At last, an interesting and difficult problem! P69284


Statement
 

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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 10105 − 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++