# Solution of;
# Project Euler Problem 726: Falling bottles
# https://projecteuler.net/problem=726
# 
# Consider a stack of bottles of wine. There are $n$ layers in the stack with 
# the top layer containing only one bottle and the bottom layer containing $n$ 
# bottles. For $n=4$ the stack looks like the picture below. The collapsing 
# process happens every time a bottle is taken. A space is created in the 
# stack and that space is filled according to the following recursive steps:No 
# bottle touching from above: nothing happens. For example, taking $F$. One 
# bottle touching from above: that will drop down to fill the space creating 
# another space. For example, taking $D$. Two bottles touching from above: one 
# will drop down to fill the space creating another space. For example, taking 
# $C$. This process happens recursively; for example, taking bottle $A$ in the 
# diagram above. Its place can be filled with either $B$ or $C$. If it is 
# filled with $C$ then the space that $C$ creates can be filled with $D$ or 
# $E$. So there are 3 different collapsing processes that can happen if $A$ is 
# taken, although the final shape (in this case) is the same. Define $f(n)$ to 
# be the number of ways that we can take all the bottles from a stack with $n$ 
# layers. Two ways are considered different if at any step we took a different 
# bottle or the collapsing process went differently. You are given $f(1) = 1$, 
# $f(2) = 6$ and $f(3) = 1008$. Also define$\displaystyle S(n) = \sum_{k=1}^n 
# f(k)$Find $S(10^4)$ and give your answer modulo $1\,000\,000\,033$.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 726
    timed.caller(dummy, n, i, prob_id)
