Description

Friendnumber is defined recursively as follows. (1) numbers 1 and 2 are friend number; (2) if a and b are friend numbers, so is ab+a+b; (3) only the numbers defined in (1) and (2) are friend number. Now your task is to judge whether an integer is a friend number.

Input

There are several lines in input, each line has a nonnegative integer a (0<=a<=2^30)。

Output

For the number a on each line of the input, if a is a friend number, output “YES!”, otherwise output “NO!”.

Sample

Input

3
13121
12131

Output

YES!
YES!
NO!