# Solution of;
# Project Euler Problem 553: Power sets of power sets
# https://projecteuler.net/problem=553
# 
# Let P(n) be the set of the first n positive integers {1, 2, . . . , n}. Let 
# Q(n) be the set of all the non-empty subsets of P(n). Let R(n) be the set of 
# all the non-empty subsets of Q(n). An element X ∈ R(n) is a non-empty subset 
# of Q(n), so it is itself a set. From X we can construct a graph as 
# follows:Each element Y ∈ X corresponds to a vertex and labeled with Y;Two 
# vertices Y1 and Y2 are connected if Y1 ∩ Y2 ≠ ∅. For example, X = {{1}, 
# {1,2,3}, {3}, {5,6}, {6,7}} results in the following graph:This graph has 
# two connected components. Let C(n,k) be the number of elements of R(n) that 
# have exactly k connected components in their graph. You are given C(2,1) = 
# 6, C(3,1) = 111, C(4,2) = 486, C(100,10) mod 1 000 000 007 = 728209718. Find 
# C(104,10) mod 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 = 553
    timed.caller(dummy, n, i, prob_id)
