Older Brother

Interview

Time limit2sMemory limit512 MB

Summary

Given an integer q up to 1e9, decide whether q is a prime power, printing yes or no.

Level: Easy3 of 10
Topics: Number theory, Math
Solved: No attempts yet

Problem

Your older brother is an amateur mathematician with plenty of experience. His memory is bad, though, and he never remembers which finite fields exist. For you this is an easy question. A finite field of order $q$ exists if and only if $q$ is a prime power, that is, $q = p^k$ for some prime $p$ and some integer $k \ge 1$ . When such a field exists, it is unique up to isomorphism.

The conversation with your brother went roughly like this.

Input

The input contains one integer $q$ ( $1 \le q \le 10^9$ ).

Output

Print yes if a finite field of order $q$ exists. Otherwise print no.

Examples3

Example 1
Input
```
1
```
Expected output
```
no
```
Example 2
Input
```
37
```
Expected output
```
yes
```
Example 3
Input
```
65536
```
Expected output
```
yes
```