from math import gcd


def euler_138():
    count = 12
    r, m, n = 0, 2, 1
    while True:
        if count == 0:
            break

        if (m - n) % 2 == 1 and gcd(m, n) == 1:  # Ensure m and n are coprime and not both odd
            a = m * m - n * n
            b = 2 * m * n
            c = m * m + n * n
            if a > b:
                a, b = b, a
            assert a * a + b * b == c * c
            if a * 2 - 1 == b or a * 2 + 1 == b:
                # print(f"{m=} {n=} l={c}")
                r += c # c is L
                count -= 1
                n = m
                m *= 4
        m += 1
    return r


if __name__ == "__main__":
    solution = euler_138()
    print("e138.py: " + str(solution))
    assert solution == 1118049290473932