KSA students got tired of studying linear algebra and came up with the following problem.
Given an integer $N$, determine if there exists a sequence satisfying the following conditions, and if so, find one.
- The sequence is a permutation of length $N$. In other words, each sequence element is in the range of 1, 2, $\dots$, $N$, and the elements are pairwise distinct.
- Let $S$ be any contiguous subsequence of the sequence whose length is 2 or greater, then the value of $\max(S)-\min(S)$ is always not a prime number.
A sequence $A$ is a contiguous subsequence of a sequence $B$ if $A$ can be obtained from $B$ by the deletion of several (possibly zero) elements from the beginning and several (possibly zero) elements from the end.
KSA students asked you to solve this problem since they forgot what a prime number is.
Input
The first line contains an integer $N$.
Output
On the first line, print YES if there exists a sequence satisfying the conditions, and NO otherwise.
If such a sequence $A$ exists, print $N$ space-separated integers $A_1, A_2, \dots, A_N$ on the second line.
If there are multiple answers, print any of them.
Constraints
- $2 \le N \le 1000$
Scoring
| No. | Points | Constraints |
|---|---|---|
| 1 | 17 | $N=17$ |
| 2 | 40 | $N$ is even |
| 3 | 43 | No additional constraints |
Examples
Input 1
5
Output 1
NO
Input 2
10
Output 2
YES 5 4 8 2 10 1 9 3 7 6