Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.
Consider a sequence [a1, a2, ... , an]. Define its prefix product sequence .
Now given n, find a permutation of [1, 2, ..., n], such that its prefix product sequence is a permutation of [0, 1, ..., n - 1].
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 ai. 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.
Examples
Input
7
Output
YES 1 4 3 6 5 2 7
Input
6
Output
NO
Note
For the second sample, there are no valid sequences.