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 $n$, $s(n)$, $s(s(n))$, $\ldots$ 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.