Prefix Product Sequence

Description:

Input:

The only input line contains an integer n (1 ≤ n ≤ 10⁵).

Output:

In the first output line, print "YES" if such sequence exists, or print "NO" if no such sequence exists.

If any solution exists, you should output n more lines. i-th line contains only an integer a_i. The elements of the sequence should be different positive integers no larger than n.

If there are multiple solutions, you are allowed to print any of them.

Sample Input:

7

Sample Output:

YES
1
4
3
6
5
2
7

Sample Input:

6

Sample Output:

NO

Note:

For the second sample, there are no valid sequences.