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.util.*;
public class Tprime {
static int prime[]=new int[1000001];

static class FastReader{
	BufferedReader br;
	StringTokenizer st;
	public FastReader()
	{
		br=new BufferedReader(new InputStreamReader(System.in));
	}
	
	String next()
	{
		while(st==null||!st.hasMoreElements())
		{
			try {
				st=new StringTokenizer(br.readLine());
			}
			catch(IOException e)
			{
				e.printStackTrace();
			}
		}
		return st.nextToken();
	}
	
	int nextInt()
	{
		return Integer.parseInt(next());
	}
	
	long nextLong()
	{
		return Long.parseLong(next());
	}

}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		
		prime[0]=1;
		prime[1]=1;
		
		for(int i=2;i*i<=1000000;i++)
		{
			if(prime[i]==0)
			{
				for(int j=i*i;j<=1000000;j+=i)
				{
					prime[j]=1;
				}
			}
		}
		FastReader sc=new FastReader();
		int t=sc.nextInt();
		while(t-->0)
		{
			long val=sc.nextLong();
			long v=(long)Math.sqrt(val);
			if(v*v==val)
			{
				if(prime[(int)v]==0)
				{
					System.out.println("YES");
				}
				else
					System.out.println("NO");
			}
			else
			{
				System.out.println("NO");
			}
		}
	}

}