Perfect primes

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 $n$ , $s(n)$ , $s(s(n))$ , $\ldots$ only contains prime numbers. For instance, $977$ is a perfect prime, because $977$ , as well as $9+7+7=23$ , $2+3=5$ , $5$ , $5$ , $\ldots$ are prime numbers.

Input

Each line of the input contains a number $1 \le n \le 16 \cdot 10^6$ . 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.

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T10:15:31.147Z