Given a natural number n, let s(n) be the sum of the digits (in base
10) of n. We say that n is a *perfect prime* if the infinite sequence
formed by n, s(n), s(s(n)), … only contains prime numbers.
For instance, 977 is a perfect prime, because 977,
as well as 9+7+7=23, 2+3=5, 5, 5, … are prime numbers.

Input

Each line of the input contains a number 1 ≤ n ≤ 16 · 10^{6}. A line
with n=0 marks the end of the input.

Output

For each n, print in a line “yes” or “no”, depending on whether n is a perfect prime or it is not.

Public test cases

**Input**

977 1 7 17 15999923 16000000 0

**Output**

yes no yes no yes no