# Solution of;
# Project Euler Problem 534: Weak Queens
# https://projecteuler.net/problem=534
# 
# The classical eight queens puzzle is the well known problem of placing eight 
# chess queens on a 8×8 chessboard so that no two queens threaten each other. 
# Allowing configurations to reappear in rotated or mirrored form, a total of 
# 92 distinct configurations can be found for eight queens. The general case 
# asks for the number of distinct ways of placing n queens on a n×n board, e. 
# g. you can find 2 distinct configurations for n=4. Let's define a weak queen 
# on a n×n board to be a piece which can move any number of squares if moved 
# horizontally, but a maximum of n−1−w squares if moved vertically or 
# diagonally, 0≤w<n being the "weakness factor". For example, a weak queen on 
# a n×n board with a weakness factor of w=1 located in the bottom row will not 
# be able to threaten any square in the top row as the weak queen would need 
# to move n−1 squares vertically or diagonally to get there, but may only move 
# n−2 squares in these directions. In contrast, the weak queen is not 
# handicapped horizontally, thus threatening every square in its own row, 
# independently from its current position in that row. Let Q(n,w) be the 
# number of ways n weak queens with weakness factor w can be placed on a n×n 
# board so that no two queens threaten each other. It can be shown, for 
# example, that Q(4,0)=2, Q(4,2)=16 and Q(4,3)=256. Let 
# $S(n)=\displaystyle\sum_{w=0}^{n-1} Q(n,w)$. You are given that S(4)=276 and 
# S(5)=3347. Find S(14).
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 534
    timed.caller(dummy, n, i, prob_id)
