Codeforces Round #416 (Div. 2) has been moved to start on 27.05.2017 09:35 (UTC). ×

C. Prefix Product Sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.