t=48.0), State(R_t=0.5, p_t=48.0), State(R_t=1.0, p_t=48.0), State(R_t=0.0, p_t=49.0), State(R_t=0.5, p_t=49.0), State(R_t=1.0, p_t=49.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=51.0), State(R_t=0.5, p_t=51.0), State(R_t=1.0, p_t=51.0), State(R_t=0.0, p_t=52.0), State(R_t=0.5, p_t=52.0), State(R_t=1.0, p_t=52.0), State(R_t=0.0, p_t=53.0), State(R_t=0.5, p_t=53.0), State(R_t=1.0, p_t=53.0), State(R_t=0.0, p_t=54.0), State(R_t=0.5, p_t=54.0), State(R_t=1.0, p_t=54.0), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=56.0), State(R_t=0.5, p_t=56.0), State(R_t=1.0, p_t=56.0), State(R_t=0.0, p_t=57.0), State(R_t=0.5, p_t=57.0), State(R_t=1.0, p_t=57.0), State(R_t=0.0, p_t=58.0), State(R_t=0.5, p_t=58.0), State(R_t=1.0, p_t=58.0), State(R_t=0.0, p_t=59.0), State(R_t=0.5, p_t=59.0), State(R_t=1.0, p_t=59.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=61.0), State(R_t=0.5, p_t=61.0), State(R_t=1.0, p_t=61.0), State(R_t=0.0, p_t=62.0), State(R_t=0.5, p_t=62.0), State(R_t=1.0, p_t=62.0), State(R_t=0.0, p_t=63.0), State(R_t=0.5, p_t=63.0), State(R_t=1.0, p_t=63.0), State(R_t=0.0, p_t=64.0), State(R_t=0.5, p_t=64.0), State(R_t=1.0, p_t=64.0), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=66.0), State(R_t=0.5, p_t=66.0), State(R_t=1.0, p_t=66.0), State(R_t=0.0, p_t=67.0), State(R_t=0.5, p_t=67.0), State(R_t=1.0, p_t=67.0), State(R_t=0.0, p_t=68.0), State(R_t=0.5, p_t=68.0), State(R_t=1.0, p_t=68.0), State(R_t=0.0, p_t=69.0), State(R_t=0.5, p_t=69.0), State(R_t=1.0, p_t=69.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=71.0), State(R_t=0.5, p_t=71.0), State(R_t=1.0, p_t=71.0), State(R_t=0.0, p_t=72.0), State(R_t=0.5, p_t=72.0), State(R_t=1.0, p_t=72.0), State(R_t=0.0, p_t=73.0), State(R_t=0.5, p_t=73.0), State(R_t=1.0, p_t=73.0), State(R_t=0.0, p_t=74.0), State(R_t=0.5, p_t=74.0), State(R_t=1.0, p_t=74.0), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=76.0), State(R_t=0.5, p_t=76.0), State(R_t=1.0, p_t=76.0), State(R_t=0.0, p_t=77.0), State(R_t=0.5, p_t=77.0), State(R_t=1.0, p_t=77.0), State(R_t=0.0, p_t=78.0), State(R_t=0.5, p_t=78.0), State(R_t=1.0, p_t=78.0), State(R_t=0.0, p_t=79.0), State(R_t=0.5, p_t=79.0), State(R_t=1.0, p_t=79.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=81.0), State(R_t=0.5, p_t=81.0), State(R_t=1.0, p_t=81.0), State(R_t=0.0, p_t=82.0), State(R_t=0.5, p_t=82.0), State(R_t=1.0, p_t=82.0), State(R_t=0.0, p_t=83.0), State(R_t=0.5, p_t=83.0), State(R_t=1.0, p_t=83.0), State(R_t=0.0, p_t=84.0), State(R_t=0.5, p_t=84.0), State(R_t=1.0, p_t=84.0), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=86.0), State(R_t=0.5, p_t=86.0), State(R_t=1.0, p_t=86.0), State(R_t=0.0, p_t=87.0), State(R_t=0.5, p_t=87.0), State(R_t=1.0, p_t=87.0), State(R_t=0.0, p_t=88.0), State(R_t=0.5, p_t=88.0), State(R_t=1.0, p_t=88.0), State(R_t=0.0, p_t=89.0), State(R_t=0.5, p_t=89.0), State(R_t=1.0, p_t=89.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=91.0), State(R_t=0.5, p_t=91.0), State(R_t=1.0, p_t=91.0), State(R_t=0.0, p_t=92.0), State(R_t=0.5, p_t=92.0), State(R_t=1.0, p_t=92.0), State(R_t=0.0, p_t=93.0), State(R_t=0.5, p_t=93.0), State(R_t=1.0, p_t=93.0), State(R_t=0.0, p_t=94.0), State(R_t=0.5, p_t=94.0), State(R_t=1.0, p_t=94.0), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=96.0), State(R_t=0.5, p_t=96.0), State(R_t=1.0, p_t=96.0), State(R_t=0.0, p_t=97.0), State(R_t=0.5, p_t=97.0), State(R_t=1.0, p_t=97.0), State(R_t=0.0, p_t=98.0), State(R_t=0.5, p_t=98.0), State(R_t=1.0, p_t=98.0), State(R_t=0.0, p_t=99.0), State(R_t=0.5, p_t=99.0), State(R_t=1.0, p_t=99.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=101.0), State(R_t=0.5, p_t=101.0), State(R_t=1.0, p_t=101.0), State(R_t=0.0, p_t=102.0), State(R_t=0.5, p_t=102.0), State(R_t=1.0, p_t=102.0), State(R_t=0.0, p_t=103.0), State(R_t=0.5, p_t=103.0), State(R_t=1.0, p_t=103.0), State(R_t=0.0, p_t=104.0), State(R_t=0.5, p_t=104.0), State(R_t=1.0, p_t=104.0), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=106.0), State(R_t=0.5, p_t=106.0), State(R_t=1.0, p_t=106.0), State(R_t=0.0, p_t=107.0), State(R_t=0.5, p_t=107.0), State(R_t=1.0, p_t=107.0), State(R_t=0.0, p_t=108.0), State(R_t=0.5, p_t=108.0), State(R_t=1.0, p_t=108.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
    l=5
    l=6
    l=7
    l=8
    l=9
    l=10
    l=11
    l=12
    l=13
    l=14
    l=15
    l=16
    l=17
    l=18
    l=19
    l=20
    l=21
    l=22
    l=23
    l=24
    l=25
    l=26
    l=27
    l=28
    l=29
    l=30
    l=31
    l=32
    l=33
    l=34
    l=35
    l=36
    l=37
    l=38
    l=39
    l=40
    l=41
    l=42
    l=43
    l=44
    l=45
    l=46
    l=47
    l=48
    l=49
Finishing inc 1.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999994
FOR COMPARISON (final evolving values): 
best_inc_evolving=1.0, best_Cbarcum_evolving=27.494999999999994
..... P.perform_bellman_search_sample_paths() .....
numIncs=1
incs=[5.0]
printing every 1th inc
=== (0 / 0), inc=5.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 69.           Exogenous info size: 50
    self.p__disc=array([  0.,   5.,  10.,  15.,  20.,  25.,  30.,  35.,  40.,  45.,  50.,
        55.,  60.,  65.,  70.,  75.,  80.,  85.,  90.,  95., 100., 105.,
       110.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=110.0), State(R_t=0.5, p_t=110.0), State(R_t=1.0, p_t=110.0)]
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
    l=1
    l=2
    l=3
    l=4
    l=5
    l=6
    l=7
    l=8
    l=9
    l=10
    l=11
    l=12
    l=13
    l=14
    l=15
    l=16
    l=17
    l=18
    l=19
    l=20
    l=21
    l=22
    l=23
    l=24
    l=25
    l=26
    l=27
    l=28
    l=29
    l=30
    l=31
    l=32
    l=33
    l=34
    l=35
    l=36
    l=37
    l=38
    l=39
    l=40
    l=41
    l=42
    l=43
    l=44
    l=45
    l=46
    l=47
    l=48
    l=49
Finishing inc 5.0 with best_inc_evolving=5.0, best_Cbarcum_evolving=15.138000000000003
FOR COMPARISON (final evolving values): 
best_inc_evolving=5.0, best_Cbarcum_evolving=15.138000000000003
CPU times: user 3min 16s, sys: 537 ms, total: 3min 16s
Wall time: 3min 18s

P.plot_records(
  df=df_Bellman_evalu_opt,
  df_non=df_Bellman_evalu_non,
  pars=defaultdict(str, {
    'suptitle': f'EVALUATION OF X__Bellman POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$inc^*=$'+f'{best_inc_Bellman_evalu_opt}',
  }),
)

last_n_l = int(.95*L)
P.plot_expFhat_charts(
  means={
      'Bellman optimal': incStar_expCbarcum_Bellman_evalu_opt[-last_n_l:],
      'Bellman non-optimal': incStar_expCbarcum_Bellman_evalu_non[-last_n_l:],
  },
  stdvs={
      'Bellman optimal': incStar_expCtilcum_Bellman_evalu_opt[-last_n_l:],
      'Bellman non-optimal': incStar_expCtilcum_Bellman_evalu_non[-last_n_l:],
  },
  labelX='Sample paths, ' + r'$\ell$',
  labelY='Profit\n[$]',
  suptitle=f"Comparison of Optimal/Non-optimal Policies after Evaluation\n \
    L = {L}, T = {T}\n \
    last {last_n_l} records\n \
    ('exp' refers to expanding)",
  pars=defaultdict(str, {
    'colors': ['m', 'c']
  }),
)

Next, we evaluate with a single, very long sample-path:

%%time
L = 1 #N_SAMPLEPATHS
T = 192 #N_TRANSITIONS
first_n_t = int(1*L*T)

M = Model(S_0_INFO)
P = Policy(M)
incsOpt = []; incsOpt.append(best_inc_Bellman)
incStar_expCbarcum_Bellman_evalu_opt, incStar_expCtilcum_Bellman_evalu_opt, \
_, _, \
best_inc_Bellman_evalu_opt, worst_inc_Bellman_evalu_opt, \
_, _, \
_, _, \
_, _, \
record_Bellman_evalu_opt = \
  P.perform_bellman_search_sample_paths("X__Bellman", R__disc, minPrice, maxPrice, incsOpt)
df_Bellman_evalu_opt = pd.DataFrame.from_records(record_Bellman_evalu_opt[:first_n_t], columns=labels)

M = Model(S_0_INFO)
P = Policy(M)
# thetasNon = []; thetasNon.append(worst_theta_BuyLowSellHigh)
incsNon = []; incsNon.append(10.0) #5, 3, 2
incStar_expCbarcum_Bellman_evalu_non, incStar_expCtilcum_Bellman_evalu_non, \
_, _, \
best_inc_Bellman_evalu_non, worst_inc_Bellman_evalu_non, \
_, _, \
_, _, \
_, _, \
record_Bellman_evalu_non = \
  P.perform_bellman_search_sample_paths("X__Bellman", R__disc, minPrice, maxPrice, incsNon)
df_Bellman_evalu_non = pd.DataFrame.from_records(record_Bellman_evalu_non[:first_n_t], columns=labels)

# print(
#   f'{thetaStar_expCbarcum_BuyLowSellHigh_evalu_opt.iloc[-1]=:.2f}, \
#     {thetaStar_expCbarcum_BuyLowSellHigh_evalu_non.iloc[-1]=:.2f}')

..... P.perform_bellman_search_sample_paths() .....
numIncs=1
incs=[1.0]
printing every 1th inc
=== (0 / 0), inc=1.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 327.           Exogenous info size: 50
    self.p__disc=array([  0.,   1.,   2.,   3.,   4.,   5.,   6.,   7.,   8.,   9.,  10.,
        11.,  12.,  13.,  14.,  15.,  16.,  17.,  18.,  19.,  20.,  21.,
        22.,  23.,  24.,  25.,  26.,  27.,  28.,  29.,  30.,  31.,  32.,
        33.,  34.,  35.,  36.,  37.,  38.,  39.,  40.,  41.,  42.,  43.,
        44.,  45.,  46.,  47.,  48.,  49.,  50.,  51.,  52.,  53.,  54.,
        55.,  56.,  57.,  58.,  59.,  60.,  61.,  62.,  63.,  64.,  65.,
        66.,  67.,  68.,  69.,  70.,  71.,  72.,  73.,  74.,  75.,  76.,
        77.,  78.,  79.,  80.,  81.,  82.,  83.,  84.,  85.,  86.,  87.,
        88.,  89.,  90.,  91.,  92.,  93.,  94.,  95.,  96.,  97.,  98.,
        99., 100., 101., 102., 103., 104., 105., 106., 107., 108.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=1.0), State(R_t=0.5, p_t=1.0), State(R_t=1.0, p_t=1.0), State(R_t=0.0, p_t=2.0), State(R_t=0.5, p_t=2.0), State(R_t=1.0, p_t=2.0), State(R_t=0.0, p_t=3.0), State(R_t=0.5, p_t=3.0), State(R_t=1.0, p_t=3.0), State(R_t=0.0, p_t=4.0), State(R_t=0.5, p_t=4.0), State(R_t=1.0, p_t=4.0), State(R_t=0.0, p_t=5.0), State(R_t=0.5, p_t=5.0), State(R_t=1.0, p_t=5.0), State(R_t=0.0, p_t=6.0), State(R_t=0.5, p_t=6.0), State(R_t=1.0, p_t=6.0), State(R_t=0.0, p_t=7.0), State(R_t=0.5, p_t=7.0), State(R_t=1.0, p_t=7.0), State(R_t=0.0, p_t=8.0), State(R_t=0.5, p_t=8.0), State(R_t=1.0, p_t=8.0), State(R_t=0.0, p_t=9.0), State(R_t=0.5, p_t=9.0), State(R_t=1.0, p_t=9.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=11.0), State(R_t=0.5, p_t=11.0), State(R_t=1.0, p_t=11.0), State(R_t=0.0, p_t=12.0), State(R_t=0.5, p_t=12.0), State(R_t=1.0, p_t=12.0), State(R_t=0.0, p_t=13.0), State(R_t=0.5, p_t=13.0), State(R_t=1.0, p_t=13.0), State(R_t=0.0, p_t=14.0), State(R_t=0.5, p_t=14.0), State(R_t=1.0, p_t=14.0), State(R_t=0.0, p_t=15.0), State(R_t=0.5, p_t=15.0), State(R_t=1.0, p_t=15.0), State(R_t=0.0, p_t=16.0), State(R_t=0.5, p_t=16.0), State(R_t=1.0, p_t=16.0), State(R_t=0.0, p_t=17.0), State(R_t=0.5, p_t=17.0), State(R_t=1.0, p_t=17.0), State(R_t=0.0, p_t=18.0), State(R_t=0.5, p_t=18.0), State(R_t=1.0, p_t=18.0), State(R_t=0.0, p_t=19.0), State(R_t=0.5, p_t=19.0), State(R_t=1.0, p_t=19.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=21.0), State(R_t=0.5, p_t=21.0), State(R_t=1.0, p_t=21.0), State(R_t=0.0, p_t=22.0), State(R_t=0.5, p_t=22.0), State(R_t=1.0, p_t=22.0), State(R_t=0.0, p_t=23.0), State(R_t=0.5, p_t=23.0), State(R_t=1.0, p_t=23.0), State(R_t=0.0, p_t=24.0), State(R_t=0.5, p_t=24.0), State(R_t=1.0, p_t=24.0), State(R_t=0.0, p_t=25.0), State(R_t=0.5, p_t=25.0), State(R_t=1.0, p_t=25.0), State(R_t=0.0, p_t=26.0), State(R_t=0.5, p_t=26.0), State(R_t=1.0, p_t=26.0), State(R_t=0.0, p_t=27.0), State(R_t=0.5, p_t=27.0), State(R_t=1.0, p_t=27.0), State(R_t=0.0, p_t=28.0), State(R_t=0.5, p_t=28.0), State(R_t=1.0, p_t=28.0), State(R_t=0.0, p_t=29.0), State(R_t=0.5, p_t=29.0), State(R_t=1.0, p_t=29.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=31.0), State(R_t=0.5, p_t=31.0), State(R_t=1.0, p_t=31.0), State(R_t=0.0, p_t=32.0), State(R_t=0.5, p_t=32.0), State(R_t=1.0, p_t=32.0), State(R_t=0.0, p_t=33.0), State(R_t=0.5, p_t=33.0), State(R_t=1.0, p_t=33.0), State(R_t=0.0, p_t=34.0), State(R_t=0.5, p_t=34.0), State(R_t=1.0, p_t=34.0), State(R_t=0.0, p_t=35.0), State(R_t=0.5, p_t=35.0), State(R_t=1.0, p_t=35.0), State(R_t=0.0, p_t=36.0), State(R_t=0.5, p_t=36.0), State(R_t=1.0, p_t=36.0), State(R_t=0.0, p_t=37.0), State(R_t=0.5, p_t=37.0), State(R_t=1.0, p_t=37.0), State(R_t=0.0, p_t=38.0), State(R_t=0.5, p_t=38.0), State(R_t=1.0, p_t=38.0), State(R_t=0.0, p_t=39.0), State(R_t=0.5, p_t=39.0), State(R_t=1.0, p_t=39.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=41.0), State(R_t=0.5, p_t=41.0), State(R_t=1.0, p_t=41.0), State(R_t=0.0, p_t=42.0), State(R_t=0.5, p_t=42.0), State(R_t=1.0, p_t=42.0), State(R_t=0.0, p_t=43.0), State(R_t=0.5, p_t=43.0), State(R_t=1.0, p_t=43.0), State(R_t=0.0, p_t=44.0), State(R_t=0.5, p_t=44.0), State(R_t=1.0, p_t=44.0), State(R_t=0.0, p_t=45.0), State(R_t=0.5, p_t=45.0), State(R_t=1.0, p_t=45.0), State(R_t=0.0, p_t=46.0), State(R_t=0.5, p_t=46.0), State(R_t=1.0, p_t=46.0), State(R_t=0.0, p_t=47.0), State(R_t=0.5, p_t=47.0), State(R_t=1.0, p_t=47.0), State(R_t=0.0, p_t=48.0), State(R_t=0.5, p_t=48.0), State(R_t=1.0, p_t=48.0), State(R_t=0.0, p_t=49.0), State(R_t=0.5, p_t=49.0), State(R_t=1.0, p_t=49.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=51.0), State(R_t=0.5, p_t=51.0), State(R_t=1.0, p_t=51.0), State(R_t=0.0, p_t=52.0), State(R_t=0.5, p_t=52.0), State(R_t=1.0, p_t=52.0), State(R_t=0.0, p_t=53.0), State(R_t=0.5, p_t=53.0), State(R_t=1.0, p_t=53.0), State(R_t=0.0, p_t=54.0), State(R_t=0.5, p_t=54.0), State(R_t=1.0, p_t=54.0), State(R_t=0.0, p_t=55.0), State(R_t=0.5, p_t=55.0), State(R_t=1.0, p_t=55.0), State(R_t=0.0, p_t=56.0), State(R_t=0.5, p_t=56.0), State(R_t=1.0, p_t=56.0), State(R_t=0.0, p_t=57.0), State(R_t=0.5, p_t=57.0), State(R_t=1.0, p_t=57.0), State(R_t=0.0, p_t=58.0), State(R_t=0.5, p_t=58.0), State(R_t=1.0, p_t=58.0), State(R_t=0.0, p_t=59.0), State(R_t=0.5, p_t=59.0), State(R_t=1.0, p_t=59.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=61.0), State(R_t=0.5, p_t=61.0), State(R_t=1.0, p_t=61.0), State(R_t=0.0, p_t=62.0), State(R_t=0.5, p_t=62.0), State(R_t=1.0, p_t=62.0), State(R_t=0.0, p_t=63.0), State(R_t=0.5, p_t=63.0), State(R_t=1.0, p_t=63.0), State(R_t=0.0, p_t=64.0), State(R_t=0.5, p_t=64.0), State(R_t=1.0, p_t=64.0), State(R_t=0.0, p_t=65.0), State(R_t=0.5, p_t=65.0), State(R_t=1.0, p_t=65.0), State(R_t=0.0, p_t=66.0), State(R_t=0.5, p_t=66.0), State(R_t=1.0, p_t=66.0), State(R_t=0.0, p_t=67.0), State(R_t=0.5, p_t=67.0), State(R_t=1.0, p_t=67.0), State(R_t=0.0, p_t=68.0), State(R_t=0.5, p_t=68.0), State(R_t=1.0, p_t=68.0), State(R_t=0.0, p_t=69.0), State(R_t=0.5, p_t=69.0), State(R_t=1.0, p_t=69.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=71.0), State(R_t=0.5, p_t=71.0), State(R_t=1.0, p_t=71.0), State(R_t=0.0, p_t=72.0), State(R_t=0.5, p_t=72.0), State(R_t=1.0, p_t=72.0), State(R_t=0.0, p_t=73.0), State(R_t=0.5, p_t=73.0), State(R_t=1.0, p_t=73.0), State(R_t=0.0, p_t=74.0), State(R_t=0.5, p_t=74.0), State(R_t=1.0, p_t=74.0), State(R_t=0.0, p_t=75.0), State(R_t=0.5, p_t=75.0), State(R_t=1.0, p_t=75.0), State(R_t=0.0, p_t=76.0), State(R_t=0.5, p_t=76.0), State(R_t=1.0, p_t=76.0), State(R_t=0.0, p_t=77.0), State(R_t=0.5, p_t=77.0), State(R_t=1.0, p_t=77.0), State(R_t=0.0, p_t=78.0), State(R_t=0.5, p_t=78.0), State(R_t=1.0, p_t=78.0), State(R_t=0.0, p_t=79.0), State(R_t=0.5, p_t=79.0), State(R_t=1.0, p_t=79.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=81.0), State(R_t=0.5, p_t=81.0), State(R_t=1.0, p_t=81.0), State(R_t=0.0, p_t=82.0), State(R_t=0.5, p_t=82.0), State(R_t=1.0, p_t=82.0), State(R_t=0.0, p_t=83.0), State(R_t=0.5, p_t=83.0), State(R_t=1.0, p_t=83.0), State(R_t=0.0, p_t=84.0), State(R_t=0.5, p_t=84.0), State(R_t=1.0, p_t=84.0), State(R_t=0.0, p_t=85.0), State(R_t=0.5, p_t=85.0), State(R_t=1.0, p_t=85.0), State(R_t=0.0, p_t=86.0), State(R_t=0.5, p_t=86.0), State(R_t=1.0, p_t=86.0), State(R_t=0.0, p_t=87.0), State(R_t=0.5, p_t=87.0), State(R_t=1.0, p_t=87.0), State(R_t=0.0, p_t=88.0), State(R_t=0.5, p_t=88.0), State(R_t=1.0, p_t=88.0), State(R_t=0.0, p_t=89.0), State(R_t=0.5, p_t=89.0), State(R_t=1.0, p_t=89.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=91.0), State(R_t=0.5, p_t=91.0), State(R_t=1.0, p_t=91.0), State(R_t=0.0, p_t=92.0), State(R_t=0.5, p_t=92.0), State(R_t=1.0, p_t=92.0), State(R_t=0.0, p_t=93.0), State(R_t=0.5, p_t=93.0), State(R_t=1.0, p_t=93.0), State(R_t=0.0, p_t=94.0), State(R_t=0.5, p_t=94.0), State(R_t=1.0, p_t=94.0), State(R_t=0.0, p_t=95.0), State(R_t=0.5, p_t=95.0), State(R_t=1.0, p_t=95.0), State(R_t=0.0, p_t=96.0), State(R_t=0.5, p_t=96.0), State(R_t=1.0, p_t=96.0), State(R_t=0.0, p_t=97.0), State(R_t=0.5, p_t=97.0), State(R_t=1.0, p_t=97.0), State(R_t=0.0, p_t=98.0), State(R_t=0.5, p_t=98.0), State(R_t=1.0, p_t=98.0), State(R_t=0.0, p_t=99.0), State(R_t=0.5, p_t=99.0), State(R_t=1.0, p_t=99.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=101.0), State(R_t=0.5, p_t=101.0), State(R_t=1.0, p_t=101.0), State(R_t=0.0, p_t=102.0), State(R_t=0.5, p_t=102.0), State(R_t=1.0, p_t=102.0), State(R_t=0.0, p_t=103.0), State(R_t=0.5, p_t=103.0), State(R_t=1.0, p_t=103.0), State(R_t=0.0, p_t=104.0), State(R_t=0.5, p_t=104.0), State(R_t=1.0, p_t=104.0), State(R_t=0.0, p_t=105.0), State(R_t=0.5, p_t=105.0), State(R_t=1.0, p_t=105.0), State(R_t=0.0, p_t=106.0), State(R_t=0.5, p_t=106.0), State(R_t=1.0, p_t=106.0), State(R_t=0.0, p_t=107.0), State(R_t=0.5, p_t=107.0), State(R_t=1.0, p_t=107.0), State(R_t=0.0, p_t=108.0), State(R_t=0.5, p_t=108.0), State(R_t=1.0, p_t=108.0)]
    t=190
    t=180
    t=170
    t=160
    t=150
    t=140
    t=130
    t=120
    t=110
    t=100
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
Finishing inc 1.0 with best_inc_evolving=1.0, best_Cbarcum_evolving=87.48
FOR COMPARISON (final evolving values): 
best_inc_evolving=1.0, best_Cbarcum_evolving=87.48
..... P.perform_bellman_search_sample_paths() .....
numIncs=1
incs=[10.0]
printing every 1th inc
=== (0 / 0), inc=10.0 ===
    ..... BDP.compute_value_function() .....
    State dimension: 2.           State space size: 36.           Exogenous info size: 50
    self.p__disc=array([  0.,  10.,  20.,  30.,  40.,  50.,  60.,  70.,  80.,  90., 100.,
       110.])
    self.R__disc=array([0. , 0.5, 1. ])
    self.possibleStates=[State(R_t=0.0, p_t=0.0), State(R_t=0.5, p_t=0.0), State(R_t=1.0, p_t=0.0), State(R_t=0.0, p_t=10.0), State(R_t=0.5, p_t=10.0), State(R_t=1.0, p_t=10.0), State(R_t=0.0, p_t=20.0), State(R_t=0.5, p_t=20.0), State(R_t=1.0, p_t=20.0), State(R_t=0.0, p_t=30.0), State(R_t=0.5, p_t=30.0), State(R_t=1.0, p_t=30.0), State(R_t=0.0, p_t=40.0), State(R_t=0.5, p_t=40.0), State(R_t=1.0, p_t=40.0), State(R_t=0.0, p_t=50.0), State(R_t=0.5, p_t=50.0), State(R_t=1.0, p_t=50.0), State(R_t=0.0, p_t=60.0), State(R_t=0.5, p_t=60.0), State(R_t=1.0, p_t=60.0), State(R_t=0.0, p_t=70.0), State(R_t=0.5, p_t=70.0), State(R_t=1.0, p_t=70.0), State(R_t=0.0, p_t=80.0), State(R_t=0.5, p_t=80.0), State(R_t=1.0, p_t=80.0), State(R_t=0.0, p_t=90.0), State(R_t=0.5, p_t=90.0), State(R_t=1.0, p_t=90.0), State(R_t=0.0, p_t=100.0), State(R_t=0.5, p_t=100.0), State(R_t=1.0, p_t=100.0), State(R_t=0.0, p_t=110.0), State(R_t=0.5, p_t=110.0), State(R_t=1.0, p_t=110.0)]
    t=190
    t=180
    t=170
    t=160
    t=150
    t=140
    t=130
    t=120
    t=110
    t=100
    t=90
    t=80
    t=70
    t=60
    t=50
    t=40
    t=30
    t=20
    t=10
    t=0
    ..... P.run_bellman_sample_paths() .....
    l=0
Finishing inc 10.0 with best_inc_evolving=10.0, best_Cbarcum_evolving=13.689000000000004
FOR COMPARISON (final evolving values): 
best_inc_evolving=10.0, best_Cbarcum_evolving=13.689000000000004
CPU times: user 4min 26s, sys: 766 ms, total: 4min 27s
Wall time: 4min 49s

RuntimeWarning: invalid value encountered in double_scalars
  Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)
<ipython-input-303-7a5f2761a525>:384: RuntimeWarning: invalid value encountered in double_scalars
  Ctilcum_tmp = np.sum(np.square(np.array(CcumIomega__lI) - Cbarcum_tmp))/(L - 1)

P.plot_records(
  df=df_Bellman_evalu_opt,
  df_non=df_Bellman_evalu_non,
  pars=defaultdict(str, {
    'suptitle': f'EVALUATION OF X__Bellman POLICY'+'\n'+f'(first {first_n_t} records)'+'\n'+ \
    f'L = {L}, T = {T}, '+ \
    r'$\theta^*=$'+f'{best_inc_Bellman_evalu_opt}',
  }),
)

df_Bellman_evalu_opt[df_Bellman_evalu_opt['t']==T-1][['Ccum']]

	Ccum
191	87.4800

df_Bellman_evalu_non[df_Bellman_evalu_non['t']==T-1][['Ccum']]

	Ccum
191	13.6890

Comparison of Policies

P.plot_evalu_comparison(
  df1=df_BuyLowSellHigh_evalu_opt,
  df2=df_Bellman_evalu_opt,
  df3=None,
  pars= defaultdict(str, {
    'suptitle': f'EVALUATION OF ALL POLICIES (first {first_n_t} records)\n \
    L={L}, T={T}',
  }),
)