pkSingh is never interested in number sequences but once he came across a rare sequence of numbers.
In this sequence

• The first number is 1
• The next numbers are obtained by appending 001 to the corresponding previous number.

1, 1001, .....
(All the numbers in this sequence are palindromes)

Now pkSingh wants to test primality of Kth number in this sequence.Help him.

Input

Input starts with an integer N specifying number of test cases and then N numbers follow in next N lines. 2≤K≤10^18

Output

For each test case output in a seperate line "yes" if the Kth number is a prime.Otherwise output "no".

Example

Input:
1
2

Output:
no