def shortest_path_squared(l, b, h):
    s1 = l ** 2 + (h + b) ** 2
    s2 = h ** 2 + (b + l) ** 2
    s3 = b ** 2 + (h + l) ** 2
    s = min(s1, s2, s3)
    return s


def euler_086():
    square_max = (10 ** 6) ** 2
    squares = set([n * n for n in range(10**6)])

    count = 0
    m = 0
    while True:
        m += 1
        cuboids = ((m, a, b)
                   for a in range(1, m + 1)
                   for b in range(1, a + 1))
        for c in cuboids:
            s = shortest_path_squared(*c)
            if s in squares:
                count += 1
            if s > square_max:
                raise Exception()
        if count > 10 ** 6:
            return m


if __name__ == "__main__":
    solution = euler_086()
    print("e086.py: " + str(solution))
    assert(solution == 1818)