Subtract the square

Two players are engaged in the game "Take Away a Square". They start with a single pile containing n candies. During a player's turn, they can remove any number of candies k = t^2 (where t is a natural number) from the pile. The player who removes the last candy wins the game.

Your task is to identify all the losing positions in this game, given that the number of candies n does not exceed maxn.

Input

The input consists of a single line containing the integer maxn (1 ≤ maxn ≤ 10^6).

Output

First, output the total number of losing positions. Then, list all these losing positions in ascending order, each on a new line.

Examples