'''
If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.

{20,48,52}, {24,45,51}, {30,40,50}

For which value of p ≤ 1000, is the number of solutions maximised?
'''

import math

def main():
    print("Hello this is Patrick")

    ps = [0]*1000

    for a in range(1, 1000):
        for b in range(1, 1000-a):
            c2 = a**2 + b**2
            r = math.sqrt(c2)

            if c2 == int(r + 0.5) ** 2:
                r = int(r + 0.5)
                if a + b + r <= 1000:
                    ps[a + b + r - 1] += 1
    
    print(ps.index(max(ps)) + 1)

if __name__ == "__main__":
    main()