Upside-down prime

Time limit3sMemory limit256 MB

Summary

Check whether N and its 180-degree rotation are both prime, where digits 3, 4 and 7 make the rotation invalid.

Level: Medium6 of 10
Topics: Number theory, Implementation
Solved: No attempts yet

Problem

I knocked my alarm clock over in my sleep, and 08:15 had turned into 51:80. Some digits on a digital display are still digits after you turn them 180 degrees.

Turning a single digit 180 degrees gives this.

0, 2, 5 and 8 keep their shape.
1 keeps its shape and moves to the other side of its place.
6 becomes 9, and 9 becomes 6.
3, 4 and 7 turn into shapes that are not digits.

Turning the whole number also reverses the order of the places. Turning 18115211 by 180 degrees gives 11251181. A zero at the front of the result is not read.

The numbers I like are primes. Decide whether $N$ is prime and whether the number obtained by turning $N$ 180 degrees is prime as well. If $N$ contains a 3, a 4 or a 7, the rotation is not a number, so $N$ fails the condition.

Input

The first line contains $N$ ( $1 \le N \le 10^{16}$ ).

The first digit of $N$ is not 0.

Output

Print yes on the first line if $N$ is prime and the number obtained by turning it 180 degrees is prime as well. Otherwise print no.

Examples3

Example 1
Input
```
151
```
Expected output
```
yes
```
Example 2
Input
```
23
```
Expected output
```
no
```
Example 3
Input
```
18115211
```
Expected output
```
no
```