Here, we say that a natural n is primeful if it is possible to obtain a prime number by deleting some (possibly none) digits from n.

For example, 6814 is primeful because deleting 8 and 4 results in 61, which is prime.

Given several n, can you determine whether they are primeful or not?

Input

Input consists of several n, all between 1 and 10^{105} − 1.

Output

For every given n, tell if it is primeful or not.

Public test cases

**Input**

6814 1 9609 7 77 9088164 4444444444444444444 660000498 90014 46666669 60649

**Output**

yes no no yes yes yes no yes yes no yes

Information

- Author
- Félix Moreno
- Language
- English
- Official solutions
- C++
- User solutions
- C++