# Solution of;
# Project Euler Problem 609: π sequences
# https://projecteuler.net/problem=609
# 
# For every $n \ge 1$ the prime-counting function $\pi(n)$ is equal to the 
# number of primesnot exceeding $n$. E. g. $\pi(6)=3$ and $\pi(100)=25$. We 
# say that a sequence of integers $u = (u_0,\cdots,u_m)$ is a $\pi$ sequence 
# if $u_n \ge 1$ for every $n$ $u_{n+1}= \pi(u_n)$ $u$ has two or more 
# elementsFor $u_0=10$ there are three distinct $\pi$ sequences: (10,4), 
# (10,4,2) and (10,4,2,1). Let $c(u)$ be the number of elements of $u$ that 
# are not prime. Let $p(n,k)$ be the number of $\pi$ sequences $u$ for which 
# $u_0\le n$ and $c(u)=k$. Let $P(n)$ be the product of all $p(n,k)$ that are 
# larger than 0. You are given: P(10)=3×8×9×3=648 and P(100)=31038676032. Find 
# $P(10^8)$. Give your answer modulo 1000000007.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 609
    timed.caller(dummy, n, i, prob_id)
