gistfile1.txt

from math import comb
import sys

def probability_of_eights(sequence_length, total_string_length=64):
    digits = 16
    def p(k):
        placements = comb(total_string_length - k * (sequence_length - 1), k)
        combinations = digits ** (total_string_length - k * sequence_length)
        total_ways = digits ** total_string_length
        return placements * combinations / total_ways
    probability = 0
    sign = 1
    for k in range(1, total_string_length // sequence_length + 1):
        probability += sign * p(k)
        sign *= -1
    
    return probability

sequence_length = int(sys.argv[1])
print(probability_of_eights(sequence_length))