Stones
Two players are engaged in a game involving a single pile of N stones. During a turn, a player can take any pile and divide it into multiple smaller piles, ensuring that the number of stones in each new pile differs by at least K. For instance, if K = 2, a pile of 9 stones can be split into piles like (1, 8), (2, 7), (3, 6), or (1, 3, 5). The player who is unable to make a move loses the game. Given a specific N, identify all values of K (0 ≤ K ≤ N) for which the second player has a winning strategy.
Input
The input consists of a single line containing a natural number N (1 ≤ N < 100).
Output
The output should include two lines: the first line should contain the total count of such K values, and the second line should list these values in ascending order.