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* ≤ 4000000. 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 0

**Output**

yes no yes no