
from math import ceil as MC
import matplotlib
from matplotlib.animation import FuncAnimation as FA
import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from random import sample as RS
import seaborn as sns
from time import time as TT


#Initialize Territory Dictionary.
#(R0, C0) : [(R0, C0), ...].
#Player R0, C0 holds the cells in the list.

#Initialize Common Neighbors Dictionary.
#(R0, C0) : [(R0, C1), (R1, C0),...].
#Player R0, C0 is neighbors with cells in the list.
def initializeTerritoryAndCommonEdge(N) :
    
    #Get the neighbors, if they exist.  Count each neighbor once.
    def getNeighbors(r, c) :
        
        neighbors = set([])
        
        #Left.
        z=0 if c == 0 else neighbors.add((r, c-1))
        
        #Top
        z=0 if r == 0 else neighbors.add((r-1, c))
        
        #Right.
        z=0 if c == N-1 else neighbors.add((r, c+1))
        
        #Bottom
        z=0 if r == N-1 else neighbors.add((r+1, c))
        
        return(neighbors)
    
    #Territory held.
    T = {}
    #Neighbors.
    CE = {} 
    
    for r in range(N):
        for c in range(N):
            #Every N^2 player is named by its initial cell territory.
            T[(r, c)] = {(r,c)}
            CE[(r, c)] = getNeighbors(r, c)
    
    return(T, CE)





#Append the P_k's territory to that of P_j.
#Remove P_k.
def updateTerritory(j, k, T) :

    T[j] = T[j] | T[k]
    del T[k]

    return(T)





#1) For each non-winner neighbor of the loser P_k, replace P_k with P_j.
#2) Append the P_k's neighbors to that of P_j.  Remove P_k and P_j from that list.
#3) Remove P_k.
def updateCommonEdge(j, k, CE) :
    
    #Neighbors of k.
    temp = CE[k]
    
    #1)
    #Non-winner neighbors of 'Pk'.
    for n in temp :
        
        if n == j :
            pass 
        
        else :
            #Neighbors of that neighbor.
            ce_n = CE[n]
            #Remove 'Pk', add 'Pj'.
            ce_n.remove(k)
            ce_n.add(j)
            CE[n] = ce_n
      
    #2)
    CE[j] = CE[j] | CE[k]
    CE[j].remove(k)
    CE[j].remove(j)
    
    #3)
    del CE[k]
    
    return(CE)




#Play!
def theFloor(N) :
    
    #Initialize
    T, CE = initializeTerritoryAndCommonEdge(N)

    #Play
    Round = N*N
    
    #Eliminate one player each round.  THERE CAN BE ONLY ONE!
    while Round > 1 :
        
        #Get two players from those players in common_edges.  
        temp = RS(list(CE.keys()), 1)[0]
        #Randomly select winner/loser.
        wl = RS([temp, RS(list(CE[temp]), 1)[0]], 2)
        j = wl[0]
        k = wl[1]

        #Update and continue.
        T = updateTerritory(j, k, T)
        CE = updateCommonEdge(j, k, CE)
        Round -= 1

    return(j)





def monteCarlo(M, N) :

    result = {}
    for m in range(M) :
        n = theFloor(N)
        if n in result.keys():
            result[n] += 1
        else :
            result[n] = 1
    
    for k in result.keys():
        result[k] = round(result[k] / M, 5)
    

    return(result)


results = []
for N in range(2, 26) :

    current = TT()
    result = monteCarlo(1000000, N)
    run = TT()-current

    print(N)
    print("Time : " + str(round(run, 4)))
    #print(result)
    print("")

    results.append(result)

2
Time : 27.4044

3
Time : 74.2042

4
Time : 139.2628

5
Time : 227.411

6
Time : 335.6144

7
Time : 463.6079

8
Time : 615.2201

9
Time : 797.6456

10
Time : 1010.3911

11
Time : 1255.394

12
Time : 1531.1065

13
Time : 1812.2767

14
Time : 2150.4127

15
Time : 2478.8741

16
Time : 2809.1465

17
Time : 3210.6847

18
Time : 3872.341

19
Time : 4402.4093

20
Time : 5028.7635

21
Time : 5614.2806

22
Time : 6443.2651

23
Time : 7158.2499

24
Time : 7927.4967

25
Time : 8793.776


def graphPrep(results) :
    
    def symmetryCleanUp(points, r, div) :
        div_up = 0
        for op in points :
            div_up += r[op]
        div_up = div_up/div
        for op in points :
            r[op] = div_up
        return(r)
    
    #Final output.
    df = pd.DataFrame(columns = ['N', 'X', 'Y', 'P'])
    
    for i, r in enumerate(results):
        N = i+2
        for x in range(MC(N/2)) :
            for y in range(x+1) :
                div_up = 0
                
                #Diagonals, only 4.
                #Center is only 1 but repeated 4 times if N is odd.
                if x == y :
                    r = symmetryCleanUp([(x, x), (x, N-1-x), (N-1-x, N-1-x), (N-1-x, x)], r, 4)
                                
                #Odd vertical and horizontal, only 4.
                elif x == N/2-1/2 :
                    r = symmetryCleanUp([(x, y), (y, x), (x, N-1-y), (N-1-y, x)], r, 4)
                
                #All other points, come in octets.
                else :
                    r = symmetryCleanUp([(x, y), (y, x), (y, N-1-x), (x, N-1-y), (N-1-x, N-1-y),
                                         (N-1-y, N-1-x), (N-1-y, x), (N-1-x, y)], r, 8)
    
        for k in r.keys() :
            df.loc[len(df)] = [i+2, k[0], k[1], r[k]]
    
    df.sort_values(by = ['N', 'X', 'Y'], inplace = True)
    return(df)





#Clear axes.
def clearAx(ax):
    ax.spines["top"].set_visible(False)
    ax.spines["right"].set_visible(False)
    ax.spines["bottom"].set_visible(False)
    ax.spines["left"].set_visible(False)
    ax.set_xticks([])
    ax.set_yticks([])
    return(ax)





def heatMapHelper(df, N, option):
    
    #Plot area is NxN.
    ax = fig.add_subplot(xlim = (-0.5, N-0.5),
                         ylim = (-0.5, N-0.5))

    #Only one value for 2x2
    if N == 2 :
        v = [1/4, 1/4]
        ticks = [1/4]
        labels = ["1/4"]
    
    #Min, Max, and ticks for N>2.
    else :
        v = [1/(N+1)**2, 2/(N+1)**2]
        ticks = [t/(4*(N+1)**2) for t in range(4, 9)]
        #labels =[str(t) + '/' + str(4*(N+1)**2) for t in range(4, 9)]    
    
    #Subset df.
    data = df[df['N'] == N]
    
    heatmap = plt.scatter(x = data['X'],
                          y = data['Y'],
                          c = data['P'],
                          cmap = 'viridis_r',
                          marker = "s",
                          s = 72000*4/N**2,
                          alpha = 0.8,
                          vmin = v[0],
                          vmax = v[1])
                          
    #Title setup.
    ax.set_title("The Floor Probabilities - " + str(N) + 'x' + str(N), fontsize = 24)

    ax = clearAx(ax)
    
    #Borders between cells.
    for i in range(1, N) :
        ax.axhline(y = i-0.5, xmin = 0, xmax = N, c = 'w', lw = 5/N**(1/2))
        ax.axvline(x = i-0.5, ymin = 0, ymax = N, c = 'w', lw = 5/N**(1/2))

    #Print P in each territory
    if option == 'EC' :
        for row in data.iterrows():
            plt.annotate(round(row[1][3], 4),
                         (row[1][1], row[1][2]),
                          c = "k",
                          fontsize = 26,
                          ha = "center",
                          va = "center")
    
    #Colorbar.
    cb = plt.colorbar(heatmap, format = '%.4f')
    cb.set_ticks(ticks)
    #cb.set_ticklabels(labels)
    cb.set_label('Probability of Winning',
                 labelpad = 3,
                 rotation = 90,
                 fontsize = 20)
    cb.ax.tick_params(labelsize = 16)


df = graphPrep(results)
df[df['N'] == 3]


fig = plt.figure(figsize = (12.1, 9.72))
heatMapHelper(df, 3, 'EC')
fig.savefig("2024.12.13EC.png",
            bbox_inches = 'tight')


#Animate 
sns.set()
fig = plt.figure(figsize = (12.1, 9.72))

def animate(i):
    plt.clf()
    heatMapHelper(df, i+2, 'animation')

#Run animation.
anim = FA(fig, animate, frames = 24, interval = 1500)   

#Save animation.
anim.save('2024.12.13.mp4');


for i, r in enumerate(results):
    print("N = " + str(i+2))
    print(r)
    print("")

N = 2
{(1, 1): 0.25, (1, 0): 0.25, (0, 0): 0.25, (0, 1): 0.25}

N = 3
{(0, 0): 0.128965, (1, 0): 0.0993125, (1, 1): 0.08689, (2, 0): 0.128965, (1, 2): 0.0993125, (0, 1): 0.0993125, (0, 2): 0.128965, (2, 2): 0.128965, (2, 1): 0.0993125}

N = 4
{(3, 2): 0.05989374999999998, (3, 1): 0.05989374999999998, (0, 3): 0.0789925, (2, 3): 0.05989374999999998, (3, 0): 0.0789925, (0, 0): 0.0789925, (1, 0): 0.05989374999999998, (1, 2): 0.051225, (0, 1): 0.05989374999999998, (1, 3): 0.05989374999999998, (2, 0): 0.05989374999999998, (2, 2): 0.051225, (3, 3): 0.0789925, (2, 1): 0.051225, (0, 2): 0.05989374999999998, (1, 1): 0.051225}

N = 5
{(4, 4): 0.053875, (3, 2): 0.0334875, (0, 1): 0.04025875, (4, 1): 0.04025875, (0, 2): 0.0395975, (0, 4): 0.053875, (1, 1): 0.0342675, (2, 3): 0.0334875, (4, 0): 0.053875, (2, 0): 0.0395975, (1, 4): 0.04025875, (2, 2): 0.03303, (2, 4): 0.0395975, (2, 1): 0.0334875, (3, 3): 0.0342675, (1, 2): 0.0334875, (1, 3): 0.0342675, (4, 3): 0.04025875, (1, 0): 0.04025875, (3, 1): 0.0342675, (0, 0): 0.053875, (3, 4): 0.04025875, (0, 3): 0.04025875, (4, 2): 0.0395975, (3, 0): 0.04025875}

N = 6
{(0, 0): 0.03909, (2, 4): 0.02391, (2, 0): 0.028301250000000003, (1, 3): 0.02391, (1, 5): 0.029211249999999998, (1, 0): 0.029211249999999998, (3, 0): 0.028301250000000003, (4, 4): 0.024595, (2, 3): 0.0234675, (0, 5): 0.03909, (3, 4): 0.02391, (0, 1): 0.029211249999999998, (0, 3): 0.028301250000000003, (2, 1): 0.02391, (5, 4): 0.029211249999999998, (5, 3): 0.028301250000000003, (5, 2): 0.028301250000000003, (4, 5): 0.029211249999999998, (3, 3): 0.0234675, (1, 4): 0.024595, (4, 2): 0.02391, (3, 2): 0.0234675, (5, 1): 0.029211249999999998, (3, 5): 0.028301250000000003, (1, 1): 0.024595, (5, 0): 0.03909, (5, 5): 0.03909, (2, 2): 0.0234675, (0, 2): 0.028301250000000003, (4, 0): 0.029211249999999998, (1, 2): 0.02391, (4, 1): 0.024595, (0, 4): 0.029211249999999998, (4, 3): 0.02391, (3, 1): 0.02391, (2, 5): 0.028301250000000003}

N = 7
{(6, 4): 0.021376250000000006, (1, 2): 0.018025, (1, 4): 0.018025, (3, 4): 0.0175, (1, 6): 0.022156250000000002, (2, 3): 0.0175, (3, 0): 0.021027499999999998, (4, 6): 0.021376250000000006, (3, 1): 0.017805, (6, 2): 0.021376250000000006, (0, 2): 0.021376250000000006, (0, 6): 0.02996, (2, 0): 0.021376250000000006, (4, 2): 0.0176775, (5, 2): 0.018025, (4, 1): 0.018025, (6, 1): 0.022156250000000002, (2, 6): 0.021376250000000006, (1, 3): 0.017805, (4, 3): 0.0175, (0, 0): 0.02996, (4, 0): 0.021376250000000006, (4, 4): 0.0176775, (3, 6): 0.021027499999999998, (1, 5): 0.018585, (4, 5): 0.018025, (0, 3): 0.021027499999999998, (6, 5): 0.022156250000000002, (6, 3): 0.021027499999999998, (0, 1): 0.022156250000000002, (2, 4): 0.0176775, (5, 5): 0.018585, (1, 0): 0.022156250000000002, (1, 1): 0.018585, (5, 4): 0.018025, (5, 6): 0.022156250000000002, (3, 2): 0.0175, (6, 6): 0.02996, (6, 0): 0.02996, (5, 1): 0.018585, (2, 1): 0.018025, (3, 5): 0.017805, (0, 4): 0.021376250000000006, (0, 5): 0.022156250000000002, (5, 3): 0.017805, (5, 0): 0.022156250000000002, (2, 5): 0.018025, (2, 2): 0.0176775, (3, 3): 0.01731}

N = 8
{(6, 0): 0.01743875, (2, 0): 0.01675125, (7, 4): 0.016562500000000004, (1, 4): 0.013901250000000002, (2, 4): 0.013507500000000002, (1, 7): 0.01743875, (3, 0): 0.016562500000000004, (5, 5): 0.0137975, (7, 0): 0.023465, (6, 3): 0.013901250000000002, (5, 0): 0.01675125, (5, 6): 0.014136250000000001, (4, 7): 0.016562500000000004, (0, 3): 0.016562500000000004, (7, 2): 0.01675125, (3, 4): 0.0134425, (4, 6): 0.013901250000000002, (1, 3): 0.013901250000000002, (4, 3): 0.0134425, (7, 6): 0.01743875, (5, 3): 0.013507500000000002, (0, 5): 0.01675125, (4, 0): 0.016562500000000004, (3, 3): 0.0134425, (0, 7): 0.023465, (5, 7): 0.01675125, (4, 1): 0.013901250000000002, (6, 6): 0.01471, (3, 5): 0.013507500000000002, (0, 1): 0.01743875, (7, 7): 0.023465, (2, 1): 0.014136250000000001, (1, 5): 0.014136250000000001, (7, 3): 0.016562500000000004, (3, 2): 0.013507500000000002, (2, 6): 0.014136250000000001, (0, 4): 0.016562500000000004, (1, 1): 0.01471, (3, 7): 0.016562500000000004, (4, 4): 0.0134425, (0, 0): 0.023465, (4, 5): 0.013507500000000002, (5, 2): 0.0137975, (2, 2): 0.0137975, (6, 7): 0.01743875, (6, 1): 0.01471, (3, 1): 0.013901250000000002, (5, 1): 0.014136250000000001, (7, 5): 0.01675125, (1, 2): 0.014136250000000001, (6, 2): 0.014136250000000001, (2, 5): 0.0137975, (4, 2): 0.013507500000000002, (1, 0): 0.01743875, (5, 4): 0.013507500000000002, (2, 7): 0.01675125, (1, 6): 0.01471, (0, 6): 0.01743875, (6, 4): 0.013901250000000002, (6, 5): 0.014136250000000001, (2, 3): 0.013507500000000002, (7, 1): 0.01743875, (3, 6): 0.013901250000000002, (0, 2): 0.01675125}

N = 9
{(1, 4): 0.0111275, (5, 8): 0.013251249999999996, (0, 0): 0.018985000000000002, (7, 6): 0.011393749999999998, (0, 1): 0.014126250000000003, (4, 6): 0.010865, (8, 0): 0.018985000000000002, (7, 3): 0.011175000000000001, (4, 8): 0.0131375, (4, 5): 0.0107325, (0, 3): 0.013251249999999996, (3, 7): 0.011175000000000001, (2, 4): 0.010865, (3, 6): 0.0108525, (0, 8): 0.018985000000000002, (4, 2): 0.010865, (1, 8): 0.014126250000000003, (2, 5): 0.0108525, (0, 5): 0.013251249999999996, (4, 3): 0.0107325, (8, 7): 0.014126250000000003, (2, 8): 0.013598749999999996, (1, 2): 0.011393749999999998, (8, 8): 0.018985000000000002, (3, 5): 0.01069, (8, 5): 0.013251249999999996, (2, 2): 0.0110675, (7, 7): 0.011922499999999999, (3, 8): 0.013251249999999996, (4, 0): 0.0131375, (1, 6): 0.011393749999999998, (6, 6): 0.0110675, (4, 7): 0.0111275, (6, 8): 0.013598749999999996, (1, 0): 0.014126250000000003, (8, 3): 0.013251249999999996, (1, 1): 0.011922499999999999, (7, 2): 0.011393749999999998, (7, 1): 0.011922499999999999, (3, 0): 0.013251249999999996, (6, 4): 0.010865, (8, 1): 0.014126250000000003, (5, 2): 0.0108525, (1, 7): 0.011922499999999999, (5, 1): 0.011175000000000001, (0, 4): 0.0131375, (0, 2): 0.013598749999999996, (0, 6): 0.013598749999999996, (7, 8): 0.014126250000000003, (7, 5): 0.011175000000000001, (7, 0): 0.014126250000000003, (5, 6): 0.0108525, (5, 5): 0.01069, (6, 7): 0.011393749999999998, (2, 0): 0.013598749999999996, (0, 7): 0.014126250000000003, (3, 1): 0.011175000000000001, (2, 1): 0.011393749999999998, (1, 3): 0.011175000000000001, (6, 0): 0.013598749999999996, (4, 4): 0.01068, (2, 3): 0.0108525, (8, 6): 0.013598749999999996, (2, 7): 0.011393749999999998, (6, 1): 0.011393749999999998, (5, 3): 0.01069, (6, 2): 0.0110675, (5, 4): 0.0107325, (6, 3): 0.0108525, (6, 5): 0.0108525, (8, 4): 0.0131375, (2, 6): 0.0110675, (3, 4): 0.0107325, (3, 2): 0.0108525, (1, 5): 0.011175000000000001, (8, 2): 0.013598749999999996, (7, 4): 0.0111275, (3, 3): 0.01069, (5, 7): 0.011175000000000001, (5, 0): 0.013251249999999996, (4, 1): 0.0111275}

N = 10
{(8, 9): 0.0117125, (9, 5): 0.01076875, (7, 6): 0.008945, (8, 7): 0.009412500000000002, (8, 5): 0.009141250000000002, (4, 8): 0.009141250000000002, (9, 1): 0.0117125, (6, 0): 0.010933749999999999, (1, 5): 0.009141250000000002, (9, 4): 0.01076875, (4, 4): 0.008667500000000002, (5, 9): 0.01076875, (7, 7): 0.009035, (6, 2): 0.008945, (3, 2): 0.008945, (1, 2): 0.009412500000000002, (3, 9): 0.010933749999999999, (5, 6): 0.00879625, (2, 6): 0.008945, (8, 1): 0.009802499999999999, (7, 5): 0.008925, (5, 1): 0.009141250000000002, (0, 9): 0.0157, (1, 1): 0.009802499999999999, (9, 0): 0.0157, (3, 5): 0.00879625, (3, 3): 0.00878, (5, 3): 0.00879625, (4, 2): 0.008925, (8, 2): 0.009412500000000002, (5, 8): 0.009141250000000002, (6, 1): 0.009165, (4, 7): 0.008925, (6, 3): 0.00878, (0, 3): 0.010933749999999999, (2, 8): 0.009412500000000002, (1, 8): 0.009802499999999999, (1, 4): 0.009141250000000002, (3, 1): 0.009165, (4, 5): 0.008667500000000002, (3, 7): 0.008945, (0, 0): 0.0157, (1, 3): 0.009165, (9, 2): 0.011211250000000002, (5, 0): 0.01076875, (9, 9): 0.0157, (1, 9): 0.0117125, (0, 6): 0.010933749999999999, (2, 5): 0.008925, (4, 3): 0.00879625, (9, 8): 0.0117125, (6, 6): 0.00878, (6, 4): 0.00879625, (0, 8): 0.0117125, (2, 9): 0.011211250000000002, (3, 8): 0.009165, (0, 5): 0.01076875, (7, 2): 0.009035, (6, 8): 0.009165, (2, 2): 0.009035, (4, 1): 0.009141250000000002, (7, 1): 0.009412500000000002, (0, 4): 0.01076875, (4, 6): 0.00879625, (0, 7): 0.011211250000000002, (3, 0): 0.010933749999999999, (8, 8): 0.009802499999999999, (5, 4): 0.008667500000000002, (2, 3): 0.008945, (8, 4): 0.009141250000000002, (6, 7): 0.008945, (9, 6): 0.010933749999999999, (9, 3): 0.010933749999999999, (7, 4): 0.008925, (0, 2): 0.011211250000000002, (3, 6): 0.00878, (8, 6): 0.009165, (2, 7): 0.009035, (7, 3): 0.008945, (7, 0): 0.011211250000000002, (7, 9): 0.011211250000000002, (8, 3): 0.009165, (0, 1): 0.0117125, (4, 0): 0.01076875, (5, 7): 0.008925, (6, 9): 0.010933749999999999, (2, 4): 0.008925, (9, 7): 0.011211250000000002, (1, 0): 0.0117125, (2, 1): 0.009412500000000002, (1, 7): 0.009412500000000002, (8, 0): 0.0117125, (6, 5): 0.00879625, (5, 5): 0.008667500000000002, (5, 2): 0.008925, (7, 8): 0.009412500000000002, (1, 6): 0.009165, (4, 9): 0.01076875, (3, 4): 0.00879625, (2, 0): 0.011211250000000002}

N = 11
{(2, 5): 0.0073325000000000005, (3, 10): 0.009205, (8, 8): 0.0076124999999999995, (10, 6): 0.009073749999999998, (7, 7): 0.0073549999999999996, (5, 5): 0.00715, (1, 5): 0.0075875, (0, 5): 0.0089, (5, 10): 0.0089, (1, 8): 0.007963750000000004, (10, 10): 0.0132625, (6, 0): 0.009073749999999998, (8, 7): 0.0074875, (9, 6): 0.00766125, (4, 4): 0.007210000000000001, (5, 1): 0.0075875, (4, 10): 0.009073749999999998, (1, 2): 0.007963750000000004, (2, 0): 0.00939375, (10, 1): 0.009834999999999998, (3, 2): 0.0074875, (6, 2): 0.0074262500000000006, (0, 0): 0.0132625, (7, 0): 0.009205, (0, 4): 0.009073749999999998, (9, 7): 0.0077625, (6, 5): 0.0071775, (8, 2): 0.0076124999999999995, (8, 9): 0.007963750000000004, (4, 0): 0.009073749999999998, (8, 5): 0.0073325000000000005, (1, 3): 0.0077625, (2, 6): 0.0074262500000000006, (10, 2): 0.00939375, (5, 4): 0.0071775, (4, 3): 0.0072775, (7, 4): 0.0072775, (4, 9): 0.00766125, (10, 8): 0.00939375, (9, 0): 0.009834999999999998, (7, 1): 0.0077625, (3, 4): 0.0072775, (9, 4): 0.00766125, (0, 6): 0.009073749999999998, (0, 10): 0.0132625, (0, 7): 0.009205, (3, 6): 0.0072775, (8, 10): 0.00939375, (2, 9): 0.007963750000000004, (5, 2): 0.0073325000000000005, (10, 4): 0.009073749999999998, (0, 9): 0.009834999999999998, (2, 10): 0.00939375, (2, 3): 0.0074875, (6, 9): 0.00766125, (0, 8): 0.00939375, (8, 3): 0.0074875, (4, 1): 0.00766125, (7, 5): 0.0072900000000000005, (5, 9): 0.0075875, (1, 4): 0.00766125, (2, 2): 0.0076124999999999995, (3, 1): 0.0077625, (10, 5): 0.0089, (10, 9): 0.009834999999999998, (7, 6): 0.0072775, (0, 1): 0.009834999999999998, (9, 1): 0.0083125, (8, 0): 0.00939375, (6, 6): 0.007210000000000001, (6, 3): 0.0072775, (4, 5): 0.0071775, (4, 6): 0.007210000000000001, (5, 7): 0.0072900000000000005, (5, 6): 0.0071775, (3, 9): 0.0077625, (5, 8): 0.0073325000000000005, (4, 2): 0.0074262500000000006, (3, 5): 0.0072900000000000005, (2, 4): 0.0074262500000000006, (9, 2): 0.007963750000000004, (6, 10): 0.009073749999999998, (6, 1): 0.00766125, (4, 7): 0.0072775, (3, 3): 0.0073549999999999996, (6, 8): 0.0074262500000000006, (3, 8): 0.0074875, (8, 4): 0.0074262500000000006, (2, 7): 0.0074875, (7, 8): 0.0074875, (1, 0): 0.009834999999999998, (1, 7): 0.0077625, (5, 3): 0.0072900000000000005, (1, 10): 0.009834999999999998, (1, 1): 0.0083125, (7, 3): 0.0073549999999999996, (9, 5): 0.0075875, (5, 0): 0.0089, (9, 3): 0.0077625, (3, 0): 0.009205, (6, 4): 0.007210000000000001, (7, 9): 0.0077625, (10, 7): 0.009205, (10, 0): 0.0132625, (7, 2): 0.0074875, (7, 10): 0.009205, (2, 8): 0.0076124999999999995, (0, 2): 0.00939375, (10, 3): 0.009205, (0, 3): 0.009205, (1, 6): 0.00766125, (4, 8): 0.0074262500000000006, (3, 7): 0.0073549999999999996, (8, 6): 0.0074262500000000006, (9, 8): 0.007963750000000004, (8, 1): 0.007963750000000004, (9, 9): 0.0083125, (1, 9): 0.0083125, (9, 10): 0.009834999999999998, (2, 1): 0.007963750000000004, (6, 7): 0.0072775}

N = 12
{(1, 5): 0.0064087499999999995, (10, 3): 0.006625, (10, 5): 0.0064087499999999995, (4, 3): 0.00618875, (1, 4): 0.0064975000000000015, (6, 9): 0.006254999999999998, (5, 0): 0.007645, (8, 11): 0.007878750000000002, (3, 6): 0.00616875, (11, 1): 0.00844375, (5, 5): 0.005997499999999999, (3, 11): 0.007878750000000002, (3, 0): 0.007878750000000002, (9, 1): 0.006738750000000001, (10, 10): 0.007127499999999999, (9, 10): 0.006738750000000001, (6, 10): 0.0064087499999999995, (1, 2): 0.006738750000000001, (7, 8): 0.00618875, (8, 8): 0.006265, (11, 3): 0.007878750000000002, (6, 11): 0.007645, (0, 3): 0.007878750000000002, (1, 9): 0.006738750000000001, (1, 11): 0.00844375, (0, 0): 0.011365, (6, 8): 0.00616875, (10, 0): 0.00844375, (9, 4): 0.0062699999999999995, (8, 7): 0.00618875, (10, 6): 0.0064087499999999995, (11, 9): 0.008005, (7, 11): 0.0077575, (3, 2): 0.0063775, (5, 7): 0.0060750000000000005, (7, 9): 0.0062699999999999995, (0, 11): 0.011365, (11, 4): 0.0077575, (0, 7): 0.0077575, (8, 5): 0.00616875, (3, 7): 0.00618875, (6, 3): 0.00616875, (0, 6): 0.007645, (6, 4): 0.0060750000000000005, (4, 0): 0.0077575, (4, 6): 0.0060750000000000005, (2, 2): 0.006465, (6, 7): 0.0060750000000000005, (9, 8): 0.0063775, (8, 10): 0.006625, (8, 2): 0.0063775, (11, 8): 0.007878750000000002, (7, 1): 0.0064975000000000015, (0, 4): 0.0077575, (8, 4): 0.00618875, (1, 1): 0.007127499999999999, (9, 11): 0.008005, (4, 5): 0.0060750000000000005, (10, 4): 0.0064975000000000015, (11, 6): 0.007645, (9, 9): 0.006465, (5, 10): 0.0064087499999999995, (5, 1): 0.0064087499999999995, (2, 10): 0.006738750000000001, (9, 6): 0.006254999999999998, (5, 8): 0.00616875, (4, 7): 0.006115, (10, 8): 0.006625, (11, 2): 0.008005, (2, 6): 0.006254999999999998, (8, 6): 0.00616875, (4, 9): 0.0062699999999999995, (8, 0): 0.007878750000000002, (2, 7): 0.0062699999999999995, (2, 9): 0.006465, (3, 1): 0.006625, (0, 8): 0.007878750000000002, (0, 1): 0.00844375, (0, 2): 0.008005, (6, 1): 0.0064087499999999995, (11, 7): 0.0077575, (9, 0): 0.008005, (11, 10): 0.00844375, (10, 11): 0.00844375, (2, 5): 0.006254999999999998, (11, 0): 0.011365, (4, 10): 0.0064975000000000015, (10, 1): 0.007127499999999999, (9, 5): 0.006254999999999998, (3, 5): 0.00616875, (9, 3): 0.0063775, (5, 6): 0.005997499999999999, (10, 2): 0.006738750000000001, (1, 7): 0.0064975000000000015, (5, 3): 0.00616875, (6, 5): 0.005997499999999999, (0, 5): 0.007645, (11, 11): 0.011365, (1, 6): 0.0064087499999999995, (8, 1): 0.006625, (2, 4): 0.0062699999999999995, (6, 0): 0.007645, (2, 8): 0.0063775, (7, 0): 0.0077575, (3, 4): 0.00618875, (4, 4): 0.006115, (3, 3): 0.006265, (6, 6): 0.005997499999999999, (1, 0): 0.00844375, (2, 3): 0.0063775, (0, 9): 0.008005, (5, 4): 0.0060750000000000005, (4, 1): 0.0064975000000000015, (6, 2): 0.006254999999999998, (4, 2): 0.0062699999999999995, (8, 9): 0.0063775, (5, 2): 0.006254999999999998, (11, 5): 0.007645, (7, 5): 0.0060750000000000005, (2, 0): 0.008005, (5, 11): 0.007645, (9, 7): 0.0062699999999999995, (8, 3): 0.006265, (1, 10): 0.007127499999999999, (7, 6): 0.0060750000000000005, (7, 4): 0.006115, (3, 10): 0.006625, (1, 3): 0.006625, (3, 9): 0.0063775, (5, 9): 0.006254999999999998, (7, 7): 0.006115, (0, 10): 0.00844375, (10, 7): 0.0064975000000000015, (7, 10): 0.0064975000000000015, (2, 11): 0.008005, (4, 8): 0.00618875, (1, 8): 0.006625, (2, 1): 0.006738750000000001, (10, 9): 0.006738750000000001, (7, 3): 0.00618875, (9, 2): 0.006465, (7, 2): 0.0062699999999999995, (3, 8): 0.006265, (4, 11): 0.0077575}

N = 13
{(12, 3): 0.006789999999999999, (8, 1): 0.00561625, (10, 9): 0.0055025, (1, 3): 0.0056625, (3, 7): 0.005277499999999999, (2, 6): 0.005392500000000001, (7, 12): 0.0065775, (7, 2): 0.005366249999999998, (3, 5): 0.005277499999999999, (5, 6): 0.0052025000000000005, (1, 7): 0.005518750000000001, (5, 9): 0.005277499999999999, (11, 8): 0.00561625, (0, 2): 0.006971249999999999, (12, 9): 0.006789999999999999, (4, 11): 0.00561625, (8, 11): 0.00561625, (0, 6): 0.006545, (8, 3): 0.005342500000000001, (7, 10): 0.005366249999999998, (6, 8): 0.00525, (4, 1): 0.00561625, (0, 9): 0.006789999999999999, (0, 1): 0.0072525, (2, 1): 0.0058137499999999995, (10, 3): 0.0055025, (3, 2): 0.0055025, (9, 0): 0.006789999999999999, (3, 9): 0.0054600000000000004, (0, 10): 0.006971249999999999, (7, 0): 0.0065775, (11, 1): 0.006082499999999999, (1, 9): 0.0056625, (12, 0): 0.00986, (2, 4): 0.005386250000000001, (7, 3): 0.005277499999999999, (10, 4): 0.005386250000000001, (12, 10): 0.006971249999999999, (12, 7): 0.0065775, (11, 10): 0.0058137499999999995, (8, 5): 0.005279999999999999, (7, 4): 0.005279999999999999, (1, 4): 0.00561625, (4, 10): 0.005386250000000001, (3, 0): 0.006789999999999999, (2, 0): 0.006971249999999999, (11, 0): 0.0072525, (12, 12): 0.00986, (5, 3): 0.005277499999999999, (8, 8): 0.0052425, (3, 8): 0.005342500000000001, (4, 9): 0.005342500000000001, (2, 3): 0.0055025, (9, 6): 0.005274999999999999, (0, 11): 0.0072525, (6, 11): 0.0054925, (6, 6): 0.00519, (2, 10): 0.005645000000000001, (10, 11): 0.0058137499999999995, (3, 1): 0.0056625, (9, 5): 0.005277499999999999, (11, 12): 0.0072525, (8, 0): 0.006662500000000001, (6, 1): 0.0054925, (5, 8): 0.005279999999999999, (10, 12): 0.006971249999999999, (7, 8): 0.005279999999999999, (2, 8): 0.005386250000000001, (9, 10): 0.0055025, (6, 4): 0.00525, (8, 2): 0.005386250000000001, (6, 10): 0.005392500000000001, (6, 7): 0.0052025000000000005, (5, 2): 0.005366249999999998, (1, 10): 0.0058137499999999995, (5, 11): 0.005518750000000001, (11, 5): 0.005518750000000001, (1, 5): 0.005518750000000001, (12, 6): 0.006545, (10, 2): 0.005645000000000001, (10, 6): 0.005392500000000001, (4, 12): 0.006662500000000001, (9, 1): 0.0056625, (11, 4): 0.00561625, (3, 4): 0.005342500000000001, (4, 3): 0.005342500000000001, (7, 7): 0.0052049999999999996, (8, 9): 0.005342500000000001, (11, 11): 0.006082499999999999, (3, 12): 0.006789999999999999, (4, 6): 0.00525, (2, 2): 0.005645000000000001, (1, 12): 0.0072525, (6, 5): 0.0052025000000000005, (12, 8): 0.006662500000000001, (1, 2): 0.0058137499999999995, (10, 10): 0.005645000000000001, (9, 7): 0.005277499999999999, (0, 5): 0.0065775, (12, 11): 0.0072525, (12, 2): 0.006971249999999999, (9, 3): 0.0054600000000000004, (0, 3): 0.006789999999999999, (4, 2): 0.005386250000000001, (1, 1): 0.006082499999999999, (1, 0): 0.0072525, (4, 0): 0.006662500000000001, (5, 5): 0.0052049999999999996, (9, 12): 0.006789999999999999, (12, 4): 0.006662500000000001, (2, 12): 0.006971249999999999, (10, 7): 0.005366249999999998, (11, 2): 0.0058137499999999995, (5, 7): 0.0052049999999999996, (9, 4): 0.005342500000000001, (10, 0): 0.006971249999999999, (4, 7): 0.005279999999999999, (5, 4): 0.005279999999999999, (1, 11): 0.006082499999999999, (7, 6): 0.0052025000000000005, (0, 7): 0.0065775, (0, 12): 0.00986, (10, 5): 0.005366249999999998, (9, 8): 0.005342500000000001, (10, 8): 0.005386250000000001, (0, 4): 0.006662500000000001, (8, 7): 0.005279999999999999, (5, 10): 0.005366249999999998, (5, 1): 0.005518750000000001, (2, 7): 0.005366249999999998, (8, 4): 0.0052425, (7, 1): 0.005518750000000001, (1, 8): 0.00561625, (6, 3): 0.005274999999999999, (5, 0): 0.0065775, (8, 12): 0.006662500000000001, (6, 12): 0.006545, (3, 6): 0.005274999999999999, (6, 0): 0.006545, (11, 3): 0.0056625, (7, 5): 0.0052049999999999996, (5, 12): 0.0065775, (8, 6): 0.00525, (7, 9): 0.005277499999999999, (4, 5): 0.005279999999999999, (3, 3): 0.0054600000000000004, (6, 9): 0.005274999999999999, (11, 9): 0.0056625, (7, 11): 0.005518750000000001, (9, 2): 0.0055025, (4, 8): 0.0052425, (2, 11): 0.0058137499999999995, (6, 2): 0.005392500000000001, (9, 11): 0.0056625, (9, 9): 0.0054600000000000004, (10, 1): 0.0058137499999999995, (3, 11): 0.0056625, (11, 6): 0.0054925, (1, 6): 0.0054925, (12, 5): 0.0065775, (12, 1): 0.0072525, (3, 10): 0.0055025, (2, 5): 0.005366249999999998, (0, 0): 0.00986, (0, 8): 0.006662500000000001, (8, 10): 0.005386250000000001, (2, 9): 0.0055025, (11, 7): 0.005518750000000001, (4, 4): 0.0052425}

N = 14
{(2, 8): 0.00468, (0, 10): 0.00587625, (8, 4): 0.004545, (5, 2): 0.00468, (12, 1): 0.005314999999999999, (1, 8): 0.00482875, (5, 10): 0.00463125, (0, 11): 0.006045000000000001, (13, 8): 0.005767500000000001, (2, 0): 0.006045000000000001, (4, 13): 0.005826249999999999, (2, 1): 0.005083750000000001, (2, 11): 0.0049525, (12, 11): 0.005083750000000001, (7, 9): 0.00453375, (4, 11): 0.00475, (1, 5): 0.00482875, (5, 1): 0.00482875, (3, 11): 0.004778749999999999, (11, 8): 0.00468, (7, 12): 0.0048175, (11, 10): 0.004778749999999999, (13, 7): 0.005708749999999999, (9, 4): 0.0045475, (5, 7): 0.00449625, (13, 1): 0.0063625, (1, 13): 0.0063625, (6, 0): 0.005708749999999999, (7, 3): 0.0045875, (6, 4): 0.00453375, (7, 6): 0.00446, (2, 6): 0.00465875, (3, 9): 0.004594999999999999, (9, 13): 0.005826249999999999, (2, 12): 0.005083750000000001, (7, 8): 0.00449625, (12, 2): 0.005083750000000001, (1, 10): 0.00495, (8, 1): 0.00482875, (10, 9): 0.004594999999999999, (7, 1): 0.0048175, (1, 11): 0.005083750000000001, (3, 8): 0.00463125, (4, 7): 0.00453375, (12, 10): 0.00495, (6, 10): 0.0045875, (0, 7): 0.005708749999999999, (0, 8): 0.005767500000000001, (13, 6): 0.005708749999999999, (4, 2): 0.00475, (0, 9): 0.005826249999999999, (12, 8): 0.00482875, (8, 0): 0.005767500000000001, (7, 0): 0.005708749999999999, (10, 8): 0.00463125, (12, 3): 0.00495, (4, 3): 0.004594999999999999, (8, 7): 0.00449625, (7, 5): 0.00449625, (3, 12): 0.00495, (8, 13): 0.005767500000000001, (10, 0): 0.00587625, (5, 5): 0.0045075, (1, 6): 0.0048175, (13, 9): 0.005826249999999999, (11, 7): 0.00465875, (7, 13): 0.005708749999999999, (12, 7): 0.0048175, (0, 1): 0.0063625, (12, 5): 0.00482875, (1, 2): 0.005083750000000001, (10, 13): 0.00587625, (8, 10): 0.00463125, (2, 2): 0.0049525, (11, 9): 0.00475, (13, 10): 0.00587625, (0, 5): 0.005767500000000001, (6, 8): 0.00449625, (4, 9): 0.0045475, (12, 6): 0.0048175, (6, 12): 0.0048175, (2, 4): 0.00475, (13, 0): 0.00865, (7, 2): 0.00465875, (4, 8): 0.004545, (13, 3): 0.00587625, (11, 13): 0.006045000000000001, (12, 9): 0.004886250000000001, (3, 6): 0.0045875, (10, 11): 0.004778749999999999, (13, 2): 0.006045000000000001, (6, 2): 0.00465875, (6, 5): 0.00449625, (4, 4): 0.0045475, (3, 2): 0.004778749999999999, (3, 7): 0.0045875, (3, 0): 0.00587625, (5, 13): 0.005767500000000001, (4, 12): 0.004886250000000001, (9, 11): 0.00475, (9, 7): 0.00453375, (13, 11): 0.006045000000000001, (5, 3): 0.00463125, (13, 13): 0.00865, (7, 7): 0.00446, (11, 3): 0.004778749999999999, (2, 13): 0.006045000000000001, (13, 5): 0.005767500000000001, (8, 12): 0.00482875, (6, 11): 0.00465875, (3, 3): 0.0047550000000000005, (0, 13): 0.00865, (9, 6): 0.00453375, (1, 0): 0.0063625, (5, 11): 0.00468, (9, 3): 0.004594999999999999, (10, 2): 0.004778749999999999, (4, 5): 0.004545, (11, 5): 0.00468, (9, 12): 0.004886250000000001, (13, 12): 0.0063625, (0, 0): 0.00865, (9, 10): 0.004594999999999999, (12, 4): 0.004886250000000001, (1, 3): 0.00495, (0, 6): 0.005708749999999999, (11, 1): 0.005083750000000001, (9, 5): 0.004545, (1, 7): 0.0048175, (5, 6): 0.00449625, (7, 10): 0.0045875, (0, 3): 0.00587625, (6, 3): 0.0045875, (10, 10): 0.0047550000000000005, (10, 12): 0.00495, (12, 0): 0.0063625, (3, 1): 0.00495, (7, 4): 0.00453375, (7, 11): 0.00465875, (2, 10): 0.004778749999999999, (11, 6): 0.00465875, (11, 0): 0.006045000000000001, (13, 4): 0.005826249999999999, (11, 11): 0.0049525, (0, 2): 0.006045000000000001, (5, 12): 0.00482875, (3, 10): 0.0047550000000000005, (4, 1): 0.004886250000000001, (8, 5): 0.0045075, (9, 1): 0.004886250000000001, (9, 9): 0.0045475, (8, 9): 0.004545, (11, 12): 0.005083750000000001, (1, 9): 0.004886250000000001, (3, 5): 0.00463125, (11, 2): 0.0049525, (10, 1): 0.00495, (6, 9): 0.00453375, (11, 4): 0.00475, (2, 3): 0.004778749999999999, (2, 9): 0.00475, (1, 1): 0.005314999999999999, (10, 4): 0.004594999999999999, (8, 2): 0.00468, (5, 8): 0.0045075, (8, 6): 0.00449625, (6, 1): 0.0048175, (8, 11): 0.00468, (8, 3): 0.00463125, (4, 6): 0.00453375, (12, 13): 0.0063625, (10, 5): 0.00463125, (5, 4): 0.004545, (2, 5): 0.00468, (6, 13): 0.005708749999999999, (10, 3): 0.0047550000000000005, (9, 8): 0.004545, (9, 0): 0.005826249999999999, (12, 12): 0.005314999999999999, (10, 7): 0.0045875, (4, 0): 0.005826249999999999, (0, 4): 0.005826249999999999, (4, 10): 0.004594999999999999, (1, 12): 0.005314999999999999, (2, 7): 0.00465875, (0, 12): 0.0063625, (3, 13): 0.00587625, (10, 6): 0.0045875, (6, 7): 0.00446, (9, 2): 0.00475, (3, 4): 0.004594999999999999, (6, 6): 0.00446, (8, 8): 0.0045075, (5, 9): 0.004545, (5, 0): 0.005767500000000001, (1, 4): 0.004886250000000001}

N = 15
{(0, 3): 0.0052025, (2, 13): 0.00447625, (6, 13): 0.0042175, (10, 10): 0.004025, (1, 14): 0.0056324999999999995, (14, 12): 0.005372500000000001, (11, 1): 0.00438625, (12, 6): 0.00410875, (11, 10): 0.00404375, (1, 8): 0.0042175, (13, 14): 0.0056324999999999995, (8, 13): 0.0042175, (0, 4): 0.005091249999999999, (0, 0): 0.0076125, (12, 13): 0.00447625, (6, 5): 0.00391625, (13, 13): 0.0046775, (0, 12): 0.005372500000000001, (10, 9): 0.0040175, (14, 8): 0.005011250000000001, (2, 11): 0.00421125, (3, 11): 0.0041275, (12, 14): 0.005372500000000001, (11, 11): 0.0041275, (14, 4): 0.005091249999999999, (4, 9): 0.0040175, (10, 0): 0.005091249999999999, (10, 4): 0.004025, (1, 9): 0.0042475, (9, 11): 0.00401625, (4, 3): 0.00404375, (6, 3): 0.0040125, (0, 10): 0.005091249999999999, (2, 9): 0.004158749999999999, (4, 8): 0.003976250000000001, (13, 10): 0.004290000000000001, (1, 4): 0.004290000000000001, (7, 7): 0.00396, (2, 2): 0.0042875000000000005, (3, 5): 0.00401625, (14, 11): 0.0052025, (2, 4): 0.00416, (2, 5): 0.004158749999999999, (13, 9): 0.0042475, (1, 1): 0.0046775, (14, 10): 0.005091249999999999, (5, 9): 0.0039975, (13, 11): 0.00438625, (2, 8): 0.00410875, (4, 5): 0.0040175, (14, 9): 0.005038750000000001, (4, 12): 0.00416, (14, 5): 0.005038750000000001, (10, 6): 0.003976250000000001, (12, 7): 0.0040875, (6, 9): 0.00391625, (14, 0): 0.0076125, (5, 8): 0.00391625, (7, 12): 0.0040875, (11, 4): 0.00404375, (0, 14): 0.0076125, (10, 14): 0.005091249999999999, (1, 0): 0.0056324999999999995, (11, 0): 0.0052025, (11, 6): 0.0040125, (6, 0): 0.005011250000000001, (9, 0): 0.005038750000000001, (11, 14): 0.0052025, (7, 13): 0.00419, (13, 7): 0.00419, (13, 1): 0.0046775, (12, 0): 0.005372500000000001, (8, 3): 0.0040125, (9, 5): 0.0039975, (9, 4): 0.0040175, (0, 1): 0.0056324999999999995, (4, 1): 0.004290000000000001, (9, 13): 0.0042475, (11, 5): 0.00401625, (6, 10): 0.003976250000000001, (10, 3): 0.00404375, (14, 7): 0.005005, (10, 5): 0.0040175, (6, 6): 0.003935, (4, 10): 0.004025, (7, 4): 0.0039875, (7, 8): 0.0039525, (9, 3): 0.00401625, (0, 5): 0.005038750000000001, (1, 5): 0.0042475, (12, 8): 0.00410875, (10, 12): 0.00416, (5, 0): 0.005038750000000001, (5, 1): 0.0042475, (7, 5): 0.00398, (5, 7): 0.00398, (3, 8): 0.0040125, (3, 7): 0.0039625, (6, 11): 0.0040125, (1, 2): 0.00447625, (14, 3): 0.0052025, (0, 13): 0.0056324999999999995, (5, 3): 0.00401625, (14, 2): 0.005372500000000001, (8, 1): 0.0042175, (0, 8): 0.005011250000000001, (2, 14): 0.005372500000000001, (8, 5): 0.00391625, (9, 2): 0.004158749999999999, (3, 4): 0.00404375, (3, 9): 0.00401625, (8, 11): 0.0040125, (2, 12): 0.0042875000000000005, (7, 0): 0.005005, (0, 2): 0.005372500000000001, (5, 14): 0.005038750000000001, (3, 3): 0.0041275, (0, 9): 0.005038750000000001, (4, 6): 0.003976250000000001, (2, 6): 0.00410875, (7, 9): 0.00398, (6, 14): 0.005011250000000001, (10, 13): 0.004290000000000001, (9, 7): 0.00398, (5, 10): 0.0040175, (1, 6): 0.0042175, (6, 8): 0.003935, (6, 4): 0.003976250000000001, (2, 3): 0.00421125, (4, 7): 0.0039875, (3, 0): 0.0052025, (2, 10): 0.00416, (7, 3): 0.0039625, (8, 2): 0.00410875, (10, 8): 0.003976250000000001, (1, 7): 0.00419, (10, 2): 0.00416, (8, 14): 0.005011250000000001, (12, 1): 0.00447625, (9, 14): 0.005038750000000001, (5, 11): 0.00401625, (5, 4): 0.0040175, (8, 12): 0.00410875, (7, 1): 0.00419, (10, 1): 0.004290000000000001, (7, 2): 0.0040875, (8, 10): 0.003976250000000001, (11, 7): 0.0039625, (11, 13): 0.00438625, (13, 5): 0.0042475, (14, 1): 0.0056324999999999995, (1, 13): 0.0046775, (4, 11): 0.00404375, (12, 3): 0.00421125, (7, 6): 0.0039525, (2, 1): 0.00447625, (12, 11): 0.00421125, (11, 12): 0.00421125, (5, 6): 0.00391625, (3, 13): 0.00438625, (13, 2): 0.00447625, (1, 3): 0.00438625, (4, 2): 0.00416, (11, 2): 0.00421125, (2, 0): 0.005372500000000001, (4, 13): 0.004290000000000001, (12, 5): 0.004158749999999999, (3, 14): 0.0052025, (10, 7): 0.0039875, (14, 14): 0.0076125, (2, 7): 0.0040875, (9, 6): 0.00391625, (0, 7): 0.005005, (13, 3): 0.00438625, (6, 7): 0.0039525, (8, 0): 0.005011250000000001, (9, 9): 0.0039975, (8, 6): 0.003935, (14, 6): 0.005011250000000001, (13, 6): 0.0042175, (12, 10): 0.00416, (14, 13): 0.0056324999999999995, (1, 10): 0.004290000000000001, (3, 6): 0.0040125, (7, 10): 0.0039875, (5, 2): 0.004158749999999999, (6, 12): 0.00410875, (0, 11): 0.0052025, (3, 2): 0.00421125, (3, 1): 0.00438625, (7, 14): 0.005005, (8, 4): 0.003976250000000001, (1, 12): 0.00447625, (9, 8): 0.00391625, (12, 2): 0.0042875000000000005, (6, 2): 0.00410875, (13, 8): 0.0042175, (4, 14): 0.005091249999999999, (12, 9): 0.004158749999999999, (11, 3): 0.0041275, (5, 5): 0.0039975, (9, 10): 0.0040175, (10, 11): 0.00404375, (8, 9): 0.00391625, (8, 7): 0.0039525, (4, 0): 0.005091249999999999, (1, 11): 0.00438625, (9, 1): 0.0042475, (11, 9): 0.00401625, (13, 12): 0.00447625, (9, 12): 0.004158749999999999, (3, 12): 0.00421125, (6, 1): 0.0042175, (5, 12): 0.004158749999999999, (12, 4): 0.00416, (8, 8): 0.003935, (12, 12): 0.0042875000000000005, (11, 8): 0.0040125, (13, 0): 0.0056324999999999995, (13, 4): 0.004290000000000001, (5, 13): 0.0042475, (4, 4): 0.004025, (7, 11): 0.0039625, (0, 6): 0.005011250000000001, (3, 10): 0.00404375}

N = 16
{(14, 7): 0.00372, (1, 2): 0.003975, (7, 5): 0.00346875, (5, 1): 0.0037599999999999995, (3, 11): 0.003588750000000001, (7, 3): 0.0035562500000000004, (9, 6): 0.0034375000000000005, (6, 1): 0.0037512500000000002, (3, 3): 0.0036850000000000003, (14, 3): 0.003893750000000001, (15, 13): 0.00475625, (3, 15): 0.00460125, (12, 14): 0.003893750000000001, (11, 5): 0.003567500000000001, (9, 0): 0.0044325, (9, 13): 0.0036174999999999996, (9, 4): 0.0035325000000000005, (13, 8): 0.0036187500000000004, (3, 6): 0.0035600000000000002, (0, 2): 0.00475625, (14, 5): 0.0037599999999999995, (12, 0): 0.00460125, (4, 7): 0.00350125, (12, 3): 0.0036850000000000003, (2, 7): 0.0036187500000000004, (2, 14): 0.003975, (10, 1): 0.0037599999999999995, (15, 10): 0.004493749999999999, (7, 9): 0.0034825, (4, 15): 0.004528750000000001, (15, 1): 0.005011250000000001, (14, 11): 0.0037787500000000004, (14, 8): 0.00372, (1, 9): 0.0037512500000000002, (6, 2): 0.0036174999999999996, (15, 0): 0.0067075, (4, 1): 0.0037787500000000004, (13, 15): 0.00475625, (3, 8): 0.0035562500000000004, (12, 13): 0.0037699999999999995, (6, 9): 0.0034375000000000005, (7, 1): 0.00372, (4, 4): 0.0035, (10, 15): 0.004493749999999999, (10, 13): 0.00367375, (6, 6): 0.0034375000000000005, (5, 5): 0.0035199999999999997, (0, 5): 0.004493749999999999, (14, 2): 0.003975, (4, 13): 0.0037349999999999996, (3, 14): 0.003893750000000001, (14, 10): 0.0037599999999999995, (3, 9): 0.0035600000000000002, (15, 5): 0.004493749999999999, (7, 8): 0.0034575, (15, 4): 0.004528750000000001, (8, 5): 0.00346875, (13, 2): 0.00384, (15, 12): 0.00460125, (13, 0): 0.00475625, (15, 9): 0.0044325, (5, 15): 0.004493749999999999, (0, 13): 0.00475625, (2, 3): 0.0037699999999999995, (0, 12): 0.00460125, (1, 13): 0.003975, (12, 6): 0.0035600000000000002, (5, 14): 0.0037599999999999995, (7, 12): 0.0035562500000000004, (3, 13): 0.0037699999999999995, (6, 0): 0.0044325, (2, 0): 0.00475625, (4, 5): 0.003567500000000001, (3, 10): 0.0035787499999999995, (6, 12): 0.0035600000000000002, (14, 0): 0.005011250000000001, (10, 5): 0.0035199999999999997, (12, 1): 0.003893750000000001, (1, 1): 0.0042325, (15, 15): 0.0067075, (6, 15): 0.0044325, (5, 7): 0.00346875, (0, 0): 0.0067075, (5, 2): 0.00367375, (14, 6): 0.0037512500000000002, (9, 14): 0.0037512500000000002, (0, 1): 0.005011250000000001, (3, 12): 0.0036850000000000003, (10, 2): 0.00367375, (11, 10): 0.003567500000000001, (4, 2): 0.0037349999999999996, (12, 7): 0.0035562500000000004, (2, 6): 0.0036174999999999996, (5, 8): 0.00346875, (11, 8): 0.00350125, (8, 11): 0.00350125, (7, 0): 0.004415000000000001, (13, 9): 0.0036174999999999996, (12, 9): 0.0035600000000000002, (11, 15): 0.004528750000000001, (9, 8): 0.0034825, (13, 1): 0.003975, (2, 11): 0.0037349999999999996, (10, 14): 0.0037599999999999995, (11, 2): 0.0037349999999999996, (12, 11): 0.003588750000000001, (13, 13): 0.00384, (2, 5): 0.00367375, (3, 0): 0.00460125, (6, 8): 0.0034825, (15, 6): 0.0044325, (8, 15): 0.004415000000000001, (8, 14): 0.00372, (1, 0): 0.005011250000000001, (5, 4): 0.003567500000000001, (10, 6): 0.003446249999999999, (2, 13): 0.00384, (6, 14): 0.0037512500000000002, (0, 11): 0.004528750000000001, (8, 3): 0.0035562500000000004, (13, 3): 0.0037699999999999995, (15, 14): 0.005011250000000001, (5, 0): 0.004493749999999999, (6, 7): 0.0034825, (12, 15): 0.00460125, (12, 10): 0.0035787499999999995, (8, 6): 0.0034825, (13, 12): 0.0037699999999999995, (1, 8): 0.00372, (15, 7): 0.004415000000000001, (10, 0): 0.004493749999999999, (8, 4): 0.00350125, (11, 3): 0.003588750000000001, (1, 6): 0.0037512500000000002, (0, 6): 0.0044325, (4, 9): 0.0035325000000000005, (4, 10): 0.003567500000000001, (7, 11): 0.00350125, (11, 1): 0.0037787500000000004, (3, 1): 0.003893750000000001, (12, 12): 0.0036850000000000003, (0, 4): 0.004528750000000001, (2, 15): 0.00475625, (11, 4): 0.0035, (12, 5): 0.0035787499999999995, (5, 3): 0.0035787499999999995, (13, 14): 0.003975, (5, 10): 0.0035199999999999997, (10, 12): 0.0035787499999999995, (11, 0): 0.004528750000000001, (5, 11): 0.003567500000000001, (15, 11): 0.004528750000000001, (10, 10): 0.0035199999999999997, (14, 14): 0.0042325, (9, 1): 0.0037512500000000002, (14, 9): 0.0037512500000000002, (0, 8): 0.004415000000000001, (4, 8): 0.00350125, (12, 8): 0.0035562500000000004, (0, 10): 0.004493749999999999, (4, 6): 0.0035325000000000005, (4, 0): 0.004528750000000001, (3, 2): 0.0037699999999999995, (0, 9): 0.0044325, (8, 8): 0.0034575, (8, 1): 0.00372, (1, 12): 0.003893750000000001, (2, 1): 0.003975, (10, 8): 0.00346875, (13, 5): 0.00367375, (7, 10): 0.00346875, (11, 12): 0.003588750000000001, (9, 2): 0.0036174999999999996, (1, 5): 0.0037599999999999995, (0, 14): 0.005011250000000001, (5, 13): 0.00367375, (2, 12): 0.0037699999999999995, (0, 15): 0.0067075, (13, 11): 0.0037349999999999996, (10, 9): 0.003446249999999999, (11, 6): 0.0035325000000000005, (2, 8): 0.0036187500000000004, (13, 10): 0.00367375, (2, 2): 0.00384, (7, 2): 0.0036187500000000004, (2, 10): 0.00367375, (14, 15): 0.005011250000000001, (1, 14): 0.0042325, (4, 3): 0.003588750000000001, (7, 4): 0.00350125, (10, 4): 0.003567500000000001, (15, 2): 0.00475625, (8, 2): 0.0036187500000000004, (13, 7): 0.0036187500000000004, (8, 0): 0.004415000000000001, (11, 7): 0.00350125, (6, 10): 0.003446249999999999, (7, 13): 0.0036187500000000004, (12, 2): 0.0037699999999999995, (11, 11): 0.0035, (10, 3): 0.0035787499999999995, (3, 7): 0.0035562500000000004, (15, 8): 0.004415000000000001, (4, 14): 0.0037787500000000004, (7, 6): 0.0034825, (13, 4): 0.0037349999999999996, (7, 7): 0.0034575, (5, 9): 0.003446249999999999, (1, 4): 0.0037787500000000004, (6, 13): 0.0036174999999999996, (0, 7): 0.004415000000000001, (11, 9): 0.0035325000000000005, (12, 4): 0.003588750000000001, (9, 12): 0.0035600000000000002, (9, 9): 0.0034375000000000005, (9, 11): 0.0035325000000000005, (15, 3): 0.00460125, (14, 4): 0.0037787500000000004, (9, 3): 0.0035600000000000002, (2, 9): 0.0036174999999999996, (8, 10): 0.00346875, (4, 11): 0.0035, (6, 11): 0.0035325000000000005, (14, 12): 0.003893750000000001, (1, 11): 0.0037787500000000004, (11, 13): 0.0037349999999999996, (1, 7): 0.00372, (6, 4): 0.0035325000000000005, (3, 5): 0.0035787499999999995, (4, 12): 0.003588750000000001, (11, 14): 0.0037787500000000004, (9, 10): 0.003446249999999999, (6, 5): 0.003446249999999999, (5, 6): 0.003446249999999999, (3, 4): 0.003588750000000001, (7, 14): 0.00372, (2, 4): 0.0037349999999999996, (1, 10): 0.0037599999999999995, (10, 11): 0.003567500000000001, (8, 7): 0.0034575, (6, 3): 0.0035600000000000002, (9, 7): 0.0034825, (14, 1): 0.0042325, (0, 3): 0.00460125, (14, 13): 0.003975, (1, 3): 0.003893750000000001, (13, 6): 0.0036174999999999996, (8, 12): 0.0035562500000000004, (9, 5): 0.003446249999999999, (10, 7): 0.00346875, (7, 15): 0.004415000000000001, (5, 12): 0.0035787499999999995, (9, 15): 0.0044325, (1, 15): 0.005011250000000001, (8, 9): 0.0034825, (8, 13): 0.0036187500000000004}

N = 17
{(12, 15): 0.003383750000000001, (9, 15): 0.0033250000000000007, (1, 9): 0.0033250000000000007, (8, 3): 0.00316, (5, 4): 0.003145000000000001, (0, 9): 0.003935, (4, 4): 0.0032075, (5, 11): 0.0030924999999999998, (10, 15): 0.0033287499999999992, (2, 13): 0.003373750000000001, (7, 4): 0.003127499999999999, (1, 7): 0.0033250000000000007, (16, 15): 0.004445, (14, 1): 0.003545, (0, 16): 0.006045, (8, 0): 0.003935, (5, 8): 0.0031325000000000003, (16, 14): 0.004282500000000001, (13, 1): 0.0034399999999999995, (10, 2): 0.0032562499999999996, (16, 3): 0.004143750000000001, (5, 6): 0.00310125, (7, 1): 0.0033250000000000007, (14, 14): 0.00346, (6, 16): 0.003957499999999999, (7, 3): 0.0031637499999999995, (7, 5): 0.0030750000000000005, (16, 0): 0.006045, (15, 12): 0.003383750000000001, (3, 14): 0.003373750000000001, (2, 16): 0.004282500000000001, (10, 0): 0.003957499999999999, (9, 1): 0.0033250000000000007, (0, 10): 0.003957499999999999, (3, 7): 0.0031637499999999995, (6, 1): 0.0033287499999999992, (8, 13): 0.00316, (9, 3): 0.0031637499999999995, (10, 8): 0.0031075, (11, 12): 0.003145000000000001, (12, 12): 0.0032075, (3, 0): 0.004143750000000001, (10, 3): 0.0031974999999999994, (13, 2): 0.003373750000000001, (11, 0): 0.0039975, (7, 12): 0.003127499999999999, (6, 12): 0.00305625, (5, 16): 0.0039975, (16, 16): 0.006045, (1, 3): 0.0034399999999999995, (2, 7): 0.0032074999999999994, (8, 8): 0.00312, (13, 16): 0.004143750000000001, (5, 15): 0.003369999999999999, (15, 10): 0.0033287499999999992, (1, 5): 0.003369999999999999, (2, 6): 0.0032562499999999996, (6, 11): 0.00310125, (14, 15): 0.003545, (6, 5): 0.00310125, (8, 7): 0.0030825, (14, 7): 0.0032074999999999994, (4, 7): 0.003127499999999999, (2, 5): 0.00329625, (4, 15): 0.003383750000000001, (14, 5): 0.00329625, (1, 2): 0.003545, (3, 3): 0.0033225, (7, 8): 0.0030825, (3, 1): 0.0034399999999999995, (8, 5): 0.0031325000000000003, (2, 3): 0.003373750000000001, (2, 8): 0.0032, (4, 5): 0.003145000000000001, (15, 5): 0.003369999999999999, (8, 12): 0.0031325, (16, 12): 0.00405875, (11, 1): 0.003369999999999999, (0, 5): 0.0039975, (7, 16): 0.003935, (11, 13): 0.00320875, (9, 4): 0.003127499999999999, (11, 11): 0.0030924999999999998, (12, 9): 0.003127499999999999, (14, 3): 0.003373750000000001, (12, 11): 0.003145000000000001, (8, 10): 0.0031075, (16, 10): 0.003957499999999999, (6, 3): 0.0031974999999999994, (13, 13): 0.0033225, (15, 8): 0.0033225, (16, 11): 0.0039975, (12, 7): 0.003127499999999999, (15, 2): 0.003545, (0, 1): 0.004445, (10, 16): 0.003957499999999999, (3, 12): 0.0032225, (14, 9): 0.0032074999999999994, (16, 6): 0.003957499999999999, (1, 12): 0.003383750000000001, (11, 10): 0.00310125, (13, 9): 0.0031637499999999995, (5, 3): 0.00320875, (1, 15): 0.0037775, (7, 15): 0.0033250000000000007, (9, 2): 0.0032074999999999994, (16, 7): 0.003935, (13, 14): 0.003373750000000001, (6, 2): 0.0032562499999999996, (15, 4): 0.003383750000000001, (2, 2): 0.00346, (2, 15): 0.003545, (11, 16): 0.0039975, (0, 14): 0.004282500000000001, (16, 1): 0.004445, (6, 9): 0.00311875, (2, 4): 0.003279999999999999, (8, 11): 0.0031325000000000003, (0, 2): 0.004282500000000001, (8, 2): 0.0032, (4, 8): 0.0031325, (14, 4): 0.003279999999999999, (0, 3): 0.004143750000000001, (3, 16): 0.004143750000000001, (9, 5): 0.0030750000000000005, (11, 3): 0.00320875, (8, 4): 0.0031325, (5, 12): 0.003145000000000001, (16, 13): 0.004143750000000001, (9, 0): 0.003935, (14, 16): 0.004282500000000001, (4, 10): 0.00305625, (4, 16): 0.00405875, (13, 15): 0.0034399999999999995, (12, 0): 0.00405875, (5, 13): 0.00320875, (4, 13): 0.0032225, (2, 10): 0.0032562499999999996, (6, 0): 0.003957499999999999, (15, 11): 0.003369999999999999, (5, 14): 0.00329625, (10, 11): 0.00310125, (6, 4): 0.00305625, (1, 4): 0.003383750000000001, (12, 2): 0.003279999999999999, (7, 10): 0.00311875, (2, 0): 0.004282500000000001, (10, 1): 0.0033287499999999992, (1, 1): 0.0037775, (3, 4): 0.0032225, (7, 14): 0.0032074999999999994, (15, 16): 0.004445, (13, 5): 0.00320875, (9, 13): 0.0031637499999999995, (9, 12): 0.003127499999999999, (6, 10): 0.003085, (6, 15): 0.0033287499999999992, (4, 2): 0.003279999999999999, (12, 14): 0.003279999999999999, (13, 7): 0.0031637499999999995, (8, 6): 0.0031075, (7, 2): 0.0032074999999999994, (5, 0): 0.0039975, (9, 11): 0.0030750000000000005, (12, 6): 0.00305625, (6, 7): 0.00311875, (13, 3): 0.0033225, (11, 5): 0.0030924999999999998, (13, 11): 0.00320875, (1, 0): 0.004445, (5, 1): 0.003369999999999999, (1, 10): 0.0033287499999999992, (8, 1): 0.0033225, (5, 2): 0.00329625, (10, 5): 0.00310125, (15, 3): 0.0034399999999999995, (2, 12): 0.003279999999999999, (16, 8): 0.003935, (0, 13): 0.004143750000000001, (10, 7): 0.00311875, (15, 13): 0.0034399999999999995, (14, 2): 0.00346, (14, 13): 0.003373750000000001, (3, 13): 0.0033225, (12, 8): 0.0031325, (10, 14): 0.0032562499999999996, (2, 9): 0.0032074999999999994, (7, 7): 0.0030575, (12, 13): 0.0032225, (1, 8): 0.0033225, (1, 14): 0.003545, (8, 14): 0.0032, (5, 9): 0.0030750000000000005, (16, 9): 0.003935, (13, 4): 0.0032225, (4, 11): 0.003145000000000001, (11, 7): 0.0030750000000000005, (0, 0): 0.006045, (11, 8): 0.0031325000000000003, (11, 15): 0.003369999999999999, (14, 12): 0.003279999999999999, (14, 11): 0.00329625, (0, 4): 0.00405875, (13, 8): 0.00316, (15, 14): 0.003545, (11, 6): 0.00310125, (0, 12): 0.00405875, (9, 16): 0.003935, (2, 14): 0.00346, (2, 1): 0.003545, (12, 3): 0.0032225, (10, 10): 0.003085, (11, 2): 0.00329625, (13, 0): 0.004143750000000001, (13, 12): 0.0032225, (9, 8): 0.0030825, (3, 2): 0.003373750000000001, (11, 14): 0.00329625, (16, 2): 0.004282500000000001, (9, 14): 0.0032074999999999994, (4, 12): 0.0032075, (10, 4): 0.00305625, (3, 10): 0.0031974999999999994, (14, 6): 0.0032562499999999996, (14, 8): 0.0032, (6, 8): 0.0031075, (15, 6): 0.0033287499999999992, (16, 4): 0.00405875, (9, 6): 0.00311875, (4, 1): 0.003383750000000001, (15, 0): 0.004445, (5, 7): 0.0030750000000000005, (15, 1): 0.0037775, (4, 14): 0.003279999999999999, (12, 16): 0.00405875, (1, 11): 0.003369999999999999, (7, 13): 0.0031637499999999995, (7, 11): 0.0030750000000000005, (0, 7): 0.003935, (7, 9): 0.0030575, (12, 10): 0.00305625, (4, 0): 0.00405875, (0, 15): 0.004445, (13, 10): 0.0031974999999999994, (7, 0): 0.003935, (5, 10): 0.00310125, (3, 11): 0.00320875, (1, 16): 0.004445, (4, 3): 0.0032225, (3, 8): 0.00316, (4, 6): 0.00305625, (12, 1): 0.003383750000000001, (10, 6): 0.003085, (14, 0): 0.004282500000000001, (6, 6): 0.003085, (3, 9): 0.0031637499999999995, (3, 6): 0.0031974999999999994, (8, 16): 0.003935, (2, 11): 0.00329625, (6, 14): 0.0032562499999999996, (9, 9): 0.0030575, (10, 12): 0.00305625, (0, 11): 0.0039975, (14, 10): 0.0032562499999999996, (10, 9): 0.00311875, (13, 6): 0.0031974999999999994, (6, 13): 0.0031974999999999994, (10, 13): 0.0031974999999999994, (16, 5): 0.0039975, (3, 5): 0.00320875, (11, 4): 0.003145000000000001, (9, 10): 0.00311875, (8, 15): 0.0033225, (0, 8): 0.003935, (12, 4): 0.0032075, (7, 6): 0.00311875, (8, 9): 0.0030825, (1, 13): 0.0034399999999999995, (1, 6): 0.0033287499999999992, (11, 9): 0.0030750000000000005, (12, 5): 0.003145000000000001, (5, 5): 0.0030924999999999998, (15, 15): 0.0037775, (0, 6): 0.003957499999999999, (3, 15): 0.0034399999999999995, (15, 7): 0.0033250000000000007, (15, 9): 0.0033250000000000007, (9, 7): 0.0030575, (4, 9): 0.003127499999999999}

N = 18
{(11, 9): 0.0027599999999999994, (17, 1): 0.0040175, (10, 10): 0.0027674999999999996, (10, 14): 0.0028550000000000003, (6, 1): 0.0029737500000000003, (2, 12): 0.0029600000000000004, (5, 16): 0.0030349999999999995, (13, 0): 0.003637500000000001, (12, 17): 0.003605, (15, 13): 0.0029775000000000005, (3, 17): 0.0036799999999999997, (11, 17): 0.0035712500000000006, (14, 15): 0.0030325000000000005, (0, 16): 0.0040175, (11, 8): 0.0027599999999999994, (8, 11): 0.0027599999999999994, (15, 10): 0.0028912499999999997, (2, 3): 0.0030325000000000005, (7, 16): 0.002981250000000001, (5, 4): 0.0028199999999999996, (17, 7): 0.00352875, (0, 7): 0.00352875, (8, 5): 0.00276875, (6, 11): 0.002745, (16, 12): 0.0030349999999999995, (12, 11): 0.0027849999999999997, (14, 7): 0.0028550000000000003, (12, 10): 0.0027499999999999994, (13, 3): 0.0029224999999999998, (15, 16): 0.0032412500000000006, (14, 17): 0.0036799999999999997, (4, 13): 0.0028374999999999997, (17, 2): 0.0038762500000000004, (0, 2): 0.0038762500000000004, (0, 14): 0.0036799999999999997, (12, 16): 0.0030349999999999995, (12, 4): 0.0028199999999999996, (10, 17): 0.00352875, (5, 3): 0.0028675000000000003, (16, 6): 0.0029737500000000003, (7, 2): 0.0028912499999999997, (9, 15): 0.0028975000000000003, (13, 6): 0.002842500000000001, (7, 17): 0.00352875, (6, 13): 0.002842500000000001, (15, 9): 0.0028975000000000003, (17, 16): 0.0040175, (1, 8): 0.0029950000000000007, (6, 4): 0.002842500000000001, (4, 9): 0.0027737499999999993, (7, 11): 0.00277, (9, 9): 0.0027325, (5, 7): 0.0027499999999999994, (4, 0): 0.003637500000000001, (14, 2): 0.0030325000000000005, (7, 6): 0.00277, (10, 15): 0.0028912499999999997, (8, 12): 0.00276875, (13, 11): 0.002842500000000001, (10, 13): 0.0027749999999999997, (5, 9): 0.00276875, (10, 3): 0.0028550000000000003, (5, 14): 0.0028675000000000003, (0, 10): 0.00352875, (10, 5): 0.0027499999999999994, (9, 13): 0.0027737499999999993, (15, 1): 0.0032412500000000006, (5, 13): 0.0028199999999999996, (17, 6): 0.0035712500000000006, (6, 6): 0.002745, (5, 8): 0.00276875, (6, 5): 0.0027849999999999997, (8, 13): 0.0027737499999999993, (11, 4): 0.002842500000000001, (1, 11): 0.0029737500000000003, (13, 5): 0.0028199999999999996, (16, 17): 0.0040175, (14, 16): 0.0031387499999999996, (2, 7): 0.0028912499999999997, (15, 15): 0.003055, (4, 16): 0.0030937499999999997, (6, 10): 0.00277, (15, 17): 0.0038762500000000004, (2, 2): 0.003055, (15, 7): 0.0028912499999999997, (3, 0): 0.0036799999999999997, (0, 0): 0.00543, (4, 4): 0.0028374999999999997, (16, 8): 0.0029950000000000007, (10, 16): 0.002981250000000001, (16, 16): 0.0033799999999999998, (2, 0): 0.0038762500000000004, (5, 11): 0.0027849999999999997, (5, 1): 0.0030349999999999995, (3, 6): 0.0028399999999999996, (5, 5): 0.002805, (14, 4): 0.0029224999999999998, (9, 12): 0.00276875, (15, 12): 0.0029600000000000004, (17, 9): 0.0035074999999999998, (7, 13): 0.0027749999999999997, (1, 10): 0.002981250000000001, (3, 3): 0.0029575, (4, 17): 0.003637500000000001, (17, 14): 0.0036799999999999997, (1, 6): 0.0029737500000000003, (1, 2): 0.0032412500000000006, (16, 0): 0.0040175, (11, 16): 0.0029737500000000003, (1, 1): 0.0033799999999999998, (1, 14): 0.0031387499999999996, (7, 7): 0.0027674999999999996, (9, 0): 0.0035074999999999998, (1, 9): 0.0029950000000000007, (14, 13): 0.0029224999999999998, (16, 14): 0.0031387499999999996, (16, 10): 0.002981250000000001, (17, 4): 0.003637500000000001, (12, 1): 0.0030349999999999995, (17, 13): 0.003637500000000001, (4, 2): 0.0029775000000000005, (2, 17): 0.0038762500000000004, (15, 5): 0.0029600000000000004, (0, 3): 0.0036799999999999997, (3, 1): 0.0031387499999999996, (2, 9): 0.0028975000000000003, (14, 10): 0.0028550000000000003, (6, 12): 0.0027849999999999997, (11, 6): 0.002745, (1, 0): 0.0040175, (13, 12): 0.0028199999999999996, (2, 1): 0.0032412500000000006, (12, 0): 0.003605, (12, 9): 0.00276875, (4, 5): 0.0028199999999999996, (12, 8): 0.00276875, (11, 15): 0.00290875, (10, 4): 0.0027749999999999997, (0, 15): 0.0038762500000000004, (5, 0): 0.003605, (15, 3): 0.0030325000000000005, (0, 5): 0.003605, (2, 10): 0.0028912499999999997, (17, 12): 0.003605, (4, 3): 0.0029224999999999998, (0, 4): 0.003637500000000001, (14, 14): 0.0029575, (0, 17): 0.00543, (9, 5): 0.00276875, (12, 14): 0.0028675000000000003, (17, 0): 0.00543, (13, 7): 0.0027749999999999997, (9, 10): 0.0027375000000000003, (3, 5): 0.0028675000000000003, (9, 16): 0.0029950000000000007, (3, 11): 0.0028399999999999996, (14, 12): 0.0028675000000000003, (8, 15): 0.0028975000000000003, (8, 7): 0.0027375000000000003, (11, 0): 0.0035712500000000006, (10, 0): 0.00352875, (0, 8): 0.0035074999999999998, (6, 16): 0.0029737500000000003, (11, 2): 0.00290875, (0, 11): 0.0035712500000000006, (1, 17): 0.0040175, (12, 13): 0.0028199999999999996, (6, 7): 0.00277, (8, 9): 0.0027325, (12, 6): 0.0027849999999999997, (9, 3): 0.00283, (0, 13): 0.003637500000000001, (13, 14): 0.0029224999999999998, (14, 6): 0.0028399999999999996, (5, 15): 0.0029600000000000004, (17, 17): 0.00543, (5, 2): 0.0029600000000000004, (3, 12): 0.0028675000000000003, (7, 0): 0.00352875, (3, 14): 0.0029575, (4, 10): 0.0027749999999999997, (2, 11): 0.00290875, (12, 3): 0.0028675000000000003, (12, 5): 0.002805, (7, 10): 0.0027674999999999996, (7, 1): 0.002981250000000001, (12, 12): 0.002805, (14, 11): 0.0028399999999999996, (9, 8): 0.0027325, (9, 6): 0.0027599999999999994, (5, 12): 0.002805, (8, 3): 0.00283, (0, 6): 0.0035712500000000006, (16, 7): 0.002981250000000001, (7, 8): 0.0027375000000000003, (15, 4): 0.0029775000000000005, (12, 7): 0.0027499999999999994, (14, 5): 0.0028675000000000003, (0, 9): 0.0035074999999999998, (11, 13): 0.002842500000000001, (15, 0): 0.0038762500000000004, (11, 10): 0.00277, (6, 14): 0.0028399999999999996, (2, 8): 0.0028975000000000003, (7, 15): 0.0028912499999999997, (13, 15): 0.0029775000000000005, (15, 6): 0.00290875, (10, 12): 0.0027499999999999994, (6, 17): 0.0035712500000000006, (1, 16): 0.0033799999999999998, (15, 14): 0.0030325000000000005, (8, 17): 0.0035074999999999998, (6, 8): 0.0027599999999999994, (13, 17): 0.003637500000000001, (9, 14): 0.00283, (6, 9): 0.0027599999999999994, (16, 3): 0.0031387499999999996, (13, 13): 0.0028374999999999997, (2, 16): 0.0032412500000000006, (8, 8): 0.0027325, (2, 4): 0.0029775000000000005, (10, 11): 0.00277, (17, 11): 0.0035712500000000006, (7, 12): 0.0027499999999999994, (13, 1): 0.0030937499999999997, (15, 8): 0.0028975000000000003, (1, 5): 0.0030349999999999995, (9, 7): 0.0027375000000000003, (14, 3): 0.0029575, (8, 16): 0.0029950000000000007, (17, 15): 0.0038762500000000004, (4, 15): 0.0029775000000000005, (6, 3): 0.0028399999999999996, (3, 2): 0.0030325000000000005, (8, 10): 0.0027375000000000003, (2, 13): 0.0029775000000000005, (6, 15): 0.00290875, (3, 7): 0.0028550000000000003, (8, 1): 0.0029950000000000007, (5, 17): 0.003605, (4, 6): 0.002842500000000001, (12, 2): 0.0029600000000000004, (0, 1): 0.0040175, (3, 13): 0.0029224999999999998, (11, 5): 0.0027849999999999997, (14, 1): 0.0031387499999999996, (10, 6): 0.00277, (1, 3): 0.0031387499999999996, (7, 4): 0.0027749999999999997, (10, 7): 0.0027674999999999996, (16, 13): 0.0030937499999999997, (17, 10): 0.00352875, (5, 10): 0.0027499999999999994, (16, 1): 0.0033799999999999998, (9, 4): 0.0027737499999999993, (9, 11): 0.0027599999999999994, (2, 14): 0.0030325000000000005, (3, 15): 0.0030325000000000005, (14, 0): 0.0036799999999999997, (6, 0): 0.0035712500000000006, (4, 1): 0.0030937499999999997, (11, 3): 0.0028399999999999996, (3, 4): 0.0029224999999999998, (12, 15): 0.0029600000000000004, (17, 3): 0.0036799999999999997, (3, 9): 0.00283, (9, 17): 0.0035074999999999998, (13, 10): 0.0027749999999999997, (7, 14): 0.0028550000000000003, (13, 8): 0.0027737499999999993, (1, 7): 0.002981250000000001, (11, 1): 0.0029737500000000003, (2, 15): 0.003055, (6, 2): 0.00290875, (8, 4): 0.0027737499999999993, (16, 4): 0.0030937499999999997, (16, 2): 0.0032412500000000006, (8, 0): 0.0035074999999999998, (13, 16): 0.0030937499999999997, (10, 9): 0.0027375000000000003, (3, 10): 0.0028550000000000003, (4, 11): 0.002842500000000001, (5, 6): 0.0027849999999999997, (1, 15): 0.0032412500000000006, (13, 9): 0.0027737499999999993, (9, 2): 0.0028975000000000003, (4, 7): 0.0027749999999999997, (4, 12): 0.0028199999999999996, (13, 2): 0.0029775000000000005, (8, 6): 0.0027599999999999994, (10, 8): 0.0027375000000000003, (16, 11): 0.0029737500000000003, (16, 5): 0.0030349999999999995, (8, 2): 0.0028975000000000003, (3, 16): 0.0031387499999999996, (11, 7): 0.00277, (17, 8): 0.0035074999999999998, (10, 2): 0.0028912499999999997, (7, 3): 0.0028550000000000003, (11, 12): 0.0027849999999999997, (14, 8): 0.00283, (7, 9): 0.0027375000000000003, (7, 5): 0.0027499999999999994, (4, 8): 0.0027737499999999993, (1, 4): 0.0030937499999999997, (16, 9): 0.0029950000000000007, (16, 15): 0.0032412500000000006, (0, 12): 0.003605, (14, 9): 0.00283, (9, 1): 0.0029950000000000007, (15, 11): 0.00290875, (13, 4): 0.0028374999999999997, (1, 13): 0.0030937499999999997, (17, 5): 0.003605, (3, 8): 0.00283, (11, 11): 0.002745, (4, 14): 0.0029224999999999998, (2, 5): 0.0029600000000000004, (8, 14): 0.00283, (11, 14): 0.0028399999999999996, (2, 6): 0.00290875, (15, 2): 0.003055, (1, 12): 0.0030349999999999995, (10, 1): 0.002981250000000001}

N = 19
{(3, 4): 0.0026550000000000007, (5, 12): 0.0025424999999999996, (4, 17): 0.0027937500000000002, (5, 5): 0.00253, (18, 10): 0.0031575, (6, 15): 0.0025850000000000005, (10, 1): 0.002680000000000001, (4, 15): 0.0026550000000000007, (4, 0): 0.0032825000000000003, (15, 10): 0.0025799999999999994, (8, 3): 0.0025799999999999994, (10, 8): 0.00247, (5, 11): 0.0025050000000000003, (3, 14): 0.0026550000000000007, (18, 4): 0.0032825000000000003, (17, 11): 0.002705, (2, 5): 0.0026625, (10, 5): 0.0025037500000000003, (9, 12): 0.002495, (12, 13): 0.0025424999999999996, (7, 4): 0.0025487499999999994, (9, 2): 0.00263, (5, 18): 0.00324, (3, 0): 0.003377500000000001, (10, 14): 0.0025175, (3, 9): 0.0025199999999999997, (0, 7): 0.00324125, (6, 5): 0.0025424999999999996, (18, 3): 0.003377500000000001, (18, 11): 0.00324125, (6, 0): 0.0032149999999999995, (0, 16): 0.00345875, (9, 14): 0.002525, (3, 15): 0.0026775, (12, 4): 0.0025387499999999998, (0, 8): 0.0031575, (15, 7): 0.002533750000000001, (8, 1): 0.002680000000000001, (9, 11): 0.002445, (14, 4): 0.0025924999999999998, (15, 15): 0.0026775, (2, 1): 0.0029175, (8, 15): 0.0025799999999999994, (1, 14): 0.0027937500000000002, (4, 5): 0.0025524999999999996, (1, 4): 0.0027937500000000002, (17, 5): 0.002705, (1, 17): 0.0030125000000000004, (12, 11): 0.002465, (9, 8): 0.0024475, (13, 8): 0.0025037500000000003, (15, 2): 0.0027462499999999996, (4, 8): 0.0025175, (14, 17): 0.0027937500000000002, (7, 2): 0.0026324999999999994, (1, 3): 0.0028274999999999997, (2, 12): 0.0026325, (0, 18): 0.0049225, (14, 12): 0.0025387499999999998, (14, 1): 0.0027937500000000002, (14, 0): 0.0032825000000000003, (10, 2): 0.0026200000000000004, (4, 6): 0.0025387499999999998, (16, 17): 0.0029175, (4, 9): 0.002525, (16, 14): 0.0026899999999999997, (4, 13): 0.0025524999999999996, (6, 17): 0.00270625, (8, 0): 0.0031575, (17, 7): 0.002705, (3, 6): 0.0025850000000000005, (11, 12): 0.002465, (17, 17): 0.0030125000000000004, (7, 17): 0.002705, (17, 14): 0.0027937500000000002, (8, 12): 0.002502500000000001, (10, 11): 0.0024575, (2, 10): 0.0026200000000000004, (14, 11): 0.0025487499999999994, (3, 12): 0.0025850000000000005, (12, 9): 0.002495, (15, 5): 0.0025900000000000003, (17, 16): 0.0029175, (8, 5): 0.0025037500000000003, (4, 2): 0.0026899999999999997, (3, 17): 0.0028274999999999997, (14, 18): 0.0032825000000000003, (12, 8): 0.002502500000000001, (17, 0): 0.0036262500000000006, (1, 5): 0.002705, (17, 13): 0.002705, (13, 13): 0.00253, (18, 8): 0.0031575, (18, 18): 0.0049225, (12, 1): 0.00270625, (9, 15): 0.0025199999999999997, (15, 16): 0.0027462499999999996, (12, 18): 0.0032149999999999995, (11, 13): 0.0025050000000000003, (11, 5): 0.0025050000000000003, (4, 3): 0.0026550000000000007, (5, 4): 0.0025524999999999996, (15, 1): 0.0028274999999999997, (8, 4): 0.0025175, (1, 10): 0.002680000000000001, (17, 2): 0.0029175, (8, 9): 0.0024475, (0, 10): 0.0031575, (17, 1): 0.0030125000000000004, (16, 11): 0.0026324999999999994, (15, 9): 0.0025199999999999997, (11, 10): 0.0024575, (7, 12): 0.002465, (14, 15): 0.0026550000000000007, (0, 17): 0.0036262500000000006, (6, 11): 0.002465, (10, 18): 0.0031575, (16, 5): 0.0026625, (2, 15): 0.0027462499999999996, (11, 4): 0.0025487499999999994, (6, 3): 0.0025850000000000005, (16, 6): 0.0026325, (12, 0): 0.0032149999999999995, (12, 10): 0.002502500000000001, (3, 11): 0.002533750000000001, (2, 8): 0.0026200000000000004, (13, 5): 0.00253, (10, 3): 0.0025799999999999994, (17, 10): 0.002680000000000001, (18, 5): 0.00324, (12, 14): 0.0025387499999999998, (11, 14): 0.0025487499999999994, (8, 11): 0.0024575, (18, 14): 0.0032825000000000003, (4, 7): 0.0025487499999999994, (14, 14): 0.0025924999999999998, (0, 2): 0.00345875, (16, 16): 0.0028075, (11, 7): 0.002465, (3, 10): 0.0025799999999999994, (0, 5): 0.00324, (8, 8): 0.00247, (16, 0): 0.00345875, (6, 7): 0.002465, (9, 10): 0.0024475, (15, 6): 0.0025850000000000005, (2, 2): 0.0028075, (18, 15): 0.003377500000000001, (16, 10): 0.0026200000000000004, (17, 18): 0.0036262500000000006, (8, 18): 0.0031575, (5, 3): 0.0025900000000000003, (14, 3): 0.0026550000000000007, (10, 7): 0.0024575, (7, 0): 0.00324125, (5, 15): 0.0025900000000000003, (1, 15): 0.0028274999999999997, (16, 8): 0.0026200000000000004, (7, 11): 0.002465, (14, 5): 0.0025524999999999996, (7, 3): 0.002533750000000001, (1, 16): 0.0029175, (16, 7): 0.0026324999999999994, (3, 2): 0.0027462499999999996, (3, 8): 0.0025799999999999994, (18, 13): 0.00324, (12, 15): 0.0025850000000000005, (2, 7): 0.0026324999999999994, (0, 12): 0.0032149999999999995, (2, 0): 0.00345875, (6, 9): 0.002495, (5, 1): 0.002705, (16, 13): 0.0026625, (17, 4): 0.0027937500000000002, (16, 3): 0.0027462499999999996, (11, 17): 0.002705, (6, 13): 0.0025424999999999996, (2, 3): 0.0027462499999999996, (18, 7): 0.00324125, (4, 10): 0.0025175, (5, 10): 0.0025037500000000003, (2, 6): 0.0026325, (11, 16): 0.0026324999999999994, (2, 16): 0.0028075, (11, 18): 0.00324125, (0, 15): 0.003377500000000001, (3, 18): 0.003377500000000001, (0, 1): 0.0036262500000000006, (2, 17): 0.0029175, (11, 15): 0.002533750000000001, (13, 1): 0.002705, (2, 11): 0.0026324999999999994, (9, 18): 0.0031325, (18, 0): 0.0049225, (14, 8): 0.0025175, (9, 9): 0.00253, (7, 9): 0.002445, (1, 12): 0.00270625, (0, 4): 0.0032825000000000003, (2, 14): 0.0026899999999999997, (5, 2): 0.0026625, (12, 2): 0.0026325, (14, 10): 0.0025175, (1, 11): 0.002705, (5, 14): 0.0025524999999999996, (14, 16): 0.0026899999999999997, (6, 8): 0.002502500000000001, (8, 14): 0.0025175, (13, 14): 0.0025524999999999996, (7, 10): 0.0024575, (13, 12): 0.0025424999999999996, (18, 1): 0.0036262500000000006, (7, 15): 0.002533750000000001, (16, 18): 0.00345875, (1, 9): 0.00268, (9, 1): 0.00268, (1, 2): 0.0029175, (13, 2): 0.0026625, (15, 8): 0.0025799999999999994, (3, 3): 0.0026775, (10, 0): 0.0031575, (7, 18): 0.00324125, (5, 7): 0.0025050000000000003, (4, 11): 0.0025487499999999994, (18, 6): 0.0032149999999999995, (9, 3): 0.0025199999999999997, (10, 12): 0.002502500000000001, (8, 17): 0.002680000000000001, (1, 18): 0.0036262500000000006, (11, 8): 0.0024575, (4, 4): 0.0025924999999999998, (15, 12): 0.0025850000000000005, (18, 9): 0.0031325, (15, 3): 0.0026775, (9, 13): 0.0025075, (7, 6): 0.002465, (8, 16): 0.0026200000000000004, (6, 10): 0.002502500000000001, (0, 11): 0.00324125, (6, 2): 0.0026325, (3, 1): 0.0028274999999999997, (14, 9): 0.002525, (4, 16): 0.0026899999999999997, (11, 2): 0.0026324999999999994, (15, 18): 0.003377500000000001, (14, 13): 0.0025524999999999996, (6, 12): 0.0025074999999999997, (9, 5): 0.0025075, (17, 12): 0.00270625, (13, 4): 0.0025524999999999996, (15, 14): 0.0026550000000000007, (17, 3): 0.0028274999999999997, (2, 18): 0.00345875, (14, 2): 0.0026899999999999997, (7, 16): 0.0026324999999999994, (8, 2): 0.0026200000000000004, (17, 8): 0.002680000000000001, (0, 6): 0.0032149999999999995, (4, 14): 0.0025924999999999998, (13, 18): 0.00324, (7, 13): 0.0025050000000000003, (5, 9): 0.0025075, (10, 9): 0.0024475, (12, 17): 0.00270625, (1, 8): 0.002680000000000001, (4, 12): 0.0025387499999999998, (18, 12): 0.0032149999999999995, (3, 13): 0.0025900000000000003, (13, 9): 0.0025075, (4, 18): 0.0032825000000000003, (13, 17): 0.002705, (16, 9): 0.00263, (13, 16): 0.0026625, (9, 17): 0.00268, (1, 0): 0.0036262500000000006, (9, 16): 0.00263, (5, 16): 0.0026625, (3, 7): 0.002533750000000001, (16, 15): 0.0027462499999999996, (12, 12): 0.0025074999999999997, (1, 6): 0.00270625, (13, 15): 0.0025900000000000003, (18, 2): 0.00345875, (5, 8): 0.0025037500000000003, (13, 3): 0.0025900000000000003, (4, 1): 0.0027937500000000002, (10, 10): 0.00247, (5, 17): 0.002705, (11, 11): 0.002465, (16, 12): 0.0026325, (2, 13): 0.0026625, (11, 1): 0.002705, (17, 9): 0.00268, (8, 6): 0.002502500000000001, (15, 13): 0.0025900000000000003, (11, 0): 0.00324125, (0, 14): 0.0032825000000000003, (7, 1): 0.002705, (9, 0): 0.0031325, (13, 10): 0.0025037500000000003, (9, 4): 0.002525, (10, 6): 0.002502500000000001, (10, 17): 0.002680000000000001, (1, 7): 0.002705, (12, 3): 0.0025850000000000005, (15, 17): 0.0028274999999999997, (10, 16): 0.0026200000000000004, (16, 2): 0.0028075, (13, 11): 0.0025050000000000003, (2, 4): 0.0026899999999999997, (1, 1): 0.0030125000000000004, (15, 4): 0.0026550000000000007, (9, 7): 0.002445, (15, 11): 0.002533750000000001, (15, 0): 0.003377500000000001, (11, 3): 0.002533750000000001, (18, 17): 0.0036262500000000006, (10, 13): 0.0025037500000000003, (3, 16): 0.0027462499999999996, (14, 7): 0.0025487499999999994, (6, 4): 0.0025387499999999998, (7, 5): 0.0025050000000000003, (6, 16): 0.0026325, (5, 6): 0.0025424999999999996, (18, 16): 0.00345875, (3, 5): 0.0025900000000000003, (6, 14): 0.0025387499999999998, (0, 0): 0.0049225, (10, 4): 0.0025175, (13, 6): 0.0025424999999999996, (11, 9): 0.002445, (0, 13): 0.00324, (8, 7): 0.0024575, (17, 6): 0.00270625, (16, 1): 0.0029175, (7, 8): 0.0024575, (7, 14): 0.0025487499999999994, (0, 3): 0.003377500000000001, (17, 15): 0.0028274999999999997, (12, 6): 0.0025074999999999997, (12, 5): 0.0025424999999999996, (5, 13): 0.00253, (16, 4): 0.0026899999999999997, (10, 15): 0.0025799999999999994, (1, 13): 0.002705, (12, 16): 0.0026325, (13, 7): 0.0025050000000000003, (0, 9): 0.0031325, (14, 6): 0.0025387499999999998, (6, 18): 0.0032149999999999995, (8, 10): 0.00247, (5, 0): 0.00324, (11, 6): 0.002465, (6, 6): 0.0025074999999999997, (8, 13): 0.0025037500000000003, (12, 7): 0.002465, (9, 6): 0.002495, (6, 1): 0.00270625, (7, 7): 0.002465, (13, 0): 0.00324, (2, 9): 0.00263}

N = 20
{(11, 11): 0.0022, (7, 5): 0.00227375, (5, 13): 0.0023112500000000004, (0, 6): 0.0029050000000000005, (10, 13): 0.0022525000000000006, (2, 2): 0.002545, (2, 14): 0.0024375, (4, 11): 0.0023037500000000002, (11, 3): 0.00232625, (3, 2): 0.0024825, (19, 6): 0.0029050000000000005, (3, 18): 0.00259, (14, 8): 0.00226125, (6, 16): 0.00233, (9, 14): 0.0022662500000000005, (3, 0): 0.00305625, (10, 3): 0.0023024999999999994, (17, 16): 0.0024825, (19, 15): 0.0029924999999999995, (17, 8): 0.0023587499999999997, (3, 14): 0.00233625, (19, 3): 0.00305625, (4, 15): 0.0023725, (0, 5): 0.0029287500000000004, (18, 2): 0.00265, (18, 4): 0.002502500000000001, (3, 1): 0.00259, (1, 11): 0.00242625, (9, 13): 0.0022525000000000006, (14, 5): 0.002275, (16, 19): 0.00305625, (3, 11): 0.00232625, (9, 12): 0.002215, (19, 10): 0.0028712499999999997, (19, 19): 0.00448, (14, 0): 0.0029287500000000004, (0, 17): 0.0031425, (17, 7): 0.00235375, (15, 14): 0.0023287500000000005, (4, 0): 0.0029924999999999995, (17, 1): 0.00265, (6, 2): 0.00240375, (15, 2): 0.00246125, (16, 13): 0.00233, (7, 3): 0.00230375, (1, 15): 0.002502500000000001, (14, 17): 0.0024375, (18, 9): 0.002415, (15, 18): 0.002502500000000001, (9, 17): 0.0024, (5, 12): 0.00227375, (12, 7): 0.0022275000000000003, (13, 3): 0.00233, (13, 7): 0.0022487499999999994, (16, 17): 0.0024825, (0, 13): 0.0029050000000000005, (16, 15): 0.0024175, (11, 2): 0.0023587499999999997, (6, 3): 0.00233, (16, 16): 0.0024825000000000003, (18, 0): 0.0033275, (5, 0): 0.0029287500000000004, (5, 10): 0.0022662500000000005, (4, 13): 0.0023137500000000003, (2, 17): 0.002545, (2, 6): 0.00240375, (14, 2): 0.0024375, (18, 6): 0.0024762499999999997, (4, 4): 0.0023725, (3, 17): 0.0024825, (6, 0): 0.0029050000000000005, (8, 0): 0.00290375, (1, 17): 0.00265, (3, 8): 0.00232625, (16, 9): 0.0023024999999999994, (15, 12): 0.0023287500000000005, (12, 13): 0.0022487499999999994, (9, 8): 0.00221375, (17, 19): 0.0031425, (4, 1): 0.002502500000000001, (2, 11): 0.0023587499999999997, (16, 7): 0.00230375, (13, 15): 0.0023137500000000003, (1, 0): 0.0033275, (18, 16): 0.00259, (18, 11): 0.00242625, (10, 4): 0.0022887500000000004, (18, 19): 0.0033275, (15, 16): 0.0024175, (14, 13): 0.0023112500000000004, (9, 0): 0.0028712499999999997, (15, 17): 0.00246125, (19, 14): 0.0029287500000000004, (6, 15): 0.0023137500000000003, (4, 12): 0.0023287500000000005, (17, 6): 0.00240375, (10, 15): 0.0022887500000000004, (18, 13): 0.0024762499999999997, (14, 10): 0.0022662500000000005, (2, 1): 0.00265, (15, 9): 0.0022887500000000004, (16, 0): 0.00305625, (15, 6): 0.0023137500000000003, (14, 6): 0.0023112500000000004, (15, 11): 0.0023037500000000002, (18, 5): 0.0024724999999999994, (16, 2): 0.0024825, (0, 11): 0.00290375, (0, 16): 0.00305625, (7, 10): 0.002215, (10, 7): 0.002215, (6, 8): 0.00226125, (0, 19): 0.00448, (2, 5): 0.0024375, (2, 18): 0.00265, (19, 16): 0.00305625, (18, 15): 0.002502500000000001, (19, 12): 0.00292125, (4, 7): 0.0023287500000000005, (11, 14): 0.00226125, (5, 16): 0.00233625, (10, 10): 0.0022375, (14, 15): 0.0023287500000000005, (10, 14): 0.0022662500000000005, (17, 15): 0.00246125, (17, 18): 0.00265, (12, 10): 0.002215, (8, 7): 0.0022487500000000003, (16, 10): 0.0023024999999999994, (6, 13): 0.0022775, (17, 5): 0.0024375, (2, 19): 0.0031425, (2, 9): 0.0024, (13, 8): 0.00226125, (3, 9): 0.0023024999999999994, (5, 4): 0.0023287500000000005, (7, 4): 0.0023287500000000005, (17, 9): 0.0024, (8, 19): 0.00290375, (2, 8): 0.0023587499999999997, (5, 8): 0.00226125, (7, 1): 0.0024449999999999997, (1, 12): 0.0024449999999999997, (3, 7): 0.00230375, (1, 7): 0.0024449999999999997, (18, 1): 0.0027875, (14, 1): 0.0024724999999999994, (6, 4): 0.0023137500000000003, (15, 5): 0.0023287500000000005, (2, 3): 0.0024825, (13, 12): 0.0022487499999999994, (17, 11): 0.0023587499999999997, (0, 0): 0.00448, (6, 17): 0.00240375, (12, 6): 0.0022487499999999994, (6, 19): 0.0029050000000000005, (13, 16): 0.00233, (17, 2): 0.002545, (2, 0): 0.0031425, (15, 4): 0.0023725, (11, 13): 0.00226125, (17, 4): 0.00246125, (2, 13): 0.00240375, (10, 0): 0.0028712499999999997, (11, 18): 0.00242625, (1, 16): 0.00259, (18, 3): 0.00259, (14, 3): 0.00233625, (9, 16): 0.0023024999999999994, (2, 15): 0.00246125, (11, 12): 0.0022487500000000003, (1, 1): 0.0027875, (17, 10): 0.0024, (7, 0): 0.00292125, (8, 1): 0.00242625, (4, 3): 0.0024175, (19, 1): 0.0033275, (19, 2): 0.0031425, (3, 3): 0.0024825000000000003, (3, 15): 0.0024175, (2, 12): 0.00235375, (0, 4): 0.0029924999999999995, (5, 5): 0.002275, (1, 9): 0.002415, (10, 16): 0.0023024999999999994, (9, 15): 0.0022887500000000004, (14, 19): 0.0029287500000000004, (6, 7): 0.0022487499999999994, (2, 4): 0.00246125, (13, 10): 0.0022525000000000006, (9, 9): 0.0022375, (16, 4): 0.0024175, (3, 13): 0.00233, (1, 18): 0.0027875, (18, 18): 0.0027875, (11, 16): 0.00232625, (18, 17): 0.00265, (4, 18): 0.002502500000000001, (9, 19): 0.0028712499999999997, (11, 1): 0.00242625, (6, 11): 0.00226125, (0, 2): 0.0031425, (19, 5): 0.0029287500000000004, (11, 19): 0.00290375, (6, 18): 0.0024762499999999997, (10, 9): 0.0022375, (12, 17): 0.00235375, (8, 4): 0.0023037500000000002, (9, 18): 0.002415, (7, 2): 0.00235375, (13, 13): 0.0022775, (7, 14): 0.00227375, (12, 18): 0.0024449999999999997, (8, 18): 0.00242625, (13, 17): 0.00240375, (4, 8): 0.0023037500000000002, (5, 15): 0.0023287500000000005, (6, 10): 0.0022525000000000006, (16, 18): 0.00259, (6, 12): 0.0022487499999999994, (10, 5): 0.0022662500000000005, (5, 14): 0.002275, (12, 2): 0.00235375, (8, 16): 0.00232625, (12, 14): 0.00227375, (15, 10): 0.0022887500000000004, (1, 19): 0.0033275, (1, 13): 0.0024762499999999997, (7, 18): 0.0024449999999999997, (19, 13): 0.0029050000000000005, (1, 3): 0.00259, (18, 8): 0.00242625, (2, 16): 0.0024825, (16, 6): 0.00233, (15, 1): 0.002502500000000001, (1, 14): 0.0024724999999999994, (4, 19): 0.0029924999999999995, (5, 3): 0.00233625, (1, 6): 0.0024762499999999997, (0, 12): 0.00292125, (6, 14): 0.0023112500000000004, (12, 15): 0.0023287500000000005, (19, 4): 0.0029924999999999995, (5, 2): 0.0024375, (18, 12): 0.0024449999999999997, (2, 7): 0.00235375, (15, 3): 0.0024175, (0, 18): 0.0033275, (13, 9): 0.0022525000000000006, (19, 11): 0.00290375, (1, 10): 0.002415, (12, 16): 0.00230375, (10, 1): 0.002415, (4, 10): 0.0022887500000000004, (9, 4): 0.0022887500000000004, (17, 0): 0.0031425, (12, 9): 0.002215, (13, 11): 0.00226125, (4, 9): 0.0022887500000000004, (8, 13): 0.00226125, (0, 14): 0.0029287500000000004, (19, 18): 0.0033275, (8, 15): 0.0023037500000000002, (13, 18): 0.0024762499999999997, (12, 11): 0.0022487500000000003, (5, 1): 0.0024724999999999994, (0, 3): 0.00305625, (4, 5): 0.0023287500000000005, (11, 15): 0.0023037500000000002, (3, 19): 0.00305625, (8, 10): 0.00221375, (5, 11): 0.00226125, (16, 1): 0.00259, (11, 7): 0.0022487500000000003, (6, 6): 0.0022775, (7, 13): 0.0022487499999999994, (7, 16): 0.00230375, (13, 0): 0.0029050000000000005, (13, 6): 0.0022775, (14, 14): 0.002275, (1, 5): 0.0024724999999999994, (1, 8): 0.00242625, (15, 8): 0.0023037500000000002, (5, 18): 0.0024724999999999994, (0, 1): 0.0033275, (0, 10): 0.0028712499999999997, (13, 4): 0.0023137500000000003, (5, 17): 0.0024375, (17, 13): 0.00240375, (17, 3): 0.0024825, (10, 19): 0.0028712499999999997, (9, 11): 0.00221375, (6, 1): 0.0024762499999999997, (9, 3): 0.0023024999999999994, (2, 10): 0.0024, (11, 4): 0.0023037500000000002, (14, 11): 0.00226125, (13, 19): 0.0029050000000000005, (11, 10): 0.00221375, (8, 11): 0.0022, (9, 2): 0.0024, (10, 18): 0.002415, (14, 16): 0.00233625, (3, 16): 0.0024825000000000003, (4, 6): 0.0023137500000000003, (12, 1): 0.0024449999999999997, (11, 0): 0.00290375, (10, 11): 0.00221375, (13, 1): 0.0024762499999999997, (12, 8): 0.0022487500000000003, (10, 17): 0.0024, (0, 7): 0.00292125, (16, 3): 0.0024825000000000003, (3, 12): 0.00230375, (19, 9): 0.0028712499999999997, (8, 6): 0.00226125, (0, 8): 0.00290375, (11, 8): 0.0022, (16, 14): 0.00233625, (19, 8): 0.00290375, (19, 17): 0.0031425, (6, 9): 0.0022525000000000006, (12, 19): 0.00292125, (7, 7): 0.0022275000000000003, (12, 0): 0.00292125, (17, 17): 0.002545, (11, 17): 0.0023587499999999997, (8, 17): 0.0023587499999999997, (7, 11): 0.0022487500000000003, (10, 2): 0.0024, (16, 5): 0.00233625, (9, 1): 0.002415, (10, 6): 0.0022525000000000006, (8, 8): 0.0022, (3, 10): 0.0023024999999999994, (14, 12): 0.00227375, (3, 5): 0.00233625, (7, 15): 0.0023287500000000005, (8, 5): 0.00226125, (4, 2): 0.00246125, (13, 5): 0.0023112500000000004, (7, 8): 0.0022487500000000003, (8, 2): 0.0023587499999999997, (15, 13): 0.0023137500000000003, (15, 15): 0.0023725, (5, 19): 0.0029287500000000004, (16, 8): 0.00232625, (7, 12): 0.0022275000000000003, (0, 15): 0.0029924999999999995, (11, 5): 0.00226125, (10, 8): 0.00221375, (7, 6): 0.0022487499999999994, (7, 9): 0.002215, (14, 18): 0.0024724999999999994, (1, 4): 0.002502500000000001, (1, 2): 0.00265, (7, 19): 0.00292125, (15, 19): 0.0029924999999999995, (18, 14): 0.0024724999999999994, (4, 16): 0.0024175, (8, 3): 0.00232625, (9, 6): 0.0022525000000000006, (10, 12): 0.002215, (15, 0): 0.0029924999999999995, (9, 5): 0.0022662500000000005, (12, 4): 0.0023287500000000005, (3, 6): 0.00233, (15, 7): 0.0023287500000000005, (14, 4): 0.0023287500000000005, (5, 9): 0.0022662500000000005, (12, 5): 0.00227375, (5, 7): 0.00227375, (8, 14): 0.00226125, (9, 7): 0.002215, (16, 11): 0.00232625, (11, 6): 0.00226125, (9, 10): 0.0022375, (14, 9): 0.0022662500000000005, (12, 12): 0.0022275000000000003, (19, 0): 0.00448, (13, 14): 0.0023112500000000004, (12, 3): 0.00230375, (4, 17): 0.00246125, (4, 14): 0.0023287500000000005, (8, 12): 0.0022487500000000003, (17, 12): 0.00235375, (13, 2): 0.00240375, (6, 5): 0.0023112500000000004, (0, 9): 0.0028712499999999997, (14, 7): 0.00227375, (17, 14): 0.0024375, (16, 12): 0.00230375, (8, 9): 0.00221375, (11, 9): 0.00221375, (7, 17): 0.00235375, (18, 10): 0.002415, (19, 7): 0.00292125, (3, 4): 0.0024175, (18, 7): 0.0024449999999999997, (5, 6): 0.0023112500000000004}

N = 21
{(15, 4): 0.002125, (20, 14): 0.0027000000000000006, (9, 19): 0.0021949999999999995, (14, 6): 0.00209, (10, 1): 0.0022125, (8, 12): 0.002045, (5, 18): 0.0022025, (0, 18): 0.002865, (18, 14): 0.00217625, (10, 14): 0.00203, (7, 6): 0.002085, (5, 0): 0.0026925, (6, 8): 0.00204, (9, 14): 0.00205375, (10, 10): 0.00201, (6, 16): 0.002125, (18, 16): 0.0022425, (19, 1): 0.002535, (11, 8): 0.0020125, (14, 7): 0.002085, (12, 20): 0.0026400000000000004, (20, 0): 0.0040774999999999995, (5, 20): 0.0026925, (0, 20): 0.0040774999999999995, (5, 4): 0.002125, (13, 12): 0.0020512500000000006, (14, 13): 0.002085, (7, 4): 0.002135, (7, 17): 0.0021187499999999995, (19, 6): 0.00225, (15, 18): 0.0022025, (20, 1): 0.0030425000000000005, (15, 12): 0.0020787500000000003, (8, 15): 0.0020787500000000003, (20, 20): 0.0040774999999999995, (4, 0): 0.0027312500000000006, (7, 9): 0.0020625, (0, 0): 0.0040774999999999995, (2, 2): 0.00235, (1, 19): 0.002535, (16, 4): 0.00216, (16, 1): 0.00231875, (5, 2): 0.0022025, (15, 9): 0.0020800000000000003, (19, 8): 0.00222, (12, 9): 0.0020125, (5, 19): 0.0022775, (20, 9): 0.0026125, (4, 19): 0.00231875, (3, 7): 0.0021187499999999995, (6, 2): 0.00217625, (5, 12): 0.0020787500000000003, (6, 17): 0.002115, (15, 0): 0.0026925, (0, 17): 0.00278625, (16, 16): 0.00216, (15, 3): 0.002185, (17, 7): 0.0021187499999999995, (0, 2): 0.002865, (10, 8): 0.00203, (7, 19): 0.0022212500000000006, (11, 1): 0.0021949999999999995, (16, 17): 0.002175, (11, 0): 0.0026125, (16, 18): 0.0022425, (2, 10): 0.0021775, (12, 3): 0.0020975000000000004, (5, 17): 0.002185, (11, 16): 0.00207125, (12, 0): 0.0026400000000000004, (15, 6): 0.0020925, (5, 15): 0.0021325, (19, 3): 0.002385, (3, 0): 0.00278625, (8, 6): 0.00204, (10, 7): 0.0020625, (12, 2): 0.00216125, (6, 13): 0.002085, (0, 3): 0.00278625, (18, 8): 0.00216125, (17, 2): 0.0023024999999999994, (7, 7): 0.0020125, (15, 11): 0.0020800000000000003, (8, 18): 0.00216125, (18, 15): 0.0022025, (15, 7): 0.00206375, (11, 6): 0.00205375, (19, 11): 0.0021949999999999995, (18, 13): 0.0021349999999999997, (5, 16): 0.002125, (20, 8): 0.0026400000000000004, (3, 16): 0.002175, (1, 11): 0.0021949999999999995, (20, 3): 0.00278625, (17, 14): 0.002115, (0, 15): 0.0026925, (3, 14): 0.002115, (12, 19): 0.00222, (18, 11): 0.0021362499999999997, (2, 0): 0.002865, (4, 7): 0.002135, (4, 13): 0.002135, (3, 12): 0.0020975000000000004, (6, 9): 0.00205375, (19, 10): 0.0022125, (8, 19): 0.00222, (16, 14): 0.002125, (2, 1): 0.0024274999999999995, (5, 3): 0.002185, (11, 10): 0.0019950000000000002, (15, 14): 0.0020925, (4, 20): 0.0027312500000000006, (3, 1): 0.002385, (18, 0): 0.002865, (1, 9): 0.0021949999999999995, (3, 3): 0.0021775, (16, 20): 0.0027312500000000006, (5, 7): 0.00206375, (20, 18): 0.002865, (3, 19): 0.002385, (17, 13): 0.0021187499999999995, (19, 19): 0.002535, (19, 16): 0.00231875, (4, 6): 0.002125, (20, 10): 0.002645, (13, 13): 0.0020125, (0, 19): 0.0030425000000000005, (8, 14): 0.00204, (20, 6): 0.0027000000000000006, (10, 19): 0.0022125, (6, 15): 0.0020925, (18, 6): 0.00217625, (3, 20): 0.00278625, (15, 10): 0.0020275000000000002, (14, 0): 0.0027000000000000006, (18, 9): 0.0021362499999999997, (13, 7): 0.0020125, (17, 10): 0.0021075, (10, 5): 0.0020275000000000002, (9, 11): 0.0020225, (18, 20): 0.002865, (8, 20): 0.0026400000000000004, (16, 5): 0.002125, (15, 17): 0.002185, (4, 5): 0.002125, (9, 17): 0.0020962500000000005, (17, 12): 0.0020975000000000004, (17, 15): 0.002185, (9, 20): 0.0026125, (13, 10): 0.0020625, (13, 18): 0.0021349999999999997, (0, 1): 0.0030425000000000005, (16, 9): 0.00207125, (9, 1): 0.0021949999999999995, (6, 12): 0.00204, (3, 15): 0.002185, (3, 5): 0.002185, (20, 11): 0.0026125, (20, 7): 0.0026225, (11, 15): 0.0020800000000000003, (2, 11): 0.0021362499999999997, (20, 4): 0.0027312500000000006, (7, 2): 0.0021349999999999997, (17, 19): 0.002385, (10, 15): 0.0020275000000000002, (16, 11): 0.00207125, (16, 10): 0.0020749999999999996, (11, 9): 0.0020225, (3, 11): 0.0020962500000000005, (6, 19): 0.00225, (3, 8): 0.0020975000000000004, (16, 7): 0.002135, (5, 10): 0.0020275000000000002, (8, 11): 0.0020125, (19, 13): 0.0022212500000000006, (14, 1): 0.00225, (10, 2): 0.0021775, (4, 8): 0.00206125, (2, 8): 0.00216125, (0, 6): 0.0027000000000000006, (13, 15): 0.00206375, (14, 18): 0.00217625, (6, 18): 0.00217625, (6, 20): 0.0027000000000000006, (14, 4): 0.002125, (17, 5): 0.002185, (0, 5): 0.0026925, (1, 10): 0.0022125, (6, 1): 0.00225, (2, 17): 0.0023024999999999994, (17, 20): 0.00278625, (8, 9): 0.0020125, (0, 11): 0.0026125, (11, 13): 0.0020625, (7, 8): 0.0020512500000000006, (9, 12): 0.0020125, (14, 20): 0.0027000000000000006, (13, 17): 0.0021187499999999995, (7, 13): 0.0020125, (18, 18): 0.00235, (1, 2): 0.0024274999999999995, (16, 19): 0.00231875, (12, 15): 0.0020787500000000003, (5, 11): 0.0020800000000000003, (10, 11): 0.0019950000000000002, (19, 18): 0.0024274999999999995, (2, 18): 0.00235, (19, 7): 0.0022212500000000006, (18, 17): 0.0023024999999999994, (3, 18): 0.0023024999999999994, (9, 13): 0.0020625, (14, 11): 0.00205375, (15, 1): 0.0022775, (9, 0): 0.0026125, (16, 6): 0.002125, (14, 16): 0.002125, (6, 10): 0.00203, (8, 13): 0.0020512500000000006, (18, 1): 0.0024274999999999995, (16, 3): 0.002175, (2, 15): 0.0022025, (2, 20): 0.002865, (10, 3): 0.0021075, (1, 4): 0.00231875, (8, 8): 0.002045, (20, 17): 0.00278625, (16, 2): 0.0022425, (20, 13): 0.0026225, (3, 4): 0.002175, (4, 15): 0.002125, (9, 18): 0.0021362499999999997, (10, 9): 0.0019950000000000002, (12, 14): 0.00204, (19, 17): 0.002385, (17, 1): 0.002385, (14, 10): 0.00203, (0, 4): 0.0027312500000000006, (11, 2): 0.0021362499999999997, (20, 2): 0.002865, (0, 12): 0.0026400000000000004, (1, 20): 0.0030425000000000005, (1, 0): 0.0030425000000000005, (7, 18): 0.0021349999999999997, (20, 12): 0.0026400000000000004, (15, 20): 0.0026925, (7, 20): 0.0026225, (0, 7): 0.0026225, (17, 9): 0.0020962500000000005, (13, 20): 0.0026225, (4, 14): 0.002125, (11, 14): 0.00205375, (9, 3): 0.0020962500000000005, (12, 8): 0.002045, (9, 8): 0.0020125, (4, 3): 0.002175, (1, 3): 0.002385, (15, 15): 0.0021325, (1, 8): 0.00222, (16, 15): 0.002125, (9, 9): 0.0020225, (18, 3): 0.0023024999999999994, (13, 14): 0.002085, (8, 0): 0.0026400000000000004, (9, 10): 0.0019950000000000002, (9, 6): 0.00205375, (0, 9): 0.0026125, (11, 20): 0.0026125, (14, 5): 0.0020925, (12, 13): 0.0020512500000000006, (10, 13): 0.0020625, (15, 8): 0.0020787500000000003, (5, 5): 0.0021325, (1, 12): 0.00222, (8, 17): 0.0020975000000000004, (2, 3): 0.0023024999999999994, (4, 2): 0.0022425, (9, 5): 0.0020800000000000003, (17, 4): 0.002175, (15, 2): 0.0022025, (12, 1): 0.00222, (6, 3): 0.002115, (2, 6): 0.00217625, (12, 10): 0.00203, (11, 11): 0.0020225, (9, 7): 0.0020625, (8, 3): 0.0020975000000000004, (6, 5): 0.0020925, (0, 10): 0.002645, (14, 3): 0.002115, (12, 5): 0.0020787500000000003, (7, 3): 0.0021187499999999995, (2, 7): 0.0021349999999999997, (19, 0): 0.0030425000000000005, (19, 15): 0.0022775, (10, 17): 0.0021075, (9, 15): 0.0020800000000000003, (11, 12): 0.0020125, (5, 6): 0.0020925, (10, 20): 0.002645, (8, 4): 0.00206125, (18, 5): 0.0022025, (0, 8): 0.0026400000000000004, (1, 15): 0.0022775, (2, 19): 0.0024274999999999995, (14, 9): 0.00205375, (20, 5): 0.0026925, (1, 14): 0.00225, (13, 11): 0.0020625, (18, 7): 0.0021349999999999997, (3, 2): 0.0023024999999999994, (1, 5): 0.0022775, (12, 17): 0.0020975000000000004, (13, 0): 0.0026225, (4, 4): 0.00216, (14, 2): 0.00217625, (14, 15): 0.0020925, (13, 6): 0.002085, (16, 0): 0.0027312500000000006, (7, 0): 0.0026225, (3, 9): 0.0020962500000000005, (1, 7): 0.0022212500000000006, (17, 0): 0.00278625, (9, 16): 0.00207125, (7, 16): 0.002135, (3, 6): 0.002115, (13, 1): 0.0022212500000000006, (6, 14): 0.00209, (10, 4): 0.0020749999999999996, (19, 5): 0.0022775, (11, 17): 0.0020962500000000005, (8, 10): 0.00203, (13, 19): 0.0022212500000000006, (17, 6): 0.002115, (5, 1): 0.0022775, (15, 19): 0.0022775, (20, 19): 0.0030425000000000005, (15, 13): 0.00206375, (18, 19): 0.0024274999999999995, (8, 5): 0.0020787500000000003, (14, 8): 0.00204, (4, 1): 0.00231875, (1, 1): 0.002535, (17, 17): 0.0021775, (18, 4): 0.0022425, (2, 4): 0.0022425, (17, 3): 0.0021775, (7, 10): 0.0020625, (9, 4): 0.00207125, (1, 17): 0.002385, (1, 18): 0.0024274999999999995, (4, 9): 0.00207125, (10, 0): 0.002645, (19, 20): 0.0030425000000000005, (17, 11): 0.0020962500000000005, (11, 18): 0.0021362499999999997, (13, 16): 0.002135, (18, 10): 0.0021775, (20, 15): 0.0026925, (13, 8): 0.0020512500000000006, (3, 17): 0.0021775, (12, 16): 0.00206125, (11, 4): 0.00207125, (9, 2): 0.0021362499999999997, (10, 16): 0.0020749999999999996, (2, 9): 0.0021362499999999997, (7, 12): 0.0020512500000000006, (12, 18): 0.00216125, (17, 16): 0.002175, (8, 2): 0.00216125, (11, 3): 0.0020962500000000005, (7, 14): 0.002085, (18, 12): 0.00216125, (7, 5): 0.00206375, (1, 16): 0.00231875, (13, 3): 0.0021187499999999995, (2, 5): 0.0022025, (0, 14): 0.0027000000000000006, (13, 5): 0.00206375, (1, 13): 0.0022212500000000006, (14, 17): 0.002115, (4, 17): 0.002175, (14, 19): 0.00225, (7, 1): 0.0022212500000000006, (12, 7): 0.0020512500000000006, (16, 12): 0.00206125, (13, 2): 0.0021349999999999997, (6, 4): 0.002125, (6, 7): 0.002085, (2, 13): 0.0021349999999999997, (6, 0): 0.0027000000000000006, (19, 2): 0.0024274999999999995, (4, 16): 0.00216, (19, 12): 0.00222, (5, 9): 0.0020800000000000003, (5, 14): 0.0020925, (4, 18): 0.0022425, (3, 13): 0.0021187499999999995, (19, 14): 0.00225, (13, 4): 0.002135, (19, 9): 0.0021949999999999995, (2, 16): 0.0022425, (8, 16): 0.00206125, (17, 8): 0.0020975000000000004, (7, 15): 0.00206375, (5, 8): 0.0020787500000000003, (11, 19): 0.0021949999999999995, (18, 2): 0.00235, (6, 11): 0.00205375, (2, 12): 0.00216125, (8, 7): 0.0020512500000000006, (0, 13): 0.0026225, (16, 13): 0.002135, (0, 16): 0.0027312500000000006, (10, 6): 0.00203, (15, 5): 0.0021325, (7, 11): 0.0020625, (17, 18): 0.0023024999999999994, (10, 18): 0.0021775, (12, 4): 0.00206125, (15, 16): 0.002125, (20, 16): 0.0027312500000000006, (2, 14): 0.00217625, (1, 6): 0.00225, (8, 1): 0.00222, (5, 13): 0.00206375, (6, 6): 0.00209, (11, 7): 0.0020625, (4, 11): 0.00207125, (14, 14): 0.00209, (16, 8): 0.00206125, (10, 12): 0.00203, (13, 9): 0.0020625, (12, 11): 0.0020125, (4, 12): 0.00206125, (19, 4): 0.00231875, (12, 12): 0.002045, (14, 12): 0.00204, (3, 10): 0.0021075, (11, 5): 0.0020800000000000003, (12, 6): 0.00204, (4, 10): 0.0020749999999999996}

N = 22
{(16, 9): 0.0018787500000000002, (0, 4): 0.0024899999999999996, (1, 21): 0.0027800000000000004, (1, 12): 0.0020525000000000005, (10, 1): 0.00198375, (8, 14): 0.0018750000000000001, (18, 17): 0.0020062500000000007, (14, 2): 0.00199875, (15, 7): 0.0018624999999999998, (0, 5): 0.00248875, (6, 0): 0.00244875, (8, 2): 0.0019375000000000002, (15, 9): 0.0018875, (1, 14): 0.00204375, (0, 19): 0.0026400000000000004, (9, 14): 0.0018737500000000002, (4, 18): 0.0020062500000000007, (3, 20): 0.00217375, (19, 4): 0.0020325, (3, 21): 0.0025750000000000005, (20, 20): 0.00238, (8, 13): 0.0018650000000000001, (12, 3): 0.0019474999999999998, (2, 19): 0.0021400000000000004, (11, 2): 0.0019550000000000006, (14, 17): 0.0019275000000000002, (17, 3): 0.0020062500000000007, (1, 9): 0.0020525000000000005, (11, 20): 0.00198375, (0, 21): 0.00382, (17, 5): 0.00194125, (20, 8): 0.0020375, (5, 21): 0.00248875, (2, 6): 0.0019925, (10, 14): 0.00184375, (7, 13): 0.0018750000000000001, (0, 14): 0.0024187500000000003, (19, 3): 0.00209125, (6, 7): 0.0018624999999999998, (18, 13): 0.0019524999999999998, (11, 10): 0.0018475000000000002, (8, 11): 0.00187, (18, 9): 0.0019474999999999998, (8, 10): 0.00187, (1, 20): 0.00238, (4, 2): 0.0020325, (7, 0): 0.0024187500000000003, (2, 0): 0.0026400000000000004, (14, 9): 0.0018737500000000002, (15, 0): 0.00244875, (14, 19): 0.00199875, (5, 0): 0.00248875, (2, 9): 0.00195625, (3, 4): 0.0020062500000000007, (9, 3): 0.0019474999999999998, (21, 0): 0.00382, (15, 2): 0.0019925, (5, 2): 0.0020362500000000003, (9, 9): 0.0018349999999999998, (21, 13): 0.0024412499999999994, (1, 0): 0.0027800000000000004, (5, 9): 0.0018787500000000002, (7, 15): 0.0018624999999999998, (18, 1): 0.00217375, (2, 5): 0.0020362500000000003, (13, 13): 0.0018650000000000001, (14, 8): 0.0018750000000000001, (14, 21): 0.0024187500000000003, (0, 17): 0.0024899999999999996, (14, 10): 0.00184375, (12, 11): 0.001835, (1, 11): 0.00198375, (20, 7): 0.00204375, (19, 17): 0.0020325, (9, 11): 0.001835, (13, 10): 0.00187, (20, 6): 0.00206125, (4, 19): 0.0020325, (20, 19): 0.00222375, (19, 5): 0.0020362500000000003, (4, 3): 0.0020062500000000007, (16, 2): 0.0020362500000000003, (16, 18): 0.00198375, (8, 21): 0.0024412499999999994, (0, 8): 0.0024412499999999994, (11, 1): 0.00198375, (15, 21): 0.00244875, (14, 4): 0.0019275000000000002, (10, 8): 0.00187, (0, 18): 0.0025750000000000005, (10, 20): 0.00198375, (15, 19): 0.0019925, (11, 21): 0.0024099999999999994, (15, 17): 0.0019275000000000002, (17, 14): 0.0019275000000000002, (10, 19): 0.0019550000000000006, (13, 1): 0.0020375, (19, 19): 0.0021400000000000004, (21, 2): 0.0026400000000000004, (14, 13): 0.0018750000000000001, (13, 16): 0.0018899999999999998, (0, 2): 0.0026400000000000004, (13, 2): 0.0019375000000000002, (13, 11): 0.00187, (19, 6): 0.0019925, (20, 18): 0.00217375, (6, 11): 0.0018624999999999998, (17, 21): 0.0024899999999999996, (7, 21): 0.0024187500000000003, (10, 21): 0.0024099999999999994, (11, 0): 0.0024099999999999994, (11, 11): 0.0018475000000000002, (6, 21): 0.00244875, (20, 12): 0.0020525000000000005, (21, 18): 0.0025750000000000005, (13, 5): 0.0018899999999999998, (21, 20): 0.0027800000000000004, (3, 17): 0.0020062500000000007, (6, 18): 0.0019624999999999994, (3, 19): 0.00209125, (18, 19): 0.00209125, (16, 8): 0.0018899999999999998, (3, 14): 0.00194125, (16, 19): 0.0020362500000000003, (1, 10): 0.00198375, (13, 19): 0.0019375000000000002, (9, 10): 0.001835, (21, 17): 0.0024899999999999996, (15, 13): 0.0018724999999999996, (15, 8): 0.0018724999999999996, (18, 11): 0.0019349999999999997, (1, 18): 0.00217375, (18, 21): 0.0025750000000000005, (6, 2): 0.0019925, (12, 20): 0.0020525000000000005, (15, 1): 0.00206125, (21, 21): 0.00382, (9, 2): 0.00195625, (19, 12): 0.00195625, (2, 7): 0.00199875, (4, 13): 0.00191, (9, 4): 0.0019050000000000002, (8, 19): 0.0019375000000000002, (19, 21): 0.0026400000000000004, (12, 17): 0.0019050000000000002, (20, 3): 0.00217375, (2, 8): 0.0019375000000000002, (16, 20): 0.0020675000000000003, (16, 1): 0.0020675000000000003, (0, 13): 0.0024412499999999994, (18, 5): 0.00198375, (17, 11): 0.00188375, (1, 4): 0.00215125, (11, 19): 0.0019550000000000006, (10, 12): 0.001835, (4, 4): 0.0019875, (13, 0): 0.0024412499999999994, (6, 3): 0.0019624999999999994, (4, 17): 0.0019875, (17, 17): 0.0019875, (7, 6): 0.0018624999999999998, (16, 10): 0.0018575, (17, 16): 0.00194125, (20, 2): 0.00222375, (14, 1): 0.00204375, (13, 15): 0.0018724999999999996, (21, 4): 0.0024899999999999996, (20, 0): 0.0027800000000000004, (9, 15): 0.0018875, (0, 7): 0.0024187500000000003, (9, 7): 0.0018737500000000002, (13, 20): 0.0020375, (17, 0): 0.0024899999999999996, (9, 20): 0.0020525000000000005, (8, 9): 0.0018524999999999998, (11, 3): 0.0019349999999999997, (21, 14): 0.0024187500000000003, (21, 6): 0.00244875, (21, 16): 0.00248875, (13, 3): 0.0019524999999999998, (17, 20): 0.00215125, (10, 4): 0.00188375, (4, 1): 0.00215125, (12, 16): 0.0018787500000000002, (11, 18): 0.0019349999999999997, (7, 12): 0.0018737500000000002, (6, 1): 0.00206125, (14, 5): 0.0019025, (10, 5): 0.0018575, (1, 16): 0.0020675000000000003, (21, 3): 0.0025750000000000005, (2, 2): 0.0021400000000000004, (3, 0): 0.0025750000000000005, (9, 12): 0.0018349999999999998, (12, 9): 0.0018349999999999998, (21, 11): 0.0024099999999999994, (2, 12): 0.00195625, (2, 17): 0.0020325, (10, 15): 0.0018624999999999998, (17, 2): 0.0020325, (5, 13): 0.0018899999999999998, (18, 12): 0.0019474999999999998, (8, 15): 0.0018724999999999996, (5, 8): 0.0018899999999999998, (6, 19): 0.0019925, (1, 5): 0.0020675000000000003, (6, 17): 0.0019275000000000002, (13, 9): 0.0018524999999999998, (13, 18): 0.0019524999999999998, (19, 18): 0.00209125, (13, 4): 0.00191, (8, 7): 0.0018750000000000001, (5, 1): 0.0020675000000000003, (10, 0): 0.0024099999999999994, (9, 0): 0.0024325, (17, 18): 0.0020062500000000007, (4, 20): 0.00215125, (20, 5): 0.0020675000000000003, (11, 14): 0.00184375, (11, 17): 0.00188375, (19, 2): 0.0021400000000000004, (2, 11): 0.0019550000000000006, (7, 7): 0.0018800000000000002, (4, 14): 0.0019275000000000002, (5, 20): 0.0020675000000000003, (0, 10): 0.0024099999999999994, (11, 9): 0.001835, (6, 16): 0.00190625, (6, 10): 0.0018624999999999998, (8, 0): 0.0024412499999999994, (19, 15): 0.0019925, (3, 18): 0.00205, (13, 12): 0.0018524999999999998, (6, 8): 0.0018724999999999996, (14, 14): 0.0018800000000000002, (3, 8): 0.0019524999999999998, (7, 1): 0.00204375, (0, 12): 0.0024325, (16, 21): 0.00248875, (0, 11): 0.0024099999999999994, (20, 4): 0.00215125, (11, 12): 0.001835, (8, 3): 0.0019524999999999998, (5, 12): 0.0018787500000000002, (8, 12): 0.0018524999999999998, (9, 5): 0.0018787500000000002, (0, 6): 0.00244875, (2, 10): 0.0019550000000000006, (20, 21): 0.0027800000000000004, (21, 12): 0.0024325, (3, 7): 0.00194125, (12, 10): 0.001835, (0, 0): 0.00382, (17, 12): 0.0019050000000000002, (21, 10): 0.0024099999999999994, (20, 16): 0.0020675000000000003, (19, 9): 0.00195625, (7, 16): 0.0019025, (11, 7): 0.00184375, (9, 16): 0.0018787500000000002, (10, 18): 0.0019349999999999997, (8, 5): 0.0018899999999999998, (1, 3): 0.00217375, (17, 13): 0.00191, (6, 5): 0.00190625, (3, 1): 0.00217375, (4, 16): 0.00194125, (0, 3): 0.0025750000000000005, (19, 14): 0.00199875, (3, 10): 0.0019349999999999997, (2, 4): 0.0020325, (12, 21): 0.0024325, (1, 8): 0.0020375, (7, 9): 0.0018737500000000002, (7, 20): 0.00204375, (12, 5): 0.0018787500000000002, (14, 16): 0.0019025, (8, 1): 0.0020375, (7, 2): 0.00199875, (20, 11): 0.00198375, (4, 0): 0.0024899999999999996, (6, 6): 0.0019075, (14, 3): 0.00194125, (5, 10): 0.0018575, (15, 10): 0.0018624999999999998, (18, 20): 0.00217375, (5, 17): 0.00194125, (6, 20): 0.00206125, (20, 17): 0.00215125, (15, 6): 0.0019075, (3, 15): 0.0019624999999999994, (19, 20): 0.00222375, (5, 15): 0.00190625, (12, 1): 0.0020525000000000005, (19, 8): 0.0019375000000000002, (13, 8): 0.0018650000000000001, (11, 5): 0.0018575, (0, 20): 0.0027800000000000004, (4, 12): 0.0019050000000000002, (5, 4): 0.00194125, (18, 16): 0.00198375, (6, 13): 0.0018724999999999996, (4, 15): 0.0019275000000000002, (10, 17): 0.00188375, (3, 13): 0.0019524999999999998, (21, 9): 0.0024325, (0, 15): 0.00244875, (19, 7): 0.00199875, (1, 13): 0.0020375, (18, 18): 0.00205, (3, 3): 0.00205, (7, 8): 0.0018750000000000001, (13, 21): 0.0024412499999999994, (17, 9): 0.0019050000000000002, (20, 10): 0.00198375, (9, 17): 0.0019050000000000002, (14, 11): 0.00184375, (15, 15): 0.0019075, (1, 2): 0.00222375, (1, 19): 0.00222375, (5, 6): 0.00190625, (12, 8): 0.0018524999999999998, (16, 7): 0.0019025, (18, 10): 0.0019349999999999997, (21, 1): 0.0027800000000000004, (16, 17): 0.00194125, (15, 3): 0.0019624999999999994, (11, 4): 0.00188375, (1, 1): 0.00238, (21, 15): 0.00244875, (9, 6): 0.0018875, (0, 16): 0.00248875, (20, 1): 0.00238, (1, 6): 0.00206125, (12, 13): 0.0018524999999999998, (17, 15): 0.0019275000000000002, (16, 4): 0.00194125, (15, 11): 0.0018624999999999998, (7, 11): 0.00184375, (21, 5): 0.00248875, (4, 21): 0.0024899999999999996, (6, 12): 0.0018875, (2, 14): 0.00199875, (3, 16): 0.00198375, (20, 9): 0.0020525000000000005, (9, 1): 0.0020525000000000005, (12, 4): 0.0019050000000000002, (15, 14): 0.0018624999999999998, (7, 18): 0.00194125, (16, 6): 0.00190625, (17, 19): 0.0020325, (9, 19): 0.00195625, (2, 1): 0.00222375, (11, 15): 0.0018624999999999998, (8, 18): 0.0019524999999999998, (13, 17): 0.00191, (7, 17): 0.0019275000000000002, (20, 15): 0.00206125, (3, 9): 0.0019474999999999998, (5, 16): 0.0018874999999999999, (11, 6): 0.0018624999999999998, (2, 15): 0.0019925, (5, 11): 0.0018575, (10, 10): 0.0018475000000000002, (13, 6): 0.0018724999999999996, (8, 4): 0.00191, (7, 14): 0.0018800000000000002, (6, 15): 0.0019075, (4, 5): 0.00194125, (4, 10): 0.00188375, (1, 15): 0.00206125, (0, 1): 0.0027800000000000004, (4, 11): 0.00188375, (14, 18): 0.00194125, (14, 0): 0.0024187500000000003, (10, 6): 0.0018624999999999998, (21, 7): 0.0024187500000000003, (10, 11): 0.0018475000000000002, (16, 5): 0.0018874999999999999, (4, 6): 0.0019275000000000002, (4, 7): 0.0019275000000000002, (8, 17): 0.00191, (13, 14): 0.0018750000000000001, (6, 9): 0.0018875, (8, 6): 0.0018724999999999996, (2, 18): 0.00209125, (7, 19): 0.00199875, (18, 6): 0.0019624999999999994, (3, 5): 0.00198375, (14, 15): 0.0018624999999999998, (18, 2): 0.00209125, (18, 7): 0.00194125, (2, 20): 0.00222375, (20, 14): 0.00204375, (12, 0): 0.0024325, (3, 12): 0.0019474999999999998, (15, 16): 0.00190625, (6, 4): 0.0019275000000000002, (19, 16): 0.0020362500000000003, (12, 6): 0.0018875, (18, 15): 0.0019624999999999994, (19, 1): 0.00222375, (14, 12): 0.0018737500000000002, (19, 11): 0.0019550000000000006, (11, 8): 0.00187, (4, 8): 0.00191, (5, 14): 0.0019025, (17, 7): 0.0019275000000000002, (8, 8): 0.0018650000000000001, (12, 14): 0.0018737500000000002, (5, 7): 0.0019025, (16, 0): 0.00248875, (19, 0): 0.0026400000000000004, (12, 7): 0.0018737500000000002, (5, 5): 0.0018874999999999999, (2, 21): 0.0026400000000000004, (10, 9): 0.001835, (5, 18): 0.00198375, (4, 9): 0.0019050000000000002, (10, 2): 0.0019550000000000006, (0, 9): 0.0024325, (9, 13): 0.0018524999999999998, (3, 6): 0.0019624999999999994, (12, 15): 0.0018875, (10, 16): 0.0018575, (18, 14): 0.00194125, (10, 13): 0.00187, (18, 4): 0.0020062500000000007, (17, 6): 0.0019275000000000002, (2, 16): 0.0020362500000000003, (12, 19): 0.00195625, (17, 8): 0.00191, (16, 3): 0.00198375, (1, 17): 0.00215125, (10, 7): 0.00184375, (16, 16): 0.0018874999999999999, (21, 19): 0.0026400000000000004, (18, 3): 0.00205, (18, 0): 0.0025750000000000005, (17, 10): 0.00188375, (2, 3): 0.00209125, (19, 10): 0.0019550000000000006, (15, 5): 0.00190625, (19, 13): 0.0019375000000000002, (11, 16): 0.0018575, (18, 8): 0.0019524999999999998, (21, 8): 0.0024412499999999994, (10, 3): 0.0019349999999999997, (5, 19): 0.0020362500000000003, (12, 12): 0.0018349999999999998, (16, 14): 0.0019025, (12, 18): 0.0019474999999999998, (7, 5): 0.0019025, (16, 13): 0.0018899999999999998, (20, 13): 0.0020375, (16, 11): 0.0018575, (3, 11): 0.0019349999999999997, (6, 14): 0.0018624999999999998, (8, 20): 0.0020375, (1, 7): 0.00204375, (14, 20): 0.00204375, (5, 3): 0.00198375, (17, 4): 0.0019875, (2, 13): 0.0019375000000000002, (15, 4): 0.0019275000000000002, (7, 4): 0.0019275000000000002, (9, 8): 0.0018524999999999998, (7, 3): 0.00194125, (14, 6): 0.0018624999999999998, (9, 21): 0.0024325, (12, 2): 0.00195625, (9, 18): 0.0019474999999999998, (16, 12): 0.0018787500000000002, (16, 15): 0.00190625, (14, 7): 0.0018800000000000002, (3, 2): 0.00209125, (13, 7): 0.0018750000000000001, (15, 12): 0.0018875, (17, 1): 0.00215125, (15, 20): 0.00206125, (15, 18): 0.0019624999999999994, (8, 16): 0.0018899999999999998, (11, 13): 0.00187, (7, 10): 0.00184375}

N = 23
{(21, 19): 0.0019850000000000002, (4, 17): 0.0017925000000000003, (9, 17): 0.0017300000000000002, (17, 12): 0.0017199999999999997, (6, 0): 0.0022562499999999996, (0, 1): 0.0025799999999999994, (15, 19): 0.00179, (12, 2): 0.0018312499999999998, (22, 3): 0.00238, (11, 14): 0.0016825, (13, 21): 0.0018425000000000002, (16, 16): 0.001715, (21, 18): 0.0019437500000000006, (0, 4): 0.0023225, (0, 15): 0.00222875, (8, 14): 0.0017025, (18, 8): 0.0017599999999999996, (12, 3): 0.0017649999999999996, (0, 16): 0.0022562499999999996, (15, 4): 0.0017700000000000003, (10, 14): 0.0016950000000000001, (6, 5): 0.0017525000000000004, (9, 10): 0.0016937500000000004, (15, 6): 0.0017549999999999998, (0, 0): 0.0034925, (16, 11): 0.001715, (17, 20): 0.00189375, (5, 4): 0.0017925000000000003, (18, 4): 0.0018050000000000002, (12, 10): 0.0016575000000000001, (0, 3): 0.00238, (21, 5): 0.0019050000000000002, (15, 11): 0.0017000000000000001, (21, 21): 0.0021325, (14, 11): 0.0016825, (22, 18): 0.0023225, (8, 2): 0.0017975000000000003, (3, 11): 0.0017375, (4, 20): 0.0018812500000000005, (12, 0): 0.0021900000000000005, (14, 13): 0.0017024999999999996, (3, 6): 0.0018175, (10, 5): 0.0017199999999999997, (21, 12): 0.0018625, (2, 20): 0.0020325, (11, 16): 0.001715, (17, 1): 0.0019050000000000002, (15, 1): 0.0018612500000000003, (3, 13): 0.0017837500000000002, (19, 8): 0.0017724999999999998, (12, 1): 0.0018625, (8, 18): 0.0017599999999999996, (2, 22): 0.0024187499999999995, (15, 20): 0.0018187499999999996, (13, 2): 0.0018187499999999996, (10, 9): 0.0016937500000000004, (11, 7): 0.0017000000000000001, (8, 15): 0.0017075000000000003, (20, 7): 0.0018187499999999996, (14, 21): 0.00187875, (6, 10): 0.0017175, (0, 12): 0.0021900000000000005, (19, 14): 0.0017724999999999998, (13, 4): 0.00174875, (16, 10): 0.0017175, (15, 21): 0.0018612500000000003, (13, 17): 0.0017300000000000002, (5, 6): 0.0017525000000000004, (1, 7): 0.0018612500000000003, (14, 20): 0.0017975000000000003, (6, 9): 0.0017212500000000001, (1, 22): 0.0025799999999999994, (22, 21): 0.0025799999999999994, (18, 20): 0.0018812500000000005, (15, 15): 0.0017125, (2, 18): 0.0018812500000000005, (19, 3): 0.00194, (4, 4): 0.0018050000000000002, (13, 10): 0.0016937500000000004, (15, 2): 0.0018187499999999996, (0, 18): 0.0023225, (4, 7): 0.0017700000000000003, (2, 17): 0.00189375, (3, 14): 0.0017724999999999998, (13, 6): 0.0017212500000000001, (2, 0): 0.0024187499999999995, (20, 8): 0.0017975000000000003, (10, 7): 0.0017037500000000002, (16, 21): 0.0019287500000000001, (21, 8): 0.00187875, (11, 15): 0.0017000000000000001, (19, 18): 0.0018687500000000002, (3, 18): 0.0018687500000000002, (10, 12): 0.0016575000000000001, (21, 7): 0.0018612500000000003, (8, 9): 0.0017024999999999996, (4, 15): 0.0017700000000000003, (14, 22): 0.00221625, (1, 14): 0.00187875, (16, 13): 0.0017212500000000001, (7, 20): 0.0018187499999999996, (17, 2): 0.00189375, (10, 16): 0.0017175, (14, 12): 0.0016950000000000001, (7, 1): 0.0018612500000000003, (15, 18): 0.0017700000000000003, (22, 15): 0.00222875, (13, 1): 0.0018425000000000002, (5, 12): 0.0017199999999999997, (18, 2): 0.0018812500000000005, (20, 11): 0.0017825, (3, 0): 0.00238, (3, 12): 0.0017649999999999996, (21, 2): 0.00203875, (18, 14): 0.0017599999999999996, (17, 13): 0.0017300000000000002, (1, 17): 0.0019050000000000002, (20, 6): 0.0018637500000000004, (5, 20): 0.00189375, (13, 7): 0.00171875, (19, 12): 0.0017649999999999996, (22, 2): 0.0024187499999999995, (9, 1): 0.0018425000000000002, (4, 5): 0.0017925000000000003, (6, 19): 0.0018175, (13, 15): 0.00171875, (12, 12): 0.0016575000000000001, (7, 5): 0.0017350000000000002, (17, 5): 0.0017525, (8, 22): 0.00221625, (3, 22): 0.00238, (22, 9): 0.00221125, (2, 19): 0.00192, (21, 15): 0.0018612500000000003, (17, 15): 0.0017350000000000002, (2, 6): 0.0018637500000000004, (10, 1): 0.0018625, (6, 17): 0.0017525000000000004, (14, 9): 0.0017024999999999996, (20, 21): 0.00203875, (5, 7): 0.0017350000000000002, (17, 22): 0.002285, (11, 3): 0.0017375, (8, 10): 0.0016950000000000001, (14, 15): 0.0017075000000000003, (12, 21): 0.0018625, (22, 20): 0.0024187499999999995, (3, 2): 0.00192, (8, 6): 0.00172625, (14, 1): 0.00187875, (22, 4): 0.0023225, (22, 13): 0.00221125, (15, 7): 0.0017125, (6, 7): 0.0017549999999999998, (13, 16): 0.0017212500000000001, (3, 15): 0.00179, (8, 3): 0.0017724999999999998, (7, 8): 0.0017075000000000003, (6, 18): 0.0017962499999999995, (12, 4): 0.0017424999999999997, (16, 17): 0.0017525000000000004, (16, 2): 0.0018637500000000004, (13, 13): 0.0017000000000000001, (20, 0): 0.0024187499999999995, (1, 6): 0.0019287500000000001, (18, 17): 0.0017925000000000003, (17, 9): 0.0017300000000000002, (22, 6): 0.0022562499999999996, (15, 22): 0.00222875, (1, 1): 0.0021325, (0, 22): 0.0034925, (15, 5): 0.0017350000000000002, (10, 21): 0.0018625, (9, 20): 0.0018187499999999996, (17, 6): 0.0017525000000000004, (19, 4): 0.0018687500000000002, (22, 11): 0.00219, (11, 2): 0.0017825, (8, 19): 0.0017724999999999998, (4, 1): 0.0019437500000000006, (13, 9): 0.0017000000000000001, (17, 8): 0.00174125, (17, 19): 0.0018187500000000005, (18, 0): 0.0023225, (1, 3): 0.0019850000000000002, (1, 8): 0.00187875, (0, 11): 0.00219, (22, 17): 0.002285, (16, 5): 0.0017525000000000004, (19, 16): 0.0018175, (20, 5): 0.00189375, (9, 11): 0.0017175, (12, 22): 0.0021900000000000005, (17, 17): 0.0017525, (9, 18): 0.00174875, (20, 1): 0.00203875, (6, 4): 0.0017962499999999995, (5, 21): 0.0019050000000000002, (12, 5): 0.0017199999999999997, (6, 22): 0.0022562499999999996, (8, 0): 0.00221625, (20, 16): 0.0018637500000000004, (12, 13): 0.0016937500000000004, (0, 6): 0.0022562499999999996, (1, 20): 0.00203875, (8, 13): 0.0017024999999999996, (14, 6): 0.00172625, (18, 6): 0.0017962499999999995, (0, 19): 0.00238, (13, 8): 0.0017024999999999996, (1, 10): 0.0018625, (18, 5): 0.0017925000000000003, (14, 3): 0.0017724999999999998, (21, 20): 0.00203875, (22, 14): 0.00221625, (0, 14): 0.00221625, (19, 9): 0.0017837500000000002, (20, 22): 0.0024187499999999995, (8, 7): 0.0017075000000000003, (9, 8): 0.0017024999999999996, (2, 14): 0.0017975000000000003, (10, 22): 0.0021900000000000005, (12, 11): 0.0016725, (19, 22): 0.00238, (1, 18): 0.0019437500000000006, (19, 2): 0.00192, (7, 2): 0.0018187499999999996, (3, 1): 0.0019850000000000002, (16, 0): 0.0022562499999999996, (7, 22): 0.00222875, (2, 13): 0.0018187499999999996, (6, 2): 0.0018637500000000004, (13, 11): 0.0017175, (2, 4): 0.0018812500000000005, (2, 15): 0.0018187499999999996, (13, 22): 0.00221125, (1, 0): 0.0025799999999999994, (16, 7): 0.0017549999999999998, (19, 0): 0.00238, (18, 22): 0.0023225, (9, 19): 0.0017837500000000002, (22, 8): 0.00221625, (8, 5): 0.00174125, (15, 12): 0.0017037500000000002, (22, 0): 0.0034925, (2, 7): 0.0018187499999999996, (3, 3): 0.00194, (20, 19): 0.00192, (10, 19): 0.0017649999999999996, (3, 4): 0.0018687500000000002, (1, 16): 0.0019287500000000001, (16, 9): 0.0017212500000000001, (15, 0): 0.00222875, (1, 11): 0.0018275000000000001, (2, 16): 0.0018637500000000004, (11, 22): 0.00219, (11, 20): 0.0017825, (4, 9): 0.00174875, (17, 7): 0.0017350000000000002, (20, 15): 0.0018187499999999996, (18, 13): 0.00174875, (19, 5): 0.0018187500000000005, (18, 9): 0.00174875, (11, 0): 0.00219, (18, 18): 0.0018050000000000002, (15, 16): 0.0017549999999999998, (4, 13): 0.00174875, (4, 14): 0.0017599999999999996, (7, 19): 0.00179, (22, 22): 0.0034925, (11, 11): 0.00174, (14, 2): 0.0017975000000000003, (10, 11): 0.0016725, (12, 17): 0.0017199999999999997, (16, 4): 0.0017962499999999995, (6, 8): 0.00172625, (3, 19): 0.00194, (21, 1): 0.0021325, (15, 8): 0.0017075000000000003, (3, 21): 0.0019850000000000002, (11, 1): 0.0018275000000000001, (5, 13): 0.0017300000000000002, (3, 17): 0.0018187500000000005, (10, 13): 0.0016937500000000004, (2, 5): 0.00189375, (19, 10): 0.0017649999999999996, (18, 21): 0.0019437500000000006, (2, 3): 0.00192, (7, 6): 0.0017549999999999998, (7, 15): 0.0017125, (8, 1): 0.00187875, (14, 10): 0.0016950000000000001, (5, 5): 0.0017525, (4, 0): 0.0023225, (5, 22): 0.002285, (11, 5): 0.00176, (8, 8): 0.0017025, (18, 1): 0.0019437500000000006, (18, 11): 0.00174, (9, 22): 0.00221125, (7, 7): 0.0017125, (18, 16): 0.0017962499999999995, (6, 21): 0.0019287500000000001, (19, 20): 0.00192, (11, 9): 0.0017175, (20, 20): 0.0020325, (14, 5): 0.00174125, (16, 18): 0.0017962499999999995, (2, 10): 0.0018312499999999998, (5, 1): 0.0019050000000000002, (7, 17): 0.0017350000000000002, (11, 17): 0.00176, (16, 3): 0.0018175, (12, 16): 0.0017175, (4, 18): 0.0018050000000000002, (16, 14): 0.00172625, (5, 11): 0.00176, (13, 20): 0.0018187499999999996, (10, 20): 0.0018312499999999998, (10, 18): 0.0017424999999999997, (0, 20): 0.0024187499999999995, (4, 19): 0.0018687500000000002, (8, 12): 0.0016950000000000001, (12, 8): 0.0016950000000000001, (7, 11): 0.0017000000000000001, (9, 12): 0.0016937500000000004, (10, 15): 0.0017037500000000002, (17, 16): 0.0017525000000000004, (0, 17): 0.002285, (22, 12): 0.0021900000000000005, (5, 3): 0.0018187500000000005, (19, 1): 0.0019850000000000002, (5, 19): 0.0018187500000000005, (3, 16): 0.0018175, (5, 0): 0.002285, (20, 14): 0.0017975000000000003, (7, 21): 0.0018612500000000003, (0, 2): 0.0024187499999999995, (8, 11): 0.0016825, (11, 13): 0.0017175, (11, 4): 0.00174, (13, 5): 0.0017300000000000002, (21, 13): 0.0018425000000000002, (4, 12): 0.0017424999999999997, (6, 12): 0.0017175, (5, 18): 0.0017925000000000003, (21, 16): 0.0019287500000000001, (12, 6): 0.0017175, (9, 21): 0.0018425000000000002, (4, 22): 0.0023225, (10, 10): 0.0016575000000000001, (22, 19): 0.00238, (0, 9): 0.00221125, (6, 20): 0.0018637500000000004, (6, 1): 0.0019287500000000001, (21, 6): 0.0019287500000000001, (8, 17): 0.00174125, (17, 0): 0.002285, (17, 21): 0.0019050000000000002, (16, 8): 0.00172625, (15, 9): 0.00171875, (18, 7): 0.0017700000000000003, (3, 5): 0.0018187500000000005, (2, 9): 0.0018187499999999996, (18, 15): 0.0017700000000000003, (7, 16): 0.0017549999999999998, (1, 13): 0.0018425000000000002, (11, 19): 0.0017375, (15, 3): 0.00179, (2, 8): 0.0017975000000000003, (20, 10): 0.0018312499999999998, (19, 11): 0.0017375, (5, 15): 0.0017350000000000002, (21, 4): 0.0019437500000000006, (2, 1): 0.00203875, (7, 18): 0.0017700000000000003, (15, 17): 0.0017350000000000002, (1, 12): 0.0018625, (7, 3): 0.00179, (13, 0): 0.00221125, (0, 10): 0.0021900000000000005, (5, 14): 0.00174125, (7, 14): 0.0017075000000000003, (12, 14): 0.0016950000000000001, (4, 16): 0.0017962499999999995, (22, 16): 0.0022562499999999996, (9, 3): 0.0017837500000000002, (3, 7): 0.00179, (9, 6): 0.0017212500000000001, (4, 2): 0.0018812500000000005, (12, 18): 0.0017424999999999997, (17, 11): 0.00176, (21, 11): 0.0018275000000000001, (20, 2): 0.0020325, (16, 22): 0.0022562499999999996, (17, 4): 0.0017925000000000003, (7, 9): 0.00171875, (5, 16): 0.0017525000000000004, (3, 20): 0.00192, (0, 7): 0.00222875, (19, 7): 0.00179, (0, 5): 0.002285, (16, 6): 0.001715, (14, 4): 0.0017599999999999996, (2, 21): 0.00203875, (4, 21): 0.0019437500000000006, (12, 19): 0.0017649999999999996, (17, 10): 0.0017199999999999997, (6, 6): 0.001715, (7, 4): 0.0017700000000000003, (6, 3): 0.0018175, (2, 2): 0.0020325, (16, 19): 0.0018175, (10, 2): 0.0018312499999999998, (0, 21): 0.0025799999999999994, (1, 9): 0.0018425000000000002, (7, 0): 0.00222875, (11, 8): 0.0016825, (4, 10): 0.0017424999999999997, (1, 19): 0.0019850000000000002, (1, 4): 0.0019437500000000006, (21, 14): 0.00187875, (5, 17): 0.0017525, (20, 17): 0.00189375, (22, 1): 0.0025799999999999994, (9, 13): 0.0017000000000000001, (22, 5): 0.002285, (11, 18): 0.00174, (10, 0): 0.0021900000000000005, (6, 16): 0.001715, (14, 8): 0.0017025, (20, 9): 0.0018187499999999996, (17, 18): 0.0017925000000000003, (3, 9): 0.0017837500000000002, (12, 9): 0.0016937500000000004, (20, 4): 0.0018812500000000005, (14, 16): 0.00172625, (22, 10): 0.0021900000000000005, (4, 3): 0.0018687500000000002, (14, 19): 0.0017724999999999998, (21, 10): 0.0018625, (21, 22): 0.0025799999999999994, (15, 10): 0.0017037500000000002, (19, 17): 0.0018187500000000005, (15, 13): 0.00171875, (10, 4): 0.0017424999999999997, (9, 5): 0.0017300000000000002, (2, 12): 0.0018312499999999998, (10, 6): 0.0017175, (6, 15): 0.0017549999999999998, (5, 8): 0.00174125, (22, 7): 0.00222875, (4, 6): 0.0017962499999999995, (3, 8): 0.0017724999999999998, (6, 14): 0.00172625, (21, 9): 0.0018425000000000002, (14, 7): 0.0017075000000000003, (5, 2): 0.00189375, (11, 21): 0.0018275000000000001, (10, 3): 0.0017649999999999996, (21, 17): 0.0019050000000000002, (9, 4): 0.00174875, (17, 3): 0.0018187500000000005, (19, 19): 0.00194, (14, 0): 0.00221625, (20, 3): 0.00192, (7, 10): 0.0017037500000000002, (19, 15): 0.00179, (7, 12): 0.0017037500000000002, (16, 1): 0.0019287500000000001, (13, 18): 0.00174875, (18, 19): 0.0018687500000000002, (8, 20): 0.0017975000000000003, (18, 3): 0.0018687500000000002, (0, 8): 0.00221625, (15, 14): 0.0017075000000000003, (11, 12): 0.0016725, (13, 19): 0.0017837500000000002, (4, 11): 0.00174, (19, 13): 0.0017837500000000002, (9, 7): 0.00171875, (9, 14): 0.0017024999999999996, (21, 0): 0.0025799999999999994, (9, 15): 0.00171875, (14, 18): 0.0017599999999999996, (1, 2): 0.00203875, (8, 21): 0.00187875, (18, 12): 0.0017424999999999997, (6, 11): 0.001715, (5, 9): 0.0017300000000000002, (2, 11): 0.0017825, (3, 10): 0.0017649999999999996, (5, 10): 0.0017199999999999997, (1, 15): 0.0018612500000000003, (13, 3): 0.0017837500000000002, (16, 20): 0.0018637500000000004, (1, 5): 0.0019050000000000002, (17, 14): 0.00174125, (1, 21): 0.0021325, (8, 16): 0.00172625, (10, 17): 0.0017199999999999997, (4, 8): 0.0017599999999999996, (11, 6): 0.001715, (12, 7): 0.0017037500000000002, (9, 0): 0.00221125, (16, 15): 0.0017549999999999998, (7, 13): 0.00171875, (9, 16): 0.0017212500000000001, (8, 4): 0.0017599999999999996, (19, 21): 0.0019850000000000002, (20, 18): 0.0018812500000000005, (19, 6): 0.0018175, (9, 2): 0.0018187499999999996, (14, 14): 0.0017025, (11, 10): 0.0016725, (13, 14): 0.0017024999999999996, (21, 3): 0.0019850000000000002, (12, 20): 0.0018312499999999998, (9, 9): 0.0017000000000000001, (13, 12): 0.0016937500000000004, (14, 17): 0.00174125, (20, 12): 0.0018312499999999998, (10, 8): 0.0016950000000000001, (16, 12): 0.0017175, (12, 15): 0.0017037500000000002, (6, 13): 0.0017212500000000001, (20, 13): 0.0018187499999999996, (0, 13): 0.00221125, (18, 10): 0.0017424999999999997}

N = 24
{(0, 0): 0.0032375, (18, 17): 0.0016312500000000003, (16, 23): 0.0020800000000000003, (11, 1): 0.0017125000000000003, (0, 20): 0.00219375, (15, 6): 0.0016025, (11, 0): 0.00203, (3, 10): 0.0016150000000000001, (16, 20): 0.0016924999999999998, (23, 20): 0.00219375, (22, 23): 0.002375, (19, 7): 0.0016187500000000002, (7, 11): 0.0015912500000000002, (9, 11): 0.001555, (18, 0): 0.0020949999999999996, (2, 2): 0.0018475, (16, 2): 0.001705, (13, 4): 0.0016074999999999998, (10, 7): 0.0015562500000000001, (20, 0): 0.00219375, (8, 14): 0.00157875, (14, 7): 0.00157125, (14, 10): 0.0015600000000000002, (13, 8): 0.0015562500000000001, (3, 0): 0.00219375, (20, 15): 0.0016399999999999995, (9, 13): 0.0015600000000000002, (2, 11): 0.0016687499999999999, (11, 4): 0.0015925, (11, 16): 0.0015912500000000002, (15, 1): 0.0017274999999999999, (4, 7): 0.0016187500000000002, (23, 17): 0.00208125, (17, 3): 0.00165625, (8, 0): 0.0020699999999999994, (0, 22): 0.002375, (12, 5): 0.0016050000000000003, (3, 17): 0.00165625, (22, 10): 0.0017212500000000001, (2, 15): 0.0016887499999999997, (21, 19): 0.0017549999999999998, (18, 18): 0.0016350000000000002, (8, 16): 0.001575, (6, 6): 0.0016375, (0, 12): 0.00203, (2, 9): 0.00167375, (16, 14): 0.00157125, (15, 8): 0.0015825000000000001, (11, 12): 0.0015625, (13, 9): 0.0015600000000000002, (7, 16): 0.0015999999999999999, (12, 12): 0.0015625, (11, 22): 0.0017125000000000003, (6, 7): 0.00158375, (10, 17): 0.00157, (20, 2): 0.0017774999999999998, (12, 20): 0.00160125, (22, 19): 0.0017862499999999999, (4, 4): 0.0016775, (5, 0): 0.0020949999999999996, (2, 10): 0.0016725000000000002, (23, 10): 0.002045, (3, 20): 0.0017675000000000002, (23, 0): 0.0032375, (23, 22): 0.002375, (21, 21): 0.0018475, (7, 4): 0.0016187500000000002, (13, 11): 0.0015425000000000003, (6, 10): 0.00157, (0, 9): 0.00200875, (3, 6): 0.00165625, (9, 3): 0.00165, (15, 14): 0.00157875, (0, 3): 0.00219375, (14, 18): 0.0016162499999999998, (9, 22): 0.00169125, (7, 22): 0.00173125, (5, 1): 0.0017800000000000001, (2, 14): 0.00167375, (23, 5): 0.0020949999999999996, (20, 4): 0.0017274999999999999, (23, 9): 0.00200875, (20, 16): 0.0016924999999999998, (12, 4): 0.0015925, (15, 18): 0.0016012500000000002, (1, 6): 0.00173125, (20, 3): 0.0017675000000000002, (14, 13): 0.0015600000000000002, (3, 16): 0.0016924999999999998, (6, 19): 0.0016474999999999999, (22, 11): 0.0017125000000000003, (21, 2): 0.0018475, (3, 8): 0.0016399999999999995, (15, 9): 0.00157875, (9, 17): 0.0015875, (0, 14): 0.00200875, (19, 21): 0.0017549999999999998, (4, 16): 0.0016187500000000002, (2, 8): 0.0016887499999999997, (16, 22): 0.00173125, (19, 6): 0.0016474999999999999, (9, 5): 0.0016162499999999998, (9, 9): 0.00152, (1, 2): 0.00188, (9, 7): 0.00157125, (16, 11): 0.0015912500000000002, (1, 9): 0.00169125, (22, 7): 0.00173125, (16, 0): 0.0020800000000000003, (21, 23): 0.0022737499999999997, (14, 15): 0.00157875, (18, 2): 0.0017212500000000001, (17, 17): 0.0016375, (6, 1): 0.00173125, (5, 10): 0.00158875, (12, 9): 0.001555, (17, 18): 0.0016312500000000003, (16, 9): 0.00157125, (23, 15): 0.0020699999999999994, (15, 17): 0.0016025, (4, 3): 0.0017274999999999999, (13, 23): 0.002045, (9, 21): 0.00167375, (19, 0): 0.0021362499999999997, (23, 18): 0.0020949999999999996, (9, 15): 0.00157875, (3, 14): 0.00165, (6, 23): 0.00208125, (23, 16): 0.0020800000000000003, (10, 11): 0.0015425000000000003, (4, 23): 0.0021362499999999997, (5, 4): 0.0016800000000000005, (1, 11): 0.0017125000000000003, (5, 3): 0.0016975000000000007, (12, 8): 0.0015462499999999999, (17, 14): 0.0015875, (4, 18): 0.0016800000000000005, (8, 12): 0.0015462499999999999, (6, 14): 0.0015875, (17, 12): 0.0015662499999999997, (6, 8): 0.0016025, (14, 23): 0.00200875, (20, 18): 0.0016975000000000007, (0, 19): 0.0021362499999999997, (1, 23): 0.002375, (4, 0): 0.0021362499999999997, (11, 10): 0.0015425000000000003, (16, 6): 0.00158375, (21, 4): 0.0017549999999999998, (8, 11): 0.0015462499999999999, (19, 20): 0.0017274999999999999, (9, 23): 0.00200875, (16, 16): 0.0015999999999999999, (19, 22): 0.0017862499999999999, (10, 19): 0.0016074999999999998, (1, 21): 0.00188, (23, 3): 0.00219375, (18, 23): 0.0020949999999999996, (0, 11): 0.00203, (5, 11): 0.0016050000000000003, (4, 5): 0.0016800000000000005, (7, 17): 0.00158375, (3, 22): 0.00183, (22, 4): 0.0017862499999999999, (0, 2): 0.0022737499999999997, (11, 7): 0.0015912500000000002, (8, 15): 0.0015825000000000001, (6, 9): 0.0015875, (0, 1): 0.002375, (23, 21): 0.0022737499999999997, (3, 9): 0.00165, (12, 14): 0.001555, (2, 16): 0.001705, (21, 20): 0.0017774999999999998, (19, 2): 0.0017549999999999998, (13, 20): 0.0016150000000000001, (7, 9): 0.00157125, (5, 15): 0.0016012500000000002, (6, 21): 0.0016974999999999998, (3, 1): 0.00183, (20, 1): 0.00183, (23, 23): 0.0032375, (23, 14): 0.00200875, (20, 8): 0.0016399999999999995, (21, 22): 0.00188, (12, 10): 0.0015425000000000003, (7, 14): 0.00157125, (11, 9): 0.001555, (14, 17): 0.0015875, (8, 23): 0.0020699999999999994, (1, 10): 0.0017212500000000001, (17, 9): 0.0015875, (6, 12): 0.0015662499999999997, (19, 9): 0.0016137500000000002, (17, 13): 0.00157, (7, 18): 0.0016474999999999999, (10, 2): 0.0016725000000000002, (23, 6): 0.00208125, (19, 12): 0.0015925, (21, 7): 0.001705, (17, 22): 0.00173125, (13, 15): 0.0015562500000000001, (3, 19): 0.0017274999999999999, (16, 8): 0.001575, (8, 13): 0.0015562500000000001, (20, 13): 0.0016150000000000001, (10, 16): 0.0015562500000000001, (12, 0): 0.00203, (5, 6): 0.0016312500000000003, (4, 1): 0.0017862499999999999, (21, 0): 0.0022737499999999997, (15, 23): 0.0020699999999999994, (0, 13): 0.002045, (23, 1): 0.002375, (14, 8): 0.00157875, (2, 23): 0.0022737499999999997, (20, 17): 0.00165625, (20, 23): 0.00219375, (21, 18): 0.0017212500000000001, (5, 8): 0.0016012500000000002, (1, 17): 0.00173125, (8, 2): 0.0016887499999999997, (12, 1): 0.0017125000000000003, (22, 8): 0.0017274999999999999, (2, 4): 0.0017549999999999998, (4, 22): 0.0017862499999999999, (6, 5): 0.0016312500000000003, (1, 20): 0.00183, (13, 1): 0.0017212500000000001, (6, 13): 0.00157, (5, 7): 0.0016474999999999999, (12, 16): 0.0015912500000000002, (14, 3): 0.00165, (17, 0): 0.00208125, (19, 5): 0.0016800000000000005, (9, 6): 0.0015875, (16, 19): 0.0016187500000000002, (11, 3): 0.00160125, (12, 22): 0.0017125000000000003, (10, 23): 0.002045, (15, 22): 0.0017274999999999999, (8, 22): 0.0017274999999999999, (5, 14): 0.0016162499999999998, (23, 19): 0.0021362499999999997, (10, 13): 0.00156, (17, 6): 0.0016375, (21, 15): 0.0016887499999999997, (22, 3): 0.00183, (9, 8): 0.00157875, (10, 3): 0.0016150000000000001, (10, 21): 0.0016725000000000002, (7, 6): 0.00158375, (21, 14): 0.00167375, (11, 8): 0.0015462499999999999, (11, 20): 0.00160125, (19, 4): 0.0016775, (13, 21): 0.0016725000000000002, (16, 5): 0.0016474999999999999, (10, 0): 0.002045, (13, 2): 0.0016725000000000002, (15, 2): 0.0016887499999999997, (14, 9): 0.00152, (6, 20): 0.00165625, (5, 2): 0.0017212500000000001, (1, 3): 0.00183, (22, 0): 0.002375, (21, 17): 0.0016974999999999998, (13, 3): 0.0016150000000000001, (21, 10): 0.0016725000000000002, (10, 5): 0.00158875, (2, 3): 0.0017774999999999998, (10, 8): 0.0015562500000000001, (9, 16): 0.00157125, (14, 20): 0.00165, (15, 13): 0.0015562500000000001, (7, 13): 0.0015562500000000001, (12, 11): 0.0015625, (9, 20): 0.00165, (2, 19): 0.0017549999999999998, (0, 21): 0.0022737499999999997, (13, 14): 0.0015600000000000002, (6, 18): 0.0016312500000000003, (16, 15): 0.001575, (16, 17): 0.00158375, (9, 18): 0.0016162499999999998, (18, 3): 0.0016975000000000007, (12, 6): 0.0015662499999999997, (19, 18): 0.0016800000000000005, (17, 5): 0.0016312500000000003, (19, 23): 0.0021362499999999997, (15, 11): 0.0015462499999999999, (5, 21): 0.0017212500000000001, (2, 18): 0.0017212500000000001, (19, 16): 0.0016187500000000002, (7, 23): 0.0020800000000000003, (16, 4): 0.0016187500000000002, (0, 15): 0.0020699999999999994, (7, 19): 0.0016187500000000002, (3, 7): 0.0016924999999999998, (8, 8): 0.0015825000000000001, (0, 10): 0.002045, (8, 20): 0.0016399999999999995, (3, 13): 0.0016150000000000001, (18, 4): 0.0016800000000000005, (22, 6): 0.00173125, (6, 0): 0.00208125, (16, 1): 0.00173125, (20, 6): 0.00165625, (5, 5): 0.0016350000000000002, (7, 5): 0.0016474999999999999, (20, 12): 0.00160125, (23, 12): 0.00203, (23, 8): 0.0020699999999999994, (5, 23): 0.0020949999999999996, (18, 7): 0.0016474999999999999, (21, 3): 0.0017774999999999998, (6, 16): 0.00158375, (13, 12): 0.0015425000000000003, (19, 15): 0.0016025, (10, 12): 0.0015425000000000003, (14, 5): 0.0016162499999999998, (1, 0): 0.002375, (3, 15): 0.0016399999999999995, (16, 12): 0.0015912500000000002, (15, 19): 0.0016025, (7, 10): 0.0015562500000000001, (21, 16): 0.001705, (12, 23): 0.00203, (23, 2): 0.0022737499999999997, (21, 12): 0.0016687499999999999, (0, 23): 0.0032375, (7, 1): 0.00173125, (0, 18): 0.0020949999999999996, (19, 1): 0.0017862499999999999, (0, 8): 0.0020699999999999994, (8, 19): 0.0016025, (11, 18): 0.0016050000000000003, (2, 1): 0.00188, (18, 10): 0.00158875, (14, 4): 0.0016137500000000002, (18, 15): 0.0016012500000000002, (19, 8): 0.0016025, (4, 13): 0.0016074999999999998, (10, 20): 0.0016150000000000001, (3, 2): 0.0017774999999999998, (7, 21): 0.001705, (6, 4): 0.0016474999999999999, (7, 8): 0.001575, (11, 13): 0.0015425000000000003, (17, 19): 0.0016474999999999999, (17, 21): 0.0016974999999999998, (21, 6): 0.0016974999999999998, (2, 7): 0.001705, (22, 1): 0.001955, (23, 7): 0.0020800000000000003, (5, 20): 0.0016975000000000007, (3, 5): 0.0016975000000000007, (6, 11): 0.0015662499999999997, (8, 5): 0.0016012500000000002, (14, 19): 0.0016137500000000002, (1, 19): 0.0017862499999999999, (7, 3): 0.0016924999999999998, (1, 18): 0.0017800000000000001, (21, 9): 0.00167375, (13, 22): 0.0017212500000000001, (18, 20): 0.0016975000000000007, (18, 22): 0.0017800000000000001, (11, 5): 0.0016050000000000003, (1, 8): 0.0017274999999999999, (22, 20): 0.00183, (2, 12): 0.0016687499999999999, (18, 9): 0.0016162499999999998, (12, 15): 0.0015462499999999999, (16, 3): 0.0016924999999999998, (8, 18): 0.0016012500000000002, (13, 10): 0.00156, (19, 13): 0.0016074999999999998, (19, 3): 0.0017274999999999999, (13, 0): 0.002045, (14, 1): 0.00169125, (8, 1): 0.0017274999999999999, (21, 1): 0.00188, (14, 16): 0.00157125, (20, 10): 0.0016150000000000001, (14, 21): 0.00167375, (4, 17): 0.0016474999999999999, (5, 13): 0.00158875, (11, 2): 0.0016687499999999999, (22, 12): 0.0017125000000000003, (5, 17): 0.0016312500000000003, (2, 22): 0.00188, (11, 23): 0.00203, (4, 2): 0.0017549999999999998, (1, 16): 0.00173125, (22, 21): 0.00188, (12, 13): 0.0015425000000000003, (17, 10): 0.00157, (12, 19): 0.0015925, (3, 4): 0.0017274999999999999, (7, 7): 0.0015999999999999999, (10, 6): 0.00157, (4, 9): 0.0016137500000000002, (11, 14): 0.001555, (10, 4): 0.0016074999999999998, (17, 2): 0.0016974999999999998, (1, 7): 0.00173125, (11, 11): 0.0015625, (18, 19): 0.0016800000000000005, (0, 17): 0.00208125, (18, 12): 0.0016050000000000003, (15, 21): 0.0016887499999999997, (6, 2): 0.0016974999999999998, (7, 2): 0.001705, (23, 13): 0.002045, (8, 3): 0.0016399999999999995, (14, 2): 0.00167375, (11, 17): 0.0015662499999999997, (15, 16): 0.001575, (10, 14): 0.0015600000000000002, (16, 13): 0.0015562500000000001, (17, 23): 0.00208125, (18, 6): 0.0016312500000000003, (8, 4): 0.0016025, (20, 21): 0.0017774999999999998, (9, 2): 0.00167375, (1, 5): 0.0017800000000000001, (15, 7): 0.001575, (22, 15): 0.0017274999999999999, (18, 1): 0.0017800000000000001, (0, 7): 0.0020800000000000003, (2, 17): 0.0016974999999999998, (8, 21): 0.0016887499999999997, (11, 6): 0.0015662499999999997, (22, 2): 0.00188, (22, 16): 0.00173125, (3, 3): 0.0017675000000000002, (3, 21): 0.0017774999999999998, (4, 20): 0.0017274999999999999, (15, 0): 0.0020699999999999994, (1, 12): 0.0017125000000000003, (1, 14): 0.00169125, (19, 17): 0.0016474999999999999, (13, 7): 0.0015562500000000001, (23, 11): 0.00203, (17, 4): 0.0016474999999999999, (5, 9): 0.0016162499999999998, (20, 7): 0.0016924999999999998, (1, 13): 0.0017212500000000001, (13, 17): 0.00157, (12, 3): 0.00160125, (14, 14): 0.00152, (14, 6): 0.0015875, (18, 13): 0.00158875, (12, 17): 0.0015662499999999997, (15, 3): 0.0016399999999999995, (9, 14): 0.00152, (17, 16): 0.00158375, (6, 17): 0.0016375, (22, 18): 0.0017800000000000001, (14, 12): 0.001555, (0, 16): 0.0020800000000000003, (12, 7): 0.0015912500000000002, (18, 16): 0.0016474999999999999, (17, 11): 0.0015662499999999997, (5, 12): 0.0016050000000000003, (13, 5): 0.00158875, (15, 20): 0.0016399999999999995, (10, 15): 0.0015562500000000001, (18, 5): 0.0016350000000000002, (2, 20): 0.0017774999999999998, (19, 14): 0.0016137500000000002, (4, 21): 0.0017549999999999998, (4, 11): 0.0015925, (4, 14): 0.0016137500000000002, (13, 16): 0.0015562500000000001, (22, 13): 0.0017212500000000001, (20, 22): 0.00183, (0, 4): 0.0021362499999999997, (21, 8): 0.0016887499999999997, (2, 5): 0.0017212500000000001, (13, 19): 0.0016074999999999998, (10, 10): 0.00156, (4, 15): 0.0016025, (22, 9): 0.00169125, (18, 11): 0.0016050000000000003, (5, 19): 0.0016800000000000005, (0, 5): 0.0020949999999999996, (14, 0): 0.00200875, (12, 21): 0.0016687499999999999, (17, 8): 0.0016025, (15, 12): 0.0015462499999999999, (7, 15): 0.001575, (6, 3): 0.00165625, (22, 5): 0.0017800000000000001, (4, 8): 0.0016025, (5, 18): 0.0016350000000000002, (6, 15): 0.0016025, (22, 17): 0.00173125, (2, 21): 0.0018475, (9, 1): 0.00169125, (10, 1): 0.0017212500000000001, (2, 13): 0.0016725000000000002, (18, 14): 0.0016162499999999998, (15, 15): 0.0015825000000000001, (8, 6): 0.0016025, (10, 22): 0.0017212500000000001, (15, 4): 0.0016025, (8, 7): 0.001575, (15, 10): 0.0015562500000000001, (4, 12): 0.0015925, (13, 6): 0.00157, (4, 10): 0.0016074999999999998, (13, 13): 0.00156, (1, 15): 0.0017274999999999999, (1, 22): 0.001955, (20, 9): 0.00165, (9, 12): 0.001555, (13, 18): 0.00158875, (7, 12): 0.0015912500000000002, (21, 11): 0.0016687499999999999, (4, 19): 0.0016775, (17, 7): 0.00158375, (8, 9): 0.00157875, (0, 6): 0.00208125, (9, 4): 0.0016137500000000002, (11, 15): 0.0015462499999999999, (14, 11): 0.001555, (23, 4): 0.0021362499999999997, (3, 12): 0.00160125, (1, 4): 0.0017862499999999999, (18, 8): 0.0016012500000000002, (7, 20): 0.0016924999999999998, (4, 6): 0.0016474999999999999, (3, 23): 0.00219375, (17, 15): 0.0016025, (20, 19): 0.0017274999999999999, (3, 18): 0.0016975000000000007, (1, 1): 0.001955, (11, 21): 0.0016687499999999999, (20, 20): 0.0017675000000000002, (17, 1): 0.00173125, (16, 7): 0.0015999999999999999, (22, 14): 0.00169125, (5, 16): 0.0016474999999999999, (20, 5): 0.0016975000000000007, (9, 10): 0.0015600000000000002, (12, 18): 0.0016050000000000003, (17, 20): 0.00165625, (9, 19): 0.0016137500000000002, (11, 19): 0.0015925, (16, 21): 0.001705, (3, 11): 0.00160125, (19, 10): 0.0016074999999999998, (14, 22): 0.00169125, (21, 5): 0.0017212500000000001, (19, 19): 0.0016775, (8, 17): 0.0016025, (10, 9): 0.0015600000000000002, (16, 18): 0.0016474999999999999, (10, 18): 0.00158875, (19, 11): 0.0015925, (7, 0): 0.0020800000000000003, (9, 0): 0.00200875, (18, 21): 0.0017212500000000001, (21, 13): 0.0016725000000000002, (22, 22): 0.001955, (12, 2): 0.0016687499999999999, (16, 10): 0.0015562500000000001, (20, 11): 0.00160125, (15, 5): 0.0016012500000000002, (5, 22): 0.0017800000000000001, (20, 14): 0.00165, (2, 6): 0.0016974999999999998, (2, 0): 0.0022737499999999997, (8, 10): 0.0015562500000000001, (6, 22): 0.00173125}

N = 25
{(11, 17): 0.00145875, (0, 13): 0.0018587499999999997, (1, 20): 0.0016725000000000002, (7, 1): 0.0016037500000000006, (3, 11): 0.0015012500000000004, (0, 16): 0.0019025, (10, 12): 0.0014225, (24, 18): 0.0019299999999999999, (10, 6): 0.0014612500000000003, (8, 12): 0.0014175, (1, 16): 0.0016087499999999995, (12, 19): 0.00149, (17, 11): 0.00145875, (17, 8): 0.0014837499999999998, (19, 11): 0.0014649999999999997, (11, 18): 0.0014700000000000004, (3, 21): 0.0016075, (6, 16): 0.0014674999999999998, (19, 10): 0.001495, (19, 7): 0.00147625, (3, 0): 0.00203625, (12, 4): 0.001495, (1, 24): 0.00221625, (22, 8): 0.00154375, (13, 21): 0.0015012500000000004, (4, 20): 0.0015025000000000001, (0, 14): 0.0019112499999999998, (7, 11): 0.00145875, (17, 23): 0.0016037500000000006, (14, 7): 0.00143625, (10, 8): 0.0014650000000000002, (18, 10): 0.0014612500000000003, (2, 20): 0.0016212499999999999, (5, 13): 0.0014649999999999997, (20, 9): 0.00149875, (9, 2): 0.001555, (3, 24): 0.00203625, (20, 0): 0.0019750000000000006, (21, 7): 0.0015325, (17, 7): 0.00149, (6, 18): 0.001495, (12, 11): 0.001405, (15, 12): 0.001435, (13, 16): 0.0014437500000000004, (17, 15): 0.0014712500000000001, (1, 0): 0.00221625, (16, 8): 0.0014175000000000001, (19, 17): 0.00147625, (23, 3): 0.0017199999999999997, (6, 3): 0.0015525, (24, 12): 0.0018675, (0, 23): 0.00221625, (19, 12): 0.00149, (12, 21): 0.0015175, (22, 22): 0.00168, (23, 6): 0.0016150000000000001, (22, 15): 0.001555, (18, 8): 0.0014674999999999998, (9, 4): 0.00149875, (23, 24): 0.00221625, (11, 2): 0.0015262499999999998, (13, 11): 0.0014275, (16, 15): 0.0014524999999999998, (16, 6): 0.0014674999999999998, (21, 5): 0.0015674999999999997, (0, 18): 0.0019299999999999999, (14, 15): 0.00144, (18, 3): 0.0015525, (17, 0): 0.0019012500000000002, (20, 22): 0.0016212499999999999, (9, 24): 0.0018987499999999996, (2, 0): 0.0020949999999999996, (8, 15): 0.0014524999999999998, (4, 24): 0.0019750000000000006, (12, 10): 0.0014225, (18, 11): 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	N	X	Y	P
4	3.0	0.0	0.0	0.128965
9	3.0	0.0	1.0	0.099312
10	3.0	0.0	2.0	0.128965
5	3.0	1.0	0.0	0.099312
6	3.0	1.0	1.0	0.086890
8	3.0	1.0	2.0	0.099312
7	3.0	2.0	0.0	0.128965
12	3.0	2.0	1.0	0.099312
11	3.0	2.0	2.0	0.128965

Setup¶

Functions¶

Answers¶

Animation¶

Appendix¶

Rohan Lewis¶

2024.12.09¶