def euler_136():
    n = 10**8
    threshold = 50*10**6
    lookup = [0 for _ in range(0, threshold)]
    firstpositivestart = 1
    for x in range(1, n):
        firstpositive = False
        for dxy in range(firstpositivestart, x // 2 + 1):
            z = x - 2 * dxy
            if z <= 0:
                break
            y = x - dxy
            xyz = x*x - y*y - z*z
            if xyz <= 0:
                continue

            # Start when xyz is already greater than 0.
            if not firstpositive:
                firstpositivestart = dxy
                firstpositive = True

            # If xyz is greater than threshold there are no more solutions.
            if xyz >= threshold:
                break
            lookup[xyz] += 1

    r = 0
    for v in lookup:
        if v == 1:
            r += 1
    return r


if __name__ == "__main__":
    solution = euler_136()
    print("e136.py: " + str(solution))
    assert solution == 2544559