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.BufferedReader;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.Scanner;

import javax.xml.datatype.DatatypeConfigurationException;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;

/**
 * Test
 */
public class Test {
    static  boolean[] prime;
    static void sieveOfEratosthenes()
    {
        long n = 1000000;
        prime = new boolean[1000000+1];
        for(int i=0;i<n;i++)
            prime[i] = true;
         
        for(int p = 2; p*p <=n; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[p] == true)
            {
                // Update all multiples of p
                for(int i = p*2; i <= n; i += p)
                    prime[i] = false;
            }
        }
    }

    public static void main(String[] args) throws IOException {
        int n;
        long val;
        double sq;
        Scanner in = new Scanner(System.in);
        sieveOfEratosthenes();
        //Scanner in = new Scanner(new BufferedReader(new FileReader("test.txt")));
        n = in.nextInt();
        for(int i=0;i<n;i++){
            val = in.nextLong();
            if(val > 1){
            sq = Math.round(Math.sqrt(val)) ;
            
            if(val == Math.pow(sq, 2)){
                if(prime[(int)sq]){
                    System.out.println("YES");
                }else{
                    System.out.println("NO");
                }
            }else{
                System.out.println("NO");
            }
            }else{
                System.out.println("NO");
            }
        }
        in.close();
    }

}