from functools import cache


@cache
def remove(n: str, pos: int) -> str:
    assert pos < len(n)
    r = n[:pos] + n[pos + 1:]
    r = r.lstrip("0")
    return r


@cache
def player_wins(n: str) -> bool:
    if len(n) == 1:
        return True
    for i in range(len(n)):
        if not player_wins(remove(n, i)):
            return True
    return False

def w(n: int) -> int:
    r = 0
    xs = [("", 0)]
    for _ in range(n):
        nxs = []
        for x, x_count in xs:
            nxs.append(("0" + x, x_count))
            nx, nx_count = "x" + x, x_count + 1
            if player_wins(nx):
                r += (9 ** nx_count)
            nxs.append((nx, nx_count))
        xs = nxs
    return r


def euler_961():
    assert remove("105", 0) == "5"
    assert remove("105", 1) == "15"
    assert remove("105", 2) == "10"
    assert remove("10005", 0) == "5"
    assert w(2) == 18
    assert w(4) == 1656
    return w(18)


if __name__ == "__main__":
    solution = euler_961()
    print("e961.py: " + str(solution))
    # assert(solution == 0)