QRE analysis of a sender-receiver game
Valeria Burdea, December 2016

This is a 2-player sequential game the structure of which is inspired by Glazer and Rubinstein (2004, 2006). In the first stage, the sender is dealt 2 cards - one card orange, one card blue. Each card can take a value between 1 and 9; each combination of values is equally likely. A hand is good if the sum of the two cards is at least 9; a hand is bad otherwise. Upon observing the two cards, the sender chooses one to reveal to the receiver. The receiver observes the revealed card and chooses an action between 'Accept' and 'Reject'. The incentives are such that the sender would always want the receiver to accept, while the receiver would only want to accept if the hand is good and reject otherwise.

This game is studied experimentally in a working paper, "Communication with partially verifiable information: An experiment" by Valeria Burdea, Maria Montero, and Martin Sefton.

In [1]:
import gambit
In [2]:
g=gambit.Game.new_tree()
In [3]:
g.title="9x9"

Adding the two players:

In [4]:
sender=g.players.add("Sender")
receiver=g.players.add("Receiver")

Adding the chance moves. There are 81 such moves, as there are 81 (9x9) possible combinations of card values:

In [5]:
move=g.root.append_move(g.players.chance, 81)
In [6]:
i=0
b=1
while i<81 and b<10:
    for o in range(1, 10):
        move.actions[i].label=str(b)+str(o)
        i=i+1
    b=b+1

For each of the 81 states, the sender has two actions: reveal the value on the orange card (action 0) or the value on the blue card (action 1). We add these actions at different information sets as the sender has perfect information about the state of the world:

In [7]:
for j in range(0,81):
    moves=g.root.children[j].append_move(sender,2)
    moves.label='s'+move.actions[j].label
    moves.actions[0].label=move.actions[j].label[0]
    moves.actions[1].label=move.actions[j].label[1]

For each value revealed the receiver has two actions: 'Accept' and 'Reject'. We assume the receiver is colour blind, so she only has 9 information sets corresponding to the 9 possible values on either card. To do this iteratively, we define the move for the first time that card value is observed and then, every other time we append the same previously defined move. We repeat this process for each information set of the receiver..

In [8]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='1':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='1':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='1':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='1'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='1':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [9]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='2':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='2':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='2':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='2'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='2':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [10]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='3':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='3':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='3':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='3'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='3':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [11]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='4':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='4':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='4':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='4'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='4':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [12]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='5':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='5':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='5':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='5'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='5':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [13]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='6':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='6':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='6':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='6'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='6':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [14]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='7':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='7':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='7':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='7'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='7':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [15]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='8':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='8':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='8':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='8'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='8':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1
In [16]:
first=0
for i in range(0,81):
    if first>0:
        if g.root.children[i].infoset.actions[0].label=='9':
            g.root.children[i].children[0].append_move(mover)
        if g.root.children[i].infoset.actions[1].label=='9':
            g.root.children[i].children[1].append_move(mover)
    t=0
    while first<1 and t<2:
        if g.root.children[i].infoset.actions[t].label=='9':
            mover=g.root.children[i].children[t].append_move(receiver,2)
            mover.label='9'
            mover.actions[0].label="Accept"
            mover.actions[1].label="Reject"
            if t==0 and g.root.children[i].infoset.actions[1].label=='9':
                g.root.children[i].children[1].append_move(mover)
            t=t+2
            first=1
        else:
            t=t+1

We now define the outcomes. There are 4 such possible outcomes depending on whether the receiver accepts or rejects and whether the state is good or bad.

In [17]:
accept_good=g.outcomes.add("R accepts good hand")
accept_good[0]=1
accept_good[1]=1
In [18]:
reject_good=g.outcomes.add("R rejects good hand")
reject_good[0]=0
reject_good[1]=0
In [19]:
accept_bad=g.outcomes.add("R accepts bad hand")
accept_bad[0]=1
accept_bad[1]=0
In [20]:
reject_bad=g.outcomes.add("R rejects bad hand")
reject_bad[0]=0
reject_bad[1]=1

We proceed by appending the previously defined outcome pairs to the corresonding leafs.

In [21]:
for i in range(0,81):
    hand=int(g.root.children[i].infoset.actions[0].label)+int(g.root.children[i].infoset.actions[1].label)
    if hand>8:
        g.root.children[i].children[0].children[0].outcome=accept_good
        g.root.children[i].children[0].children[1].outcome=reject_good
        g.root.children[i].children[1].children[0].outcome=accept_good
        g.root.children[i].children[1].children[1].outcome=reject_good
    else:
        g.root.children[i].children[0].children[0].outcome=accept_bad
        g.root.children[i].children[0].children[1].outcome=reject_bad
        g.root.children[i].children[1].children[0].outcome=accept_bad
        g.root.children[i].children[1].children[1].outcome=reject_bad

We write the game out to disk in order to be able to use the Gambit command-line tools to compute the principle branch of the QRE.

In [22]:
with file("extensive9x9.efg", "w") as f:
    f.write(g.write('efg'))

Computing the principal branch of the QRE:

In [24]:
!gambit-logit extensive9x9.efg
Compute a branch of the logit equilibrium correspondence
Gambit version 14.1.0, Copyright (C) 1994-2014, The Gambit Project
This is free software, distributed under the GNU GPL

0.000000,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5,0.5
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1.002021,0.5,0.5,0.487664,0.512336,0.4744,0.5256,0.460492,0.539508,0.446331,0.553669,0.432369,0.567631,0.419053,0.580947,0.406758,0.593242,0.406758,0.593242,0.512336,0.487664,0.5,0.5,0.486719,0.513281,0.472775,0.527225,0.458556,0.541444,0.444519,0.555481,0.431113,0.568887,0.41872,0.58128,0.41872,0.58128,0.5256,0.4744,0.513281,0.486719,0.5,0.5,0.486035,0.513965,0.471775,0.528225,0.457675,0.542325,0.44419,0.55581,0.431706,0.568294,0.431706,0.568294,0.539508,0.460492,0.527225,0.472775,0.513965,0.486035,0.5,0.5,0.485717,0.514283,0.471573,0.528427,0.458024,0.541976,0.445462,0.554538,0.445462,0.554538,0.553669,0.446331,0.541444,0.458556,0.528225,0.471775,0.514283,0.485717,0.5,0.5,0.485832,0.514168,0.47224,0.52776,0.459619,0.540381,0.459619,0.540381,0.567631,0.432369,0.555481,0.444519,0.542325,0.457675,0.528427,0.471573,0.514168,0.485832,0.5,0.5,0.486386,0.513614,0.473727,0.526273,0.473727,0.526273,0.580947,0.419053,0.568887,0.431113,0.55581,0.44419,0.541976,0.458024,0.52776,0.47224,0.513614,0.486386,0.5,0.5,0.487322,0.512678,0.487322,0.512678,0.593242,0.406758,0.58128,0.41872,0.568294,0.431706,0.554538,0.445462,0.540381,0.459619,0.526273,0.473727,0.512678,0.487322,0.5,0.5,0.5,0.5,0.593242,0.406758,0.58128,0.41872,0.568294,0.431706,0.554538,0.445462,0.540381,0.459619,0.526273,0.473727,0.512678,0.487322,0.5,0.5,0.5,0.5,0.354834,0.645166,0.404086,0.595914,0.457115,0.542885,0.512876,0.487124,0.569907,0.430093,0.626478,0.373522,0.680837,0.319163,0.731456,0.268544,0.731456,0.268544
1.082759,0.5,0.5,0.485934,0.514066,0.470599,0.529401,0.454364,0.545636,0.437771,0.562229,0.421467,0.578533,0.406082,0.593918,0.392116,0.607884,0.392116,0.607884,0.514066,0.485934,0.5,0.5,0.48464,0.51536,0.468349,0.531651,0.451668,0.548332,0.435247,0.564753,0.419724,0.580276,0.405609,0.594391,0.405609,0.594391,0.529401,0.470599,0.51536,0.48464,0.5,0.5,0.483677,0.516323,0.46693,0.53307,0.45041,0.54959,0.434762,0.565238,0.420508,0.579492,0.420508,0.579492,0.545636,0.454364,0.531651,0.468349,0.516323,0.483677,0.5,0.5,0.483217,0.516783,0.466625,0.533375,0.450876,0.549124,0.436501,0.563499,0.436501,0.563499,0.562229,0.437771,0.548332,0.451668,0.53307,0.46693,0.516783,0.483217,0.5,0.5,0.483371,0.516629,0.467552,0.532448,0.453085,0.546915,0.453085,0.546915,0.578533,0.421467,0.564753,0.435247,0.54959,0.45041,0.533375,0.466625,0.516629,0.483371,0.5,0.5,0.484147,0.515853,0.469619,0.530381,0.469619,0.530381,0.593918,0.406082,0.580276,0.419724,0.565238,0.434762,0.549124,0.450876,0.532448,0.467552,0.515853,0.484147,0.5,0.5,0.485444,0.514556,0.485444,0.514556,0.607884,0.392116,0.594391,0.405609,0.579492,0.420508,0.563499,0.436501,0.546915,0.453085,0.530381,0.469619,0.514556,0.485444,0.5,0.5,0.5,0.5,0.607884,0.392116,0.594391,0.405609,0.579492,0.420508,0.563499,0.436501,0.546915,0.453085,0.530381,0.469619,0.514556,0.485444,0.5,0.5,0.5,0.5,0.342099,0.657901,0.394077,0.605923,0.450839,0.549161,0.511161,0.488839,0.573187,0.426813,0.634642,0.365358,0.693226,0.306774,0.747016,0.252984,0.747016,0.252984
1.166732,0.5,0.5,0.484117,0.515883,0.466522,0.533478,0.447677,0.552323,0.428329,0.571671,0.409396,0.590604,0.391759,0.608241,0.376068,0.623932,0.376068,0.623932,0.515883,0.484117,0.5,0.5,0.482368,0.517632,0.463438,0.536562,0.443957,0.556043,0.424847,0.575153,0.407003,0.592997,0.391094,0.608906,0.391094,0.608906,0.533478,0.466522,0.517632,0.482368,0.5,0.5,0.481022,0.518978,0.461437,0.538563,0.442173,0.557827,0.424138,0.575862,0.40802,0.59198,0.40802,0.59198,0.552323,0.447677,0.536562,0.463438,0.518978,0.481022,0.5,0.5,0.480358,0.519642,0.46098,0.53902,0.442786,0.557214,0.426484,0.573516,0.426484,0.573516,0.571671,0.428329,0.556043,0.443957,0.538563,0.461437,0.519642,0.480358,0.5,0.5,0.480563,0.519437,0.462259,0.537741,0.445814,0.554186,0.445814,0.554186,0.590604,0.409396,0.575153,0.424847,0.557827,0.442173,0.53902,0.46098,0.519437,0.480563,0.5,0.5,0.481643,0.518357,0.465104,0.534896,0.465104,0.534896,0.608241,0.391759,0.592997,0.407003,0.575862,0.424138,0.557214,0.442786,0.537741,0.462259,0.518357,0.481643,0.5,0.5,0.483419,0.516581,0.483419,0.516581,0.623932,0.376068,0.608906,0.391094,0.59198,0.40802,0.573516,0.426484,0.554186,0.445814,0.534896,0.465104,0.516581,0.483419,0.5,0.5,0.5,0.5,0.623932,0.376068,0.608906,0.391094,0.59198,0.40802,0.573516,0.426484,0.554186,0.445814,0.534896,0.465104,0.516581,0.483419,0.5,0.5,0.5,0.5,0.328631,0.671369,0.383104,0.616896,0.443579,0.556421,0.508675,0.491325,0.576051,0.423949,0.642723,0.357277,0.705687,0.294313,0.762554,0.237446,0.762554,0.237446
1.253925,0.5,0.5,0.482248,0.517752,0.462214,0.537786,0.440455,0.559545,0.417991,0.582009,0.396122,0.603878,0.376063,0.623937,0.358637,0.641363,0.358637,0.641363,0.517752,0.482248,0.5,0.5,0.479912,0.520088,0.45803,0.54197,0.435367,0.564633,0.413234,0.586766,0.392873,0.607127,0.375136,0.624864,0.375136,0.624864,0.537786,0.462214,0.520088,0.479912,0.5,0.5,0.478044,0.521956,0.455223,0.544777,0.432854,0.567146,0.412205,0.587795,0.394162,0.605838,0.394162,0.605838,0.559545,0.440455,0.54197,0.45803,0.521956,0.478044,0.5,0.5,0.477089,0.522911,0.454542,0.545458,0.43365,0.56635,0.415331,0.584669,0.415331,0.584669,0.582009,0.417991,0.564633,0.435367,0.544777,0.455223,0.522911,0.477089,0.5,0.5,0.477359,0.522641,0.456295,0.543705,0.437759,0.562241,0.437759,0.562241,0.603878,0.396122,0.586766,0.413234,0.567146,0.432854,0.545458,0.454542,0.522641,0.477359,0.5,0.5,0.478852,0.521148,0.460176,0.539824,0.460176,0.539824,0.623937,0.376063,0.607127,0.392873,0.587795,0.412205,0.56635,0.43365,0.543705,0.456295,0.521148,0.478852,0.5,0.5,0.48126,0.51874,0.48126,0.51874,0.641363,0.358637,0.624864,0.375136,0.605838,0.394162,0.584669,0.415331,0.562241,0.437759,0.539824,0.460176,0.51874,0.48126,0.5,0.5,0.5,0.5,0.641363,0.358637,0.624864,0.375136,0.605838,0.394162,0.584669,0.415331,0.562241,0.437759,0.539824,0.460176,0.51874,0.48126,0.5,0.5,0.5,0.5,0.314406,0.685594,0.37106,0.62894,0.435174,0.564826,0.505259,0.494741,0.578397,0.421603,0.650671,0.349329,0.718171,0.281829,0.777979,0.222021,0.777979,0.222021
1.344299,0.5,0.5,0.480375,0.519625,0.457746,0.542254,0.432751,0.567249,0.406768,0.593232,0.38163,0.61837,0.359005,0.640995,0.339889,0.660111,0.339889,0.660111,0.519625,0.480375,0.5,0.5,0.477296,0.522704,0.452123,0.547877,0.42585,0.57415,0.400329,0.599671,0.377272,0.622728,0.357726,0.642274,0.357726,0.642274,0.542254,0.457746,0.522704,0.477296,0.5,0.5,0.474718,0.525282,0.448205,0.551795,0.42233,0.57767,0.398849,0.601151,0.378865,0.621135,0.378865,0.621135,0.567249,0.432751,0.547877,0.452123,0.525282,0.474718,0.5,0.5,0.473348,0.526652,0.447198,0.552802,0.423347,0.576653,0.402958,0.597042,0.402958,0.597042,0.593232,0.406768,0.57415,0.42585,0.551795,0.448205,0.526652,0.473348,0.5,0.5,0.473701,0.526299,0.449587,0.550413,0.428874,0.571126,0.428874,0.571126,0.61837,0.38163,0.599671,0.400329,0.57767,0.42233,0.552802,0.447198,0.526299,0.473701,0.5,0.5,0.475757,0.524243,0.454835,0.545165,0.454835,0.545165,0.640995,0.359005,0.622728,0.377272,0.601151,0.398849,0.576653,0.423347,0.550413,0.449587,0.524243,0.475757,0.5,0.5,0.478986,0.521014,0.478986,0.521014,0.660111,0.339889,0.642274,0.357726,0.621135,0.378865,0.597042,0.402958,0.571126,0.428874,0.545165,0.454835,0.521014,0.478986,0.5,0.5,0.5,0.5,0.660111,0.339889,0.642274,0.357726,0.621135,0.378865,0.597042,0.402958,0.571126,0.428874,0.545165,0.454835,0.521014,0.478986,0.5,0.5,0.5,0.5,0.299416,0.700584,0.35784,0.64216,0.425444,0.574556,0.500736,0.499264,0.580115,0.419885,0.658439,0.341561,0.730632,0.269368,0.793196,0.206804,0.793196,0.206804
1.437787,0.5,0.5,0.478563,0.521437,0.453223,0.546777,0.424653,0.575347,0.394695,0.605305,0.365936,0.634064,0.340637,0.659363,0.319943,0.680057,0.319943,0.680057,0.521437,0.478563,0.5,0.5,0.474558,0.525442,0.445739,0.554261,0.415368,0.584632,0.386063,0.613937,0.360163,0.639837,0.338892,0.661108,0.338892,0.661108,0.546777,0.453223,0.525442,0.474558,0.5,0.5,0.471022,0.528978,0.440296,0.559704,0.410468,0.589532,0.383954,0.616046,0.362073,0.637927,0.362073,0.637927,0.575347,0.424653,0.554261,0.445739,0.528978,0.471022,0.5,0.5,0.46906,0.53094,0.438811,0.561189,0.411745,0.588255,0.389282,0.610718,0.389282,0.610718,0.605305,0.394695,0.584632,0.415368,0.559704,0.440296,0.53094,0.46906,0.5,0.5,0.46952,0.53048,0.442052,0.557948,0.419113,0.580887,0.419113,0.580887,0.634064,0.365936,0.613937,0.386063,0.589532,0.410468,0.561189,0.438811,0.53048,0.46952,0.5,0.5,0.472337,0.527663,0.449091,0.550909,0.449091,0.550909,0.659363,0.340637,0.639837,0.360163,0.616046,0.383954,0.588255,0.411745,0.557948,0.442052,0.527663,0.472337,0.5,0.5,0.476623,0.523377,0.476623,0.523377,0.680057,0.319943,0.661108,0.338892,0.637927,0.362073,0.610718,0.389282,0.580887,0.419113,0.550909,0.449091,0.523377,0.476623,0.5,0.5,0.5,0.5,0.680057,0.319943,0.661108,0.338892,0.637927,0.362073,0.610718,0.389282,0.580887,0.419113,0.550909,0.449091,0.523377,0.476623,0.5,0.5,0.5,0.5,0.283671,0.716329,0.343346,0.656654,0.41419,0.58581,0.494899,0.505101,0.581086,0.418914,0.665988,0.334012,0.743027,0.256973,0.808112,0.191888,0.808112,0.191888
1.534291,0.5,0.5,0.476892,0.523108,0.448785,0.551215,0.416293,0.583707,0.381843,0.618157,0.349089,0.650911,0.32106,0.67894,0.298975,0.701025,0.298975,0.701025,0.523108,0.476892,0.5,0.5,0.47176,0.52824,0.438928,0.561072,0.403902,0.596098,0.370389,0.629611,0.341548,0.658452,0.318715,0.681285,0.318715,0.681285,0.551215,0.448785,0.52824,0.47176,0.5,0.5,0.466941,0.533059,0.431397,0.568603,0.397124,0.602876,0.367415,0.632585,0.343755,0.656245,0.343755,0.656245,0.583707,0.416293,0.561072,0.438928,0.533059,0.466941,0.5,0.5,0.464131,0.535869,0.42922,0.57078,0.398698,0.601302,0.374216,0.625784,0.374216,0.625784,0.618157,0.381843,0.596098,0.403902,0.568603,0.431397,0.535869,0.464131,0.5,0.5,0.464731,0.535269,0.433602,0.566398,0.408432,0.591568,0.408432,0.591568,0.650911,0.349089,0.629611,0.370389,0.602876,0.397124,0.57078,0.42922,0.535269,0.464731,0.5,0.5,0.468577,0.531423,0.442965,0.557035,0.442965,0.557035,0.67894,0.32106,0.658452,0.341548,0.632585,0.367415,0.601302,0.398698,0.566398,0.433602,0.531423,0.468577,0.5,0.5,0.474203,0.525797,0.474203,0.525797,0.701025,0.298975,0.681285,0.318715,0.656245,0.343755,0.625784,0.374216,0.591568,0.408432,0.557035,0.442965,0.525797,0.474203,0.5,0.5,0.5,0.5,0.701025,0.298975,0.681285,0.318715,0.656245,0.343755,0.625784,0.374216,0.591568,0.408432,0.557035,0.442965,0.525797,0.474203,0.5,0.5,0.5,0.5,0.267209,0.732791,0.327496,0.672504,0.401199,0.598801,0.487513,0.512487,0.581186,0.418814,0.673289,0.326711,0.755319,0.244681,0.822633,0.177367,0.822633,0.177367
1.633694,0.5,0.5,0.475456,0.524544,0.444619,0.555381,0.407858,0.592142,0.368322,0.631678,0.331177,0.668823,0.300433,0.699567,0.277221,0.722779,0.277221,0.722779,0.524544,0.475456,0.5,0.5,0.468994,0.531006,0.431784,0.568216,0.391462,0.608538,0.353289,0.646711,0.321479,0.678521,0.297332,0.702668,0.297332,0.702668,0.555381,0.444619,0.531006,0.468994,0.5,0.5,0.462473,0.537527,0.42141,0.57859,0.38215,0.61785,0.349145,0.650855,0.323912,0.676088,0.323912,0.676088,0.592142,0.407858,0.568216,0.431784,0.537527,0.462473,0.5,0.5,0.458447,0.541553,0.418231,0.581769,0.384046,0.615954,0.357677,0.642323,0.357677,0.642323,0.631678,0.368322,0.608538,0.391462,0.57859,0.42141,0.541553,0.458447,0.5,0.5,0.45923,0.54077,0.424137,0.575863,0.396789,0.603211,0.396789,0.603211,0.668823,0.331177,0.646711,0.353289,0.61785,0.38215,0.581769,0.418231,0.54077,0.45923,0.5,0.5,0.464468,0.535532,0.43649,0.56351,0.43649,0.56351,0.699567,0.300433,0.678521,0.321479,0.650855,0.349145,0.615954,0.384046,0.575863,0.424137,0.535532,0.464468,0.5,0.5,0.471767,0.528233,0.471767,0.528233,0.722779,0.277221,0.702668,0.297332,0.676088,0.323912,0.642323,0.357677,0.603211,0.396789,0.56351,0.43649,0.528233,0.471767,0.5,0.5,0.5,0.5,0.722779,0.277221,0.702668,0.297332,0.676088,0.323912,0.642323,0.357677,0.603211,0.396789,0.56351,0.43649,0.528233,0.471767,0.5,0.5,0.5,0.5,0.250098,0.749902,0.31024,0.68976,0.386254,0.613746,0.47831,0.52169,0.580284,0.419716,0.68033,0.31967,0.767475,0.232525,0.836675,0.163325,0.836675,0.163325
1.735867,0.5,0.5,0.474363,0.525637,0.440956,0.559044,0.399599,0.600401,0.354282,0.645718,0.312329,0.687671,0.278972,0.721028,0.254972,0.745028,0.254972,0.745028,0.525637,0.474363,0.5,0.5,0.466389,0.533611,0.424458,0.575542,0.378097,0.621903,0.334786,0.665214,0.300077,0.699923,0.274954,0.725046,0.274954,0.725046,0.559044,0.440956,0.533611,0.466389,0.5,0.5,0.457639,0.542361,0.410237,0.589763,0.365408,0.634592,0.329095,0.670905,0.302593,0.697407,0.302593,0.697407,0.600401,0.399599,0.575542,0.424458,0.542361,0.457639,0.5,0.5,0.451866,0.548134,0.405616,0.594384,0.367622,0.632378,0.339588,0.660412,0.339588,0.660412,0.645718,0.354282,0.621903,0.378097,0.589763,0.410237,0.548134,0.451866,0.5,0.5,0.452894,0.547106,0.413553,0.586447,0.384144,0.615856,0.384144,0.615856,0.687671,0.312329,0.665214,0.334786,0.634592,0.365408,0.594384,0.405616,0.547106,0.452894,0.5,0.5,0.460007,0.539993,0.429715,0.570285,0.429715,0.570285,0.721028,0.278972,0.699923,0.300077,0.670905,0.329095,0.632378,0.367622,0.586447,0.413553,0.539993,0.460007,0.5,0.5,0.469363,0.530637,0.469363,0.530637,0.745028,0.254972,0.725046,0.274954,0.697407,0.302593,0.660412,0.339588,0.615856,0.384144,0.570285,0.429715,0.530637,0.469363,0.5,0.5,0.5,0.5,0.745028,0.254972,0.725046,0.274954,0.697407,0.302593,0.660412,0.339588,0.615856,0.384144,0.570285,0.429715,0.530637,0.469363,0.5,0.5,0.5,0.5,0.232449,0.767551,0.291576,0.708424,0.369144,0.630856,0.466992,0.533008,0.578253,0.421747,0.687123,0.312877,0.779476,0.220524,0.850161,0.149839,0.850161,0.149839
1.840694,0.5,0.5,0.473719,0.526281,0.438066,0.561934,0.391838,0.608162,0.339914,0.660086,0.292715,0.707285,0.256948,0.743052,0.23256,0.76744,0.23256,0.76744,0.526281,0.473719,0.5,0.5,0.464113,0.535887,0.417177,0.582823,0.363905,0.636095,0.314964,0.685036,0.277546,0.722454,0.251865,0.748135,0.251865,0.748135,0.561934,0.438066,0.535887,0.464113,0.5,0.5,0.452499,0.547501,0.397795,0.602205,0.346781,0.653219,0.307279,0.692721,0.279913,0.720087,0.279913,0.720087,0.608162,0.391838,0.582823,0.417177,0.547501,0.452499,0.5,0.5,0.444212,0.555788,0.391112,0.608888,0.349259,0.650741,0.319881,0.680119,0.319881,0.680119,0.660086,0.339914,0.636095,0.363905,0.602205,0.397795,0.555788,0.444212,0.5,0.5,0.445577,0.554423,0.401742,0.598258,0.370462,0.629538,0.370462,0.629538,0.707285,0.292715,0.685036,0.314964,0.653219,0.346781,0.608888,0.391112,0.554423,0.445577,0.5,0.5,0.455207,0.544793,0.422705,0.577295,0.422705,0.577295,0.743052,0.256948,0.722454,0.277546,0.692721,0.307279,0.650741,0.349259,0.598258,0.401742,0.544793,0.455207,0.5,0.5,0.467042,0.532958,0.467042,0.532958,0.76744,0.23256,0.748135,0.251865,0.720087,0.279913,0.680119,0.319881,0.629538,0.370462,0.577295,0.422705,0.532958,0.467042,0.5,0.5,0.5,0.5,0.76744,0.23256,0.748135,0.251865,0.720087,0.279913,0.680119,0.319881,0.629538,0.370462,0.577295,0.422705,0.532958,0.467042,0.5,0.5,0.5,0.5,0.21441,0.78559,0.271574,0.728426,0.349694,0.650306,0.45323,0.54677,0.574969,0.425031,0.693705,0.306295,0.791307,0.208693,0.863031,0.136969,0.863031,0.136969
1.948109,0.5,0.5,0.473618,0.526382,0.436243,0.563757,0.384968,0.615032,0.32544,0.67456,0.272535,0.727465,0.234675,0.765325,0.210336,0.789664,0.210336,0.789664,0.526382,0.473618,0.5,0.5,0.462372,0.537628,0.410261,0.589739,0.349042,0.650958,0.293972,0.706028,0.254175,0.745825,0.228417,0.771583,0.228417,0.771583,0.563757,0.436243,0.537628,0.462372,0.5,0.5,0.447176,0.552824,0.384035,0.615965,0.326211,0.673789,0.283804,0.716196,0.256074,0.743926,0.256074,0.743926,0.615032,0.384968,0.589739,0.410261,0.552824,0.447176,0.5,0.5,0.435273,0.564727,0.374424,0.625576,0.328807,0.671193,0.298513,0.701487,0.298513,0.701487,0.67456,0.32544,0.650958,0.349042,0.615965,0.384035,0.564727,0.435273,0.5,0.5,0.437106,0.562894,0.388597,0.611403,0.355714,0.644286,0.355714,0.644286,0.727465,0.272535,0.706028,0.293972,0.673789,0.326211,0.625576,0.374424,0.562894,0.437106,0.5,0.5,0.450092,0.549908,0.415542,0.584458,0.415542,0.584458,0.765325,0.234675,0.745825,0.254175,0.716196,0.283804,0.671193,0.328807,0.611403,0.388597,0.549908,0.450092,0.5,0.5,0.464857,0.535143,0.464857,0.535143,0.789664,0.210336,0.771583,0.228417,0.743926,0.256074,0.701487,0.298513,0.644286,0.355714,0.584458,0.415542,0.535143,0.464857,0.5,0.5,0.5,0.5,0.789664,0.210336,0.771583,0.228417,0.743926,0.256074,0.701487,0.298513,0.644286,0.355714,0.584458,0.415542,0.535143,0.464857,0.5,0.5,0.5,0.5,0.196172,0.803828,0.250392,0.749608,0.327799,0.672201,0.436668,0.563332,0.57032,0.42968,0.700146,0.299854,0.802963,0.197037,0.87524,0.12476,0.87524,0.12476
2.058136,0.5,0.5,0.474123,0.525877,0.435771,0.564229,0.379452,0.620548,0.3111,0.6889,0.252009,0.747991,0.212487,0.787513,0.188645,0.811355,0.188645,0.811355,0.525877,0.474123,0.5,0.5,0.461392,0.538608,0.404133,0.595867,0.333726,0.666274,0.272034,0.727966,0.230339,0.769661,0.205015,0.794985,0.205015,0.794985,0.564229,0.435771,0.538608,0.461392,0.5,0.5,0.44188,0.55812,0.368969,0.631031,0.303733,0.696267,0.258907,0.741093,0.231386,0.768614,0.231386,0.768614,0.620548,0.379452,0.595867,0.404133,0.55812,0.44188,0.5,0.5,0.424798,0.575202,0.355248,0.644752,0.306162,0.693838,0.275486,0.724514,0.275486,0.724514,0.6889,0.3111,0.666274,0.333726,0.631031,0.368969,0.575202,0.424798,0.5,0.5,0.427283,0.572717,0.374018,0.625982,0.339873,0.660127,0.339873,0.660127,0.747991,0.252009,0.727966,0.272034,0.696267,0.303733,0.644752,0.355248,0.572717,0.427283,0.5,0.5,0.444708,0.555292,0.40832,0.59168,0.40832,0.59168,0.787513,0.212487,0.769661,0.230339,0.741093,0.258907,0.693838,0.306162,0.625982,0.374018,0.555292,0.444708,0.5,0.5,0.462858,0.537142,0.462858,0.537142,0.811355,0.188645,0.794985,0.205015,0.768614,0.231386,0.724514,0.275486,0.660127,0.339873,0.59168,0.40832,0.537142,0.462858,0.5,0.5,0.5,0.5,0.811355,0.188645,0.794985,0.205015,0.768614,0.231386,0.724514,0.275486,0.660127,0.339873,0.59168,0.40832,0.537142,0.462858,0.5,0.5,0.5,0.5,0.17795,0.82205,0.228287,0.771713,0.303473,0.696527,0.416941,0.583059,0.564214,0.435786,0.706548,0.293452,0.814449,0.185551,0.886767,0.113233,0.886767,0.113233
2.170954,0.5,0.5,0.475251,0.524749,0.436878,0.563122,0.375798,0.624202,0.297131,0.702869,0.231357,0.768643,0.190709,0.809291,0.167791,0.832209,0.167791,0.832209,0.524749,0.475251,0.5,0.5,0.461386,0.538614,0.399309,0.600691,0.318229,0.681771,0.249443,0.750557,0.206471,0.793529,0.182085,0.817915,0.182085,0.817915,0.563122,0.436878,0.538614,0.461386,0.5,0.5,0.436943,0.563057,0.352708,0.647292,0.279524,0.720476,0.232979,0.767021,0.206276,0.793724,0.206276,0.793724,0.624202,0.375798,0.600691,0.399309,0.563057,0.436943,0.5,0.5,0.412515,0.587485,0.333312,0.666688,0.281307,0.718693,0.250876,0.749124,0.250876,0.749124,0.702869,0.297131,0.681771,0.318229,0.647292,0.352708,0.587485,0.412515,0.5,0.5,0.415891,0.584109,0.357918,0.642082,0.322924,0.677076,0.322924,0.677076,0.768643,0.231357,0.750557,0.249443,0.720476,0.279524,0.666688,0.333312,0.584109,0.415891,0.5,0.5,0.439117,0.560883,0.401144,0.598856,0.401144,0.598856,0.809291,0.190709,0.793529,0.206471,0.767021,0.232979,0.718693,0.281307,0.642082,0.357918,0.560883,0.439117,0.5,0.5,0.46109,0.53891,0.46109,0.53891,0.832209,0.167791,0.817915,0.182085,0.793724,0.206276,0.749124,0.250876,0.677076,0.322924,0.598856,0.401144,0.53891,0.46109,0.5,0.5,0.5,0.5,0.832209,0.167791,0.817915,0.182085,0.793724,0.206276,0.749124,0.250876,0.677076,0.322924,0.598856,0.401144,0.53891,0.46109,0.5,0.5,0.5,0.5,0.159978,0.840022,0.205616,0.794384,0.276905,0.723095,0.39371,0.60629,0.556578,0.443422,0.713037,0.286963,0.825773,0.174227,0.897611,0.102389,0.897611,0.102389
2.286967,0.5,0.5,0.476958,0.523042,0.439671,0.560329,0.374527,0.625473,0.283749,0.716251,0.210785,0.789215,0.169633,0.830367,0.148017,0.851983,0.148017,0.851983,0.523042,0.476958,0.5,0.5,0.462504,0.537496,0.396371,0.603629,0.302861,0.697139,0.226537,0.773463,0.183023,0.816977,0.16003,0.83997,0.16003,0.83997,0.560329,0.439671,0.537496,0.462504,0.5,0.5,0.432822,0.567178,0.335493,0.664507,0.253941,0.746059,0.206569,0.793431,0.181274,0.818726,0.181274,0.818726,0.625473,0.374527,0.603629,0.396371,0.567178,0.432822,0.5,0.5,0.398169,0.601831,0.308454,0.691546,0.25438,0.74562,0.224889,0.775111,0.224889,0.775111,0.716251,0.283749,0.697139,0.302861,0.664507,0.335493,0.601831,0.398169,0.5,0.5,0.402692,0.597308,0.340226,0.659774,0.304852,0.695148,0.304852,0.695148,0.789215,0.210785,0.773463,0.226537,0.746059,0.253941,0.691546,0.308454,0.597308,0.402692,0.5,0.5,0.433391,0.566609,0.394117,0.605883,0.394117,0.605883,0.830367,0.169633,0.816977,0.183023,0.793431,0.206569,0.74562,0.25438,0.659774,0.340226,0.566609,0.433391,0.5,0.5,0.459586,0.540414,0.459586,0.540414,0.851983,0.148017,0.83997,0.16003,0.818726,0.181274,0.775111,0.224889,0.695148,0.304852,0.605883,0.394117,0.540414,0.459586,0.5,0.5,0.5,0.5,0.851983,0.148017,0.83997,0.16003,0.818726,0.181274,0.775111,0.224889,0.695148,0.304852,0.605883,0.394117,0.540414,0.459586,0.5,0.5,0.5,0.5,0.142481,0.857519,0.182811,0.817189,0.248516,0.751484,0.366727,0.633273,0.547359,0.452641,0.719753,0.280247,0.836952,0.163048,0.907792,0.0922081,0.907792,0.0922081
2.406899,0.5,0.5,0.479146,0.520854,0.444088,0.555912,0.376097,0.623903,0.271137,0.728863,0.190466,0.809534,0.149488,0.850512,0.129485,0.870515,0.129485,0.870515,0.520854,0.479146,0.5,0.5,0.464777,0.535223,0.395875,0.604125,0.287943,0.712057,0.203669,0.796331,0.160414,0.839586,0.139187,0.860813,0.139187,0.860813,0.555912,0.444088,0.535223,0.464777,0.5,0.5,0.430072,0.569928,0.31772,0.68228,0.227516,0.772484,0.180342,0.819658,0.156972,0.843028,0.156972,0.843028,0.623903,0.376097,0.604125,0.395875,0.569928,0.430072,0.5,0.5,0.381611,0.618389,0.280732,0.719268,0.225749,0.774251,0.197915,0.802085,0.197915,0.802085,0.728863,0.271137,0.712057,0.287943,0.68228,0.31772,0.618389,0.381611,0.5,0.5,0.387432,0.612568,0.320874,0.679126,0.285639,0.714361,0.285639,0.714361,0.809534,0.190466,0.796331,0.203669,0.772484,0.227516,0.719268,0.280732,0.612568,0.387432,0.5,0.5,0.427603,0.572397,0.387332,0.612668,0.387332,0.612668,0.850512,0.149488,0.839586,0.160414,0.819658,0.180342,0.774251,0.225749,0.679126,0.320874,0.572397,0.427603,0.5,0.5,0.458371,0.541629,0.458371,0.541629,0.870515,0.129485,0.860813,0.139187,0.843028,0.156972,0.802085,0.197915,0.714361,0.285639,0.612668,0.387332,0.541629,0.458371,0.5,0.5,0.5,0.5,0.870515,0.129485,0.860813,0.139187,0.843028,0.156972,0.802085,0.197915,0.714361,0.285639,0.612668,0.387332,0.541629,0.458371,0.5,0.5,0.5,0.5,0.12566,0.87434,0.160337,0.839663,0.21897,0.78103,0.33595,0.66405,0.536504,0.463496,0.726841,0.273159,0.848008,0.151992,0.917352,0.0826481,0.917352,0.0826481
2.531898,0.5,0.5,0.481673,0.518327,0.449873,0.550127,0.380787,0.619213,0.259451,0.740549,0.170536,0.829464,0.130429,0.869571,0.112271,0.887729,0.112271,0.887729,0.518327,0.481673,0.5,0.5,0.468083,0.531917,0.398225,0.601775,0.273789,0.726211,0.181162,0.818838,0.138975,0.861025,0.119792,0.880208,0.119792,0.880208,0.550127,0.449873,0.531917,0.468083,0.5,0.5,0.429222,0.570778,0.299927,0.700073,0.200904,0.799096,0.15499,0.84501,0.13394,0.86606,0.13394,0.86606,0.619213,0.380787,0.601775,0.398225,0.570778,0.429222,0.5,0.5,0.362942,0.637058,0.25056,0.74944,0.196083,0.803917,0.170578,0.829422,0.170578,0.829422,0.740549,0.259451,0.726211,0.273789,0.700073,0.299927,0.637058,0.362942,0.5,0.5,0.369815,0.630185,0.299781,0.700219,0.265238,0.734762,0.265238,0.734762,0.829464,0.170536,0.818838,0.181162,0.799096,0.200904,0.74944,0.25056,0.630185,0.369815,0.5,0.5,0.421814,0.578186,0.380857,0.619143,0.380857,0.619143,0.869571,0.130429,0.861025,0.138975,0.84501,0.15499,0.803917,0.196083,0.700219,0.299781,0.578186,0.421814,0.5,0.5,0.457459,0.542541,0.457459,0.542541,0.887729,0.112271,0.880208,0.119792,0.86606,0.13394,0.829422,0.170578,0.734762,0.265238,0.619143,0.380857,0.542541,0.457459,0.5,0.5,0.5,0.5,0.887729,0.112271,0.880208,0.119792,0.86606,0.13394,0.829422,0.170578,0.734762,0.265238,0.619143,0.380857,0.542541,0.457459,0.5,0.5,0.5,0.5,0.10967,0.89033,0.138637,0.861363,0.189129,0.810871,0.301703,0.698297,0.523915,0.476085,0.734432,0.265568,0.858976,0.141024,0.926348,0.073652,0.926348,0.073652
2.663647,0.5,0.5,0.484377,0.515623,0.456612,0.543388,0.38855,0.61145,0.248849,0.751151,0.151085,0.848915,0.112537,0.887463,0.0963831,0.903617,0.0963831,0.903617,0.515623,0.484377,0.5,0.5,0.472159,0.527841,0.403501,0.596499,0.260717,0.739283,0.159279,0.840721,0.118933,0.881067,0.101966,0.898034,0.101966,0.898034,0.543388,0.456612,0.527841,0.472159,0.5,0.5,0.430596,0.569404,0.282769,0.717231,0.174779,0.825221,0.131119,0.868881,0.112637,0.887363,0.112637,0.887363,0.61145,0.38855,0.596499,0.403501,0.569404,0.430596,0.5,0.5,0.342686,0.657314,0.218794,0.781206,0.166356,0.833644,0.143728,0.856272,0.143728,0.856272,0.751151,0.248849,0.739283,0.260717,0.717231,0.282769,0.657314,0.342686,0.5,0.5,0.349473,0.650527,0.276812,0.723188,0.24355,0.75645,0.24355,0.75645,0.848915,0.151085,0.840721,0.159279,0.825221,0.174779,0.781206,0.218794,0.650527,0.349473,0.5,0.5,0.416059,0.583941,0.374735,0.625265,0.374735,0.625265,0.887463,0.112537,0.881067,0.118933,0.868881,0.131119,0.833644,0.166356,0.723188,0.276812,0.583941,0.416059,0.5,0.5,0.456861,0.543139,0.456861,0.543139,0.903617,0.0963831,0.898034,0.101966,0.887363,0.112637,0.856272,0.143728,0.75645,0.24355,0.625265,0.374735,0.543139,0.456861,0.5,0.5,0.5,0.5,0.903617,0.0963831,0.898034,0.101966,0.887363,0.112637,0.856272,0.143728,0.75645,0.24355,0.625265,0.374735,0.543139,0.456861,0.5,0.5,0.5,0.5,0.0946176,0.905382,0.118086,0.881914,0.159937,0.840063,0.264839,0.735161,0.509372,0.490628,0.742645,0.257355,0.869903,0.130097,0.934847,0.0651529,0.934847,0.0651529
2.804409,0.5,0.5,0.487103,0.512897,0.463803,0.536197,0.398892,0.601108,0.239559,0.760441,0.13218,0.86782,0.0958424,0.904158,0.081783,0.918217,0.081783,0.918217,0.512897,0.487103,0.5,0.5,0.476657,0.523343,0.411327,0.588673,0.249085,0.750915,0.138212,0.861788,0.100408,0.899592,0.0857425,0.914258,0.0857425,0.914258,0.536197,0.463803,0.523343,0.476657,0.5,0.5,0.434125,0.565875,0.266969,0.733031,0.149722,0.850278,0.109169,0.890831,0.0933565,0.906644,0.0933565,0.906644,0.601108,0.398892,0.588673,0.411327,0.565875,0.434125,0.5,0.5,0.321908,0.678092,0.186678,0.813322,0.137737,0.862263,0.118336,0.881664,0.118336,0.881664,0.760441,0.239559,0.750915,0.249085,0.733031,0.266969,0.678092,0.321908,0.5,0.5,0.325914,0.674086,0.251769,0.748231,0.220412,0.779588,0.220412,0.779588,0.86782,0.13218,0.861788,0.138212,0.850278,0.149722,0.813322,0.186678,0.674086,0.325914,0.5,0.5,0.41036,0.58964,0.368992,0.631008,0.368992,0.631008,0.904158,0.0958424,0.899592,0.100408,0.890831,0.109169,0.862263,0.137737,0.748231,0.251769,0.58964,0.41036,0.5,0.5,0.456593,0.543407,0.456593,0.543407,0.918217,0.081783,0.914258,0.0857425,0.906644,0.0933565,0.881664,0.118336,0.779588,0.220412,0.631008,0.368992,0.543407,0.456593,0.5,0.5,0.5,0.5,0.918217,0.081783,0.914258,0.0857425,0.906644,0.0933565,0.881664,0.118336,0.779588,0.220412,0.631008,0.368992,0.543407,0.456593,0.5,0.5,0.5,0.5,0.0805701,0.91943,0.0989699,0.90103,0.132289,0.867711,0.226798,0.773202,0.492456,0.507544,0.751593,0.248407,0.880845,0.119155,0.942914,0.0570864,0.942914,0.0570864
2.956926,0.5,0.5,0.48971,0.51029,0.470946,0.529054,0.410878,0.589122,0.231937,0.768063,0.113895,0.886105,0.0803727,0.919627,0.0684343,0.931566,0.0684343,0.931566,0.51029,0.48971,0.5,0.5,0.481213,0.518787,0.420877,0.579123,0.23935,0.76065,0.118116,0.881884,0.0834683,0.916532,0.0711056,0.928894,0.0711056,0.928894,0.529054,0.470946,0.518787,0.481213,0.5,0.5,0.439304,0.560696,0.253305,0.746695,0.126175,0.873825,0.0894031,0.910597,0.0762345,0.923766,0.0762345,0.923766,0.589122,0.410878,0.579123,0.420877,0.560696,0.439304,0.5,0.5,0.302152,0.697848,0.155615,0.844385,0.111357,0.888643,0.0952929,0.904707,0.0952929,0.904707,0.768063,0.231937,0.76065,0.23935,0.746695,0.253305,0.697848,0.302152,0.5,0.5,0.298563,0.701437,0.224456,0.775544,0.195669,0.804331,0.195669,0.804331,0.886105,0.113895,0.881884,0.118116,0.873825,0.126175,0.844385,0.155615,0.701437,0.298563,0.5,0.5,0.404745,0.595255,0.363679,0.636321,0.363679,0.636321,0.919627,0.0803727,0.916532,0.0834683,0.910597,0.0894031,0.888643,0.111357,0.775544,0.224456,0.595255,0.404745,0.5,0.5,0.456684,0.543316,0.456684,0.543316,0.931566,0.0684343,0.928894,0.0711056,0.923766,0.0762345,0.904707,0.0952929,0.804331,0.195669,0.636321,0.363679,0.543316,0.456684,0.5,0.5,0.5,0.5,0.931566,0.0684343,0.928894,0.0711056,0.923766,0.0762345,0.904707,0.0952929,0.804331,0.195669,0.636321,0.363679,0.543316,0.456684,0.5,0.5,0.5,0.5,0.0675806,0.932419,0.0815018,0.918498,0.106928,0.893072,0.189443,0.810557,0.472531,0.527469,0.761395,0.238605,0.891847,0.108153,0.95059,0.0494102,0.95059,0.0494102
3.124109,0.5,0.5,0.492087,0.507913,0.477605,0.522395,0.423326,0.576674,0.226485,0.773515,0.0963638,0.903636,0.0661908,0.933809,0.0563357,0.943664,0.0563357,0.943664,0.507913,0.492087,0.5,0.5,0.485507,0.514493,0.431071,0.568929,0.232079,0.767921,0.0991556,0.900844,0.0681743,0.931826,0.0580423,0.941958,0.0580423,0.941958,0.522395,0.477605,0.514493,0.485507,0.5,0.5,0.445345,0.554655,0.242573,0.757427,0.104457,0.895543,0.0719516,0.928048,0.0612951,0.938705,0.0612951,0.938705,0.576674,0.423326,0.568929,0.431071,0.554655,0.445345,0.5,0.5,0.285136,0.714864,0.126844,0.873156,0.0880569,0.911943,0.0752083,0.924792,0.0752083,0.924792,0.773515,0.226485,0.767921,0.232079,0.757427,0.242573,0.714864,0.285136,0.5,0.5,0.266974,0.733026,0.194902,0.805098,0.169359,0.830641,0.169359,0.830641,0.903636,0.0963638,0.900844,0.0991556,0.895543,0.104457,0.873156,0.126844,0.733026,0.266974,0.5,0.5,0.399287,0.600713,0.358899,0.641101,0.358899,0.641101,0.933809,0.0661908,0.931826,0.0681743,0.928048,0.0719516,0.911943,0.0880569,0.805098,0.194902,0.600713,0.399287,0.5,0.5,0.457177,0.542823,0.457177,0.542823,0.943664,0.0563357,0.941958,0.0580423,0.938705,0.0612951,0.924792,0.0752083,0.830641,0.169359,0.641101,0.358899,0.542823,0.457177,0.5,0.5,0.5,0.5,0.943664,0.0563357,0.941958,0.0580423,0.938705,0.0612951,0.924792,0.0752083,0.830641,0.169359,0.641101,0.358899,0.542823,0.457177,0.5,0.5,0.5,0.5,0.0557175,0.944283,0.0658495,0.93415,0.0844107,0.915589,0.154669,0.845331,0.448874,0.551126,0.772177,0.227823,0.902913,0.097087,0.957876,0.0421237,0.957876,0.0421237
3.308684,0.5,0.5,0.49415,0.50585,0.483454,0.516546,0.435131,0.564869,0.223759,0.776241,0.0798053,0.920195,0.0534057,0.946594,0.045527,0.954473,0.045527,0.954473,0.50585,0.49415,0.5,0.5,0.4893,0.5107,0.440892,0.559108,0.22785,0.77215,0.0815408,0.918459,0.0546012,0.945399,0.0465548,0.953445,0.0465548,0.953445,0.516546,0.483454,0.5107,0.4893,0.5,0.5,0.451469,0.548531,0.235469,0.764531,0.0848046,0.915195,0.0568534,0.943147,0.0484921,0.951508,0.0484921,0.951508,0.564869,0.435131,0.559108,0.440892,0.548531,0.451469,0.5,0.5,0.272307,0.727693,0.101192,0.898808,0.0682424,0.931758,0.0583096,0.94169,0.0583096,0.94169,0.776241,0.223759,0.77215,0.22785,0.764531,0.235469,0.727693,0.272307,0.5,0.5,0.231279,0.768721,0.163685,0.836315,0.141978,0.858022,0.141978,0.858022,0.920195,0.0798053,0.918459,0.0815408,0.915195,0.0848046,0.898808,0.101192,0.768721,0.231279,0.5,0.5,0.394137,0.605863,0.354834,0.645166,0.354834,0.645166,0.946594,0.0534057,0.945399,0.0546012,0.943147,0.0568534,0.931758,0.0682424,0.836315,0.163685,0.605863,0.394137,0.5,0.5,0.458123,0.541877,0.458123,0.541877,0.954473,0.045527,0.953445,0.0465548,0.951508,0.0484921,0.94169,0.0583096,0.858022,0.141978,0.645166,0.354834,0.541877,0.458123,0.5,0.5,0.5,0.5,0.954473,0.045527,0.953445,0.0465548,0.951508,0.0484921,0.94169,0.0583096,0.858022,0.141978,0.645166,0.354834,0.541877,0.458123,0.5,0.5,0.5,0.5,0.0450686,0.954931,0.0521415,0.947858,0.0650789,0.934921,0.123935,0.876065,0.421016,0.578984,0.784032,0.215968,0.91398,0.0860202,0.964726,0.0352745,0.964726,0.0352745
3.513083,0.5,0.5,0.495851,0.504149,0.488303,0.511697,0.445561,0.554439,0.224115,0.775885,0.0645008,0.935499,0.0421347,0.957865,0.0360566,0.963943,0.0360566,0.963943,0.504149,0.495851,0.5,0.5,0.492451,0.507549,0.449664,0.550336,0.227015,0.772985,0.0655095,0.934491,0.0428097,0.95719,0.0366379,0.963362,0.0366379,0.963362,0.511697,0.488303,0.507549,0.492451,0.5,0.5,0.457149,0.542851,0.232358,0.767642,0.0673827,0.932617,0.0440644,0.955936,0.0377189,0.962281,0.0377189,0.962281,0.554439,0.445561,0.550336,0.449664,0.542851,0.457149,0.5,0.5,0.264401,0.735599,0.0790169,0.920983,0.0518965,0.948103,0.0444756,0.955524,0.0444756,0.955524,0.775885,0.224115,0.772985,0.227015,0.767642,0.232358,0.735599,0.264401,0.5,0.5,0.1927,0.8073,0.13216,0.86784,0.11465,0.88535,0.11465,0.88535,0.935499,0.0645008,0.934491,0.0655095,0.932617,0.0673827,0.920983,0.0790169,0.8073,0.1927,0.5,0.5,0.389496,0.610504,0.351708,0.648292,0.351708,0.648292,0.957865,0.0421347,0.95719,0.0428097,0.955936,0.0440644,0.948103,0.0518965,0.86784,0.13216,0.610504,0.389496,0.5,0.5,0.459562,0.540438,0.459562,0.540438,0.963943,0.0360566,0.963362,0.0366379,0.962281,0.0377189,0.955524,0.0444756,0.88535,0.11465,0.648292,0.351708,0.540438,0.459562,0.5,0.5,0.5,0.5,0.963943,0.0360566,0.963362,0.0366379,0.962281,0.0377189,0.955524,0.0444756,0.88535,0.11465,0.648292,0.351708,0.540438,0.459562,0.5,0.5,0.5,0.5,0.0357134,0.964287,0.0404374,0.959563,0.0490338,0.950966,0.0979445,0.902055,0.389204,0.610796,0.796983,0.203017,0.924914,0.0750862,0.971058,0.0289423,0.971058,0.0289423
3.739727,0.5,0.5,0.497184,0.502816,0.492104,0.507896,0.454366,0.545634,0.227445,0.772555,0.050727,0.949273,0.0324475,0.967553,0.0279389,0.972061,0.0279389,0.972061,0.502816,0.497184,0.5,0.5,0.494919,0.505081,0.457159,0.542841,0.22943,0.77057,0.051272,0.948728,0.0328029,0.967197,0.0282464,0.971754,0.0282464,0.971754,0.507896,0.492104,0.505081,0.494919,0.5,0.5,0.462208,0.537792,0.233043,0.766957,0.0522698,0.94773,0.0334539,0.966546,0.0288097,0.97119,0.0288097,0.97119,0.545634,0.454366,0.542841,0.457159,0.537792,0.462208,0.5,0.5,0.261198,0.738802,0.060302,0.939698,0.0387129,0.961287,0.0333637,0.966636,0.0333637,0.966636,0.772555,0.227445,0.77057,0.22943,0.766957,0.233043,0.738802,0.261198,0.5,0.5,0.153626,0.846374,0.102261,0.897739,0.0889437,0.911056,0.0889437,0.911056,0.949273,0.050727,0.948728,0.051272,0.94773,0.0522698,0.939698,0.060302,0.846374,0.153626,0.5,0.5,0.385585,0.614415,0.349745,0.650255,0.349745,0.650255,0.967553,0.0324475,0.967197,0.0328029,0.966546,0.0334539,0.961287,0.0387129,0.897739,0.102261,0.614415,0.385585,0.5,0.5,0.461513,0.538487,0.461513,0.538487,0.972061,0.0279389,0.971754,0.0282464,0.97119,0.0288097,0.966636,0.0333637,0.911056,0.0889437,0.650255,0.349745,0.538487,0.461513,0.5,0.5,0.5,0.5,0.972061,0.0279389,0.971754,0.0282464,0.97119,0.0288097,0.966636,0.0333637,0.911056,0.0889437,0.650255,0.349745,0.538487,0.461513,0.5,0.5,0.5,0.5,0.0276843,0.972316,0.0306958,0.969304,0.0361309,0.963869,0.0766306,0.923369,0.354659,0.645341,0.810961,0.189039,0.935544,0.0644559,0.976791,0.0232091,0.976791,0.0232091
3.991441,0.5,0.5,0.498178,0.501822,0.494925,0.505075,0.46168,0.53832,0.233112,0.766888,0.0386929,0.961307,0.0243385,0.975662,0.0211361,0.978864,0.0211361,0.978864,0.501822,0.498178,0.5,0.5,0.496747,0.503253,0.463492,0.536508,0.234418,0.765582,0.038965,0.961035,0.0245122,0.975488,0.0212874,0.978713,0.0212874,0.978713,0.505075,0.494925,0.503253,0.496747,0.5,0.5,0.466729,0.533271,0.236761,0.763239,0.0394552,0.960545,0.0248252,0.975175,0.0215602,0.97844,0.0215602,0.97844,0.53832,0.46168,0.536508,0.463492,0.533271,0.466729,0.5,0.5,0.261683,0.738317,0.0448281,0.955172,0.0282645,0.971735,0.0245585,0.975441,0.0245585,0.975441,0.766888,0.233112,0.765582,0.234418,0.763239,0.236761,0.738317,0.261683,0.5,0.5,0.116931,0.883069,0.0758416,0.924158,0.0663232,0.933677,0.0663232,0.933677,0.961307,0.0386929,0.961035,0.038965,0.960545,0.0394552,0.955172,0.0448281,0.883069,0.116931,0.5,0.5,0.382625,0.617375,0.349151,0.650849,0.349151,0.650849,0.975662,0.0243385,0.975488,0.0245122,0.975175,0.0248252,0.971735,0.0282645,0.924158,0.0758416,0.617375,0.382625,0.5,0.5,0.463974,0.536026,0.463974,0.536026,0.978864,0.0211361,0.978713,0.0212874,0.97844,0.0215602,0.975441,0.0245585,0.933677,0.0663232,0.650849,0.349151,0.536026,0.463974,0.5,0.5,0.5,0.5,0.978864,0.0211361,0.978713,0.0212874,0.97844,0.0215602,0.975441,0.0245585,0.933677,0.0663232,0.650849,0.349151,0.536026,0.463974,0.5,0.5,0.5,0.5,0.0209532,0.979047,0.0227795,0.97722,0.0260394,0.973961,0.0594308,0.940569,0.319297,0.680703,0.825835,0.174165,0.945696,0.0543039,0.981862,0.018138,0.981862,0.018138
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