from math import isqrt


def iq(n):
    isq = isqrt(n)
    return isq * isq == n


def euler_142():
    # x + y x - y x + z x - z y + z y - z
    NMAX = 1_000_000
    squares = [n * n for n in range(1, NMAX)]
    for x in range(1, NMAX):
        for s1 in squares:
            y = x - s1 # s1 = x - y
            if y <= 0:
                break
            if not iq(x + y): # s2 = x + y
                continue
            for s3 in squares:
                z = y - s3 # s3 = y - z
                if x - z <= 0:
                    continue
                if z <= 0:
                    break
                if not iq(y + z): # s4 = y + z
                    continue
                if iq(x + z) and iq(x - z):
                    print(x, y, z, x + y + z)
                    return x + y + z
    return None


if __name__ == "__main__":
    solution = euler_142()
    print("e142.py: " + str(solution))
    assert solution == 1006193