def fib():
    a, b = 1, 1
    yield a
    yield b
    while True:
        a, b = b, a + b
        yield b


def pisano_period(fibs, n):
    for period in range(2, 130):
        if fibs[0] % n == fibs[period] % n and fibs[1] % n == fibs[period + 1] % n:
            return period
    return None


def euler_853():
    r = 0
    fs = fib()
    fibs = [next(fs) for _ in range(400)]
    upper = 10**9
    pi_target = 120
    for n in range(2, upper + 1):
        # Check if pi_target is a period.
        if fibs[0] % n == fibs[pi_target] % n and fibs[1] % n == fibs[pi_target + 1] % n:
            # Make sure that no lower period than pi_target exits.
            if pisano_period(fibs, n) == pi_target:
                r += n
                # print(n, prime_factors(n))
                # I have noticed that the highest prime factor is always 61 or
                # 2521, so we could probably also get the solution by
                # enumerating the prime factors that yield a sum smaller than
                # upper and have 61 or 2521 as their last factor.
    return r


if __name__ == "__main__":
    solution = euler_853()
    print("e853.py: " + str(solution))
    assert solution == 44511058204