from lib_prime import primes
from math import sqrt


def pascal_numbers_till(row):
    def pascal_next(xs):
        r = [xs[0]]
        for i in range(len(xs) - 1):
            r.append(xs[i] + xs[i + 1])
        r.append(xs[-1])
        return r

    all = set([1])
    xs = [1]
    for _ in range(row - 1):
        xs = pascal_next(xs)
        all |= set(xs)
    return sorted(list(set(all)))


def is_square_free(ps, n):
    for p in ps:
        if n % p == 0:
            return False
    return True


def solve(n):
    r = 0
    pascals = pascal_numbers_till(n)
    ps = [p * p for p in primes(int(sqrt(max(pascals))))]
    for n in pascals:
        if is_square_free(ps, n):
            r += n
    return r


def test():
    assert pascal_numbers_till(1) == [1]
    assert pascal_numbers_till(2) == [1]
    assert pascal_numbers_till(3) == [1, 2]
    assert pascal_numbers_till(8) == [1, 2, 3, 4, 5, 6, 7, 10, 15, 20, 21, 35]
    assert solve(8) == 105


def euler_203():
    test()
    return solve(51)


if __name__ == "__main__":
    solution = euler_203()
    print("e203.py: " + str(solution))
    assert solution == 34029210557338