Problem: We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer t Т-prime, if t has exactly three distinct positive divisors.

You are given an array of n positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, n (1 ≤ n ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print n lines: the i-th line should contain "YES" (without the quotes), if number xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".

Solution (in JAVA):

Solution:
import java.io.*;
import java.lang.annotation.Target;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashSet;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeSet;
 


public class Main 
{

	public static void main(String[] args) throws java.lang.Exception
	{
		Scanner s=new Scanner(System.in);
		boolean[] prime=new boolean[1000001];
		Arrays.fill(prime, true);
		prime[1]=false;
		for(int i=2;i<prime.length;i++)
			for(int j=2;j*i<prime.length;j++)
				prime[i*j]=false;
		int t=s.nextInt();
		while(t-->0)
		{
			long n=s.nextLong();
			double d1=Math.sqrt(n);
			double d2=Math.floor(d1);
			if(d1-d2==0)
			{
			if(prime[(int)d1])
			System.out.println("YES");
			else
			System.out.println("NO");
			}
			else
			System.out.println("NO");

		}
	
	s.close();
	} 
}