import concurrent.futures
from math import isqrt, gcd


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


def have_same_ratio(a, b, c, d):
    if b == 0 or d == 0:
        raise ValueError("Denominators must be non-zero")
    return a * d == b * c


def check_range(start, end):
    local_sum = 0
    for i in range(start, end):
        if i % 10000 == 0:
            print(i)
        n = i * i
        for d in range(1, i):
            q = n // d
            r = n % d
            if r == 0:
                continue
            assert r < d and d < q
            if have_same_ratio(d, r, q, d):
                print(f"{n=} {i=} {r=} {d=} {q=}")
                local_sum += n
                break
    return local_sum


def euler_141_brute_force():
    s = 0
    m = 1_000_000
    range_size = 10_000

    with concurrent.futures.ProcessPoolExecutor() as executor:
        futures = []
        for start in range(1, m, range_size):
            end = min(start + range_size, m)
            futures.append(executor.submit(check_range, start, end))
        for future in concurrent.futures.as_completed(futures):
            s += future.result()
    return s


def euler_141():
    r = 0
    NMAX = 10**12
    a = 1
    while True:
        if a**3 > NMAX:
            break
        for b in range(1, a):
            if a**3 * b**2 > NMAX:
                break

            if gcd(a, b) != 1:
                continue

            c = 1
            while True:
                n = a**3 * b * c**2 + c * b**2
                if n > NMAX:
                    break
                if issqrt(n):
                    # print(n)
                    r += n
                c += 1
        a += 1
    return r


if __name__ == "__main__":
    solution = euler_141()
    print("e141.py: " + str(solution))
    assert solution == 878454337159