# Solution of;
# Project Euler Problem 547: Distance of random points within hollow square laminae
# https://projecteuler.net/problem=547
# 
# Assuming that two points are chosen randomly (with uniform distribution) 
# within a rectangle, it is possible to determine the expected value of the 
# distance between these two points. For example, the expected distance 
# between two random points in a unit square is about 0. 521405, while the 
# expected distance between two random points in a rectangle with side lengths 
# 2 and 3 is about 1. 317067. Now we define a hollow square lamina of size n 
# to be an integer sized square with side length n ≥ 3 consisting of n2 unit 
# squares from which a rectangle consisting of x × y unit squares (1 ≤ x,y ≤ n 
# - 2) within the original square has been removed. For n = 3 there exists 
# only one hollow square lamina:For n = 4 you can find 9 distinct hollow 
# square laminae, allowing shapes to reappear in rotated or mirrored form:Let 
# S(n) be the sum of the expected distance between two points chosen randomly 
# within each of the possible hollow square laminae of size n. The two points 
# have to lie within the area left after removing the inner rectangle, i. e. 
# the gray-colored areas in the illustrations above. For example, S(3) = 1. 
# 6514 and S(4) = 19. 6564, rounded to four digits after the decimal point. 
# Find S(40) rounded to four digits after the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 547
    timed.caller(dummy, n, i, prob_id)
