Description:
Let's call a set of positive integers $$$a_1, a_2, \dots, a_k$$$ quadratic if the product of the factorials of its elements is a square of an integer, i. e. $$$\prod\limits_{i=1}^{k} a_i! = m^2$$$, for some integer $$$m$$$.
You are given a positive integer $$$n$$$.
Your task is to find a quadratic subset of a set $$$1, 2, \dots, n$$$ of maximum size. If there are multiple answers, print any of them.
Input Format:
A single line contains a single integer $$$n$$$ ($$$1 \le n \le 10^6$$$).
Output Format:
In the first line, print a single integer — the size of the maximum subset. In the second line, print the subset itself in an arbitrary order.
Note:
None