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:
/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */


import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.stream.Stream;

/**
 *
 * @author sanchit
 */
public class another {
    public static void main(String[] args) throws IOException{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    int k = Integer.parseInt(br.readLine().trim());
    String[] input = br.readLine().trim().split(" ");
    long[] arr = Stream.of(input).mapToLong(Long::parseLong).toArray();
    
    boolean[] prime = new boolean[1000001];
    for(int i=0;i<=1000000;i++)
        prime[i] = true;
    for(int i=2;i*i<=1000000;i++)
    {
        if(prime[i]==true)
        {
            for(int j=i*i;j<=1000000;j+=i)
            {
                prime[j]=false;
            }
        }
    }
    prime[1]=false;
    for(int i=0;i<k;i++)
    {
        double n = (double)Math.sqrt(arr[i]);
        //System.out.print(n+" ");
        if(n/(int)n !=1)
        {
            System.out.println("NO");
            continue;
        }
        if(prime[(int)n]==true)
            System.out.println("YES");
        else
            System.out.println("NO");
        
    }
    
}

    
    
}