Description

Input

The only line contains the integer $n$ ($2 \le n \le 10^5$).

Output

The first line should contain a single integer, the length of the longest subsequence.

The second line should contain the elements of the subsequence, in increasing order.

If there are multiple solutions, you can print any.

5

3
1 2 3

8

4
1 3 5 7

Note

In the first example, the product of the elements is $6$ which is congruent to $1$ modulo $5$. The only longer subsequence is $[1,2,3,4]$. Its product is $24$ which is congruent to $4$ modulo $5$. Hence, the answer is $[1,2,3]$.