# #  Problem 9:
# 
# [Euler Project #9](https://projecteuler.net/problem=9)
# 
# 
# 
# >A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
# a2 + b2 = c2
# 
# >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.
# 
# 
# 
# ---
import os
import pprint
import time  # Typically imported for sleep function, to slow down execution in terminal.
import typing
import decorators  # Typically imported to compute execution duration of functions.
import math
import numpy

def get_c(a,b):
    c = math.sqrt(a*a+b*b)
    return c

def check_constraint(a,b,c,limit):
    return (a+b+c)==limit

exit=False
for a in range(1,1000):
    for b in range(a,1000):
        c = get_c(a,b)
        if check_constraint(a,b,c,1000):
            #print(a,b,c)
            #print(not_done)
            exit=True
            break
    if exit:
        break
print(a,b,c,a+b+c,a*b*c)