There are ~N~ objects each with a value ~v_i~. An object ~i~ is defined as shady if ~v_i~ has a prime number of digits, and the sum of its digits is prime.

Output whether each object is a shady object or not!

Input Specification

The first line will contain the integer ~N~ ~(1 \le N \le 1000)~.

The next ~N~ lines will each contain one integer, ~v_i~ ~(1 \le v_i < 10^{1000})~, the values of the objects.

Output Specification

Output ~N~ lines, the ~i^{th}~ line is YES if the ~i^{th}~ object is shady, and NO otherwise.

Sample Input

3
59
2132
3920393

Sample Output

NO
NO
YES