# Solution of;
# Project Euler Problem 462: Permutation of 3-smooth numbers
# https://projecteuler.net/problem=462
# 
# A 3-smooth number is an integer which has no prime factor larger than 3. For 
# an integer N, we define S(N) as the set of 3-smooth numbers less than or 
# equal to N . For example, S(20) = { 1, 2, 3, 4, 6, 8, 9, 12, 16, 18 }. We 
# define F(N) as the number of permutations of S(N) in which each element 
# comes after all of its proper divisors. This is one of the possible 
# permutations for N = 20. - 1, 2, 4, 3, 9, 8, 16, 6, 18, 12. This is not a 
# valid permutation because 12 comes before its divisor 6. - 1, 2, 4, 3, 9, 8, 
# 12, 16, 6, 18. We can verify that F(6) = 5, F(8) = 9, F(20) = 450 and 
# F(1000) ≈ 8. 8521816557e21. Find F(1018). Give as your answer its scientific 
# notation rounded to ten digits after the decimal point. When giving your 
# answer, use a lowercase e to separate mantissa and exponent. E. g. if the 
# answer is 112,233,445,566,778,899 then the answer format would be 1. 
# 1223344557e17.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 462
    timed.caller(dummy, n, i, prob_id)
