""" Problem Statement: A Pythagorean triplet is a set of three natural numbers, a < b < c, for which, a^2 + b^2 = c^2 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product abc. """ def solution(n): """ Return the product of a,b,c which are Pythagorean Triplet that satisfies the following: 1. a < b < c 2. a**2 + b**2 = c**2 3. a + b + c = 1000 >>> solution(1000) 31875000 """ product = -1 d = 0 for a in range(1, n // 3): """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c""" b = (n * n - 2 * a * n) // (2 * n - 2 * a) c = n - a - b if c * c == (a * a + b * b): d = a * b * c if d >= product: product = d return product if __name__ == "__main__": print(solution(int(input().strip())))