#P1622F. Quadratic Set

    ID: 7565 Type: RemoteJudge 4000ms 256MiB 尝试: 1 已通过: 1 难度: 10 上传者: 标签>constructive algorithmshashingnumber theory

Quadratic Set

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.

A single line contains a single integer $n$ ($1 \le n \le 10^6$).

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.

Input

A single line contains a single integer $n$ ($1 \le n \le 10^6$).

Output

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.

Samples

1
1
1
4
3
1 3 4
7
4
1 4 5 6
9
7
1 2 4 5 6 7 9