Composite Sequence

Time limit1sMemory limit256 MB

Summary

Decide whether some non-empty subsequence of the given positive integers sums to a composite number.

Level: Medium7 of 10
Topics: Math, Number theory, Greedy, Brute force
Solved: No attempts yet

Problem

A sequence $S$ of positive integers is a composite sequence if and only if there is a non-empty subsequence $T$ of $S$ such that the sum of all integers in $T$ is a composite number.

Given $S$ , determine whether $S$ is a composite sequence.

$1$ is not a composite number.

$T$ is a subsequence of $S$ if and only if we can obtain $T$ by removing some elements of $S$ (possibly none or all).

Input

The first line contains a single integer $n$ ( $1 \le n \le 10^5$ ), the size of $S$ .

The second line contains $n$ integers $S_1, S_2, \ldots, S_n$ : the elements of $S$ ( $1 \le S_i \le 10^9$ ).

Output

If $S$ is a composite sequence, output Yes. Otherwise, output No.

Examples2

Example 1
Input
```
2
5 7
```
Expected output
```
Yes
```
Example 2
Input
```
1
97
```
Expected output
```
No
```