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.IOException;
import java.io.InputStreamReader;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {

    
    static int[] isPrime;
    
    public static void sieve(int N) {                   //generates all primes [2,N]
                                                        
        isPrime = new int[N+1];         
        isPrime[0] = isPrime[1] = 1;            // 0 indicates a prime number
        
        for (long i = 2; i <= N; i++)                   //you can loop till i*i <= N
            if (isPrime[(int)i]==0) 
            {
                for (long j = i * 2; j <= N; j += i)    //to test primality of N, loop till j*j <= N
                        isPrime[(int)j] = 1;
            }
    }
    
    public static void main(String[] args) throws IOException {
        
        StringBuilder sb = new StringBuilder();
        
        Scanner sc = new Scanner(System.in);

        
        
        sieve(1000000);
        int n = sc.nextInt();
        while(n-->0)
        {
            long x = sc.nextLong();
            
            double root = Math.sqrt(x);
            if(root==(int)root && isPrime[(int)root]==0)
                sb.append("YES\n");
            else
                sb.append("NO\n");
            
            
        }
        
        System.out.print(sb);
        
    }
}