$N$ distinct integers $A_1, A_2, \cdots, A_N$ are placed in front of Changha.
Since Changha has been suffering from prime-number phobia for three years, he wants to select at least two integers from them without repetition so that their least common multiple is not a prime number. Write a program to help Changha out.
Input
The first line contains a single integer $N$.
The second line contains $N$ space-separated integers $A_1, A_2, \cdots, A_N$.
Output
On the first line, print `YES` if it is possible to select integers so that their least common multiple is not a prime number, and print `NO` otherwise.
If there is such a way, print the number of selected integers $K$ on the second line, and the corresponding $K$ space-separated integers on the third line. The order in which the integers are printed does not matter.
If there are multiple solutions, print any of them.
Constraints
- $2 \le N \le 1000$
- $1 \le A_i \le 1000$
- If $i \ne j$, then $A_i \ne A_j$
Scoring
| No. | Points | Constraints |
|---|---|---|
| 1 | 20 | $N = 2$ |
| 2 | 80 | No additional constraints |
Examples
Input 1
4 2 5 6 4
Output 1
YES 2 4 5
Input 2
2 3 1
Output 2
NO
Note
In Example 1, the least common multiple of $4$ and $5$ is $20$, so choose $4$ and $5$. The least common multiple of $2$, $4$, and $6$ is $12$, so it is also possible to choose $2$, $4$, and $6$.