# Solution of;
# Project Euler Problem 720: Unpredictable Permutations
# https://projecteuler.net/problem=720
# 
# Consider all permutations of $\{1, 2, \ldots N\}$, listed in lexicographic 
# order. For example, for $N=4$, the list starts as 
# follows:$$\displaylines{(1, 2, 3, 4) \\(1, 2, 4, 3) \\(1, 3, 2, 4) \\(1, 3, 
# 4, 2) \\(1, 4, 2, 3) \\(1, 4, 3, 2) \\(2, 1, 3, 4) \\\vdots}$$Let us call a 
# permutation $P$ unpredictable if there is no choice of three indices $i \lt 
# j \lt k$ such that $P(i)$, $P(j)$ and $P(k)$ constitute an arithmetic 
# progression. For example, $P=(3, 4, 2, 1)$ is not unpredictable because 
# $P(1), P(3), P(4)$ is an arithmetic progression. Let $S(N)$ be the position 
# within the list of the first unpredictable permutation. For example, given 
# $N = 4$, the first unpredictable permutation is $(1, 3, 2, 4)$ so $S(4) = 
# 3$. You are also given that $S(8) = 2295$ and $S(32) \equiv 641839205 
# \pmod{1\,000\,000\,007}$. Find $S(2^{25})$. Give your answer modulo 
# $1\,000\,000\,007$.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 720
    timed.caller(dummy, n, i, prob_id)
