def is_valid(circle_with_seen, n):
    circle, seen = circle_with_seen
    if len(circle) < n:
        return True

    end = tuple(circle[-n:])
    if end in seen:
        return False
    seen.add(end)
    return True


def overlap_valid(circle_with_seen, n):
    circle, seen = circle_with_seen
    for i in range(1, n):
        end = tuple(circle[-i:] + circle[: n - i])
        if end in seen:
            return False
        seen.add(end)
    return True


def s(n):
    length = 2**n
    start = [0 for _ in range(n)]
    xs = [(start, set([tuple(start)]))]
    for _ in range(length - n):
        nxs = []
        for circle, seen in xs:
            for d in [0, 1]:
                nx = (circle + [d], seen.copy())
                if is_valid(nx, n):
                    nxs.append(nx)
        xs = nxs
    circles = [x[0] for x in xs if overlap_valid(x, n)]
    return sum(int("".join(map(str, circle)), 2) for circle in circles)


def euler_265():
    assert s(3) == 52
    return s(5)


if __name__ == "__main__":
    solution = euler_265()
    print(f"e265.py: {solution}")
    assert solution == 209110240768