Description

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

Input

There are several lines in input file,each line has a nonnegative interger a ,(a is no more than 2^30)

Output

For the number a on each line of the input file ,if a is a friend number ,output ‘YES!’,otherwise output ‘NO!’

Sample Input

3
13121
12131

Sample Output

YES!
YES!
NO!

HINT

Source

HDU - 1719