Consider a sequence $[*a*_{1}, *a*_{2}, ... , *a*_{*n*}]$. 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 $*n*$ ($1 ≤ *n* ≤ 10^{5}$).

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.

Note

For the second sample, there are no valid sequences.