Perfect primes (2) P16356

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 · 10⁶. 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.