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import matplotlib.pyplot as plt
from pylab import savefig
import numpy as np
from numpy.random import rand, randint

def flipsome(n):
	flip = lambda: randint(0,2)
	return sum(flip() for _ in range(n)) / float(n)

interval = 1000

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digits = [

#          B C                  D           A B C             A B C   
#        E     F                F                 F                 F 
#        G     H                H                 H                 H 
#        I     L                L             J K               J K   
#        M     N                N           M                       N 
#        O     P                P           O                       P 
#          R S                  T           Q R S T           Q R S   

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from math import sqrt
from itertools import permutations

def squarable(sides):
	area = sum(map(lambda (a,b): a*b, sides))
	S = sqrt(area)
	if S == int(S):

		# check Ken's conditions

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from fractions import gcd

M = 19*41*47*61
totient = 18*40*46*60

def p(n):
  return (n*n*n*n + n*n + n + 1) % M

# compute inverse of  a  mod  M
#  or None if no inverse exists