import math


def is_square(apositiveint):
    """ From: https://stackoverflow.com/a/2489519 """
    x = apositiveint // 2
    seen = set([x])
    while x * x != apositiveint:
         x = (x + (apositiveint // x)) // 2
         if x in seen: return False
         seen.add(x)
    return True


def canditates(current_value, depth):
    if depth <= 0:
        yield current_value
    else:
        d = 10 ** depth
        for i in range(10):
            for new_value in canditates(current_value - i * d, depth - 2):
                yield new_value


def euler_206():
    c = 1929394959697989990
    for i, c in enumerate(canditates(c, 17)):
        if is_square(c):
            return int(math.sqrt(c))


if __name__ == "__main__":
    solution = euler_206()
    print("e206.py: " + str(solution))
    assert(solution == 1389019170)