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.util.*;

public class P230B {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        int casos = sc.nextInt();
        long valor;

        int maxLimit = 1000000; // la sqrt de 10^12

        long[] array = new long[casos];
        for (int k = 0; k < casos; k++)
            array[k] = sc.nextLong();

        boolean[] primes = new boolean[maxLimit + 1];
        primes[0] = primes[1] = false;
        
        for (int k = 2; k <= maxLimit; k++)
            primes[k] = true;
        
        for (int k = 2; k <= sqrt(maxLimit); k++)
            if (primes[k])
                for (int m = 2; m <= maxLimit / k; m++)
                    primes[m * k] = false;

        int inputRoot;
        for (int k = 0; k < casos; k++) {
            inputRoot = (int) sqrt(array[k]);
            if (primes[inputRoot] && (long)inputRoot * (long)inputRoot == array[k])
                System.out.println("YES");
            else
                System.out.println("NO");
        }

    }
    
    private static boolean isPrime(long numero)
    {
        long max = numero;
        long i = 1;
        
        if ( numero == 2 )
            return true;
        
        while( i++ <= max)
        {
            if(numero%i == 0)
                return false;
            
            max = numero / i;           
        }
        
        return true;
    }
    
    private static long sqrt(long x)
    {
        long min = 0, max = 303700050l, med = 0;
        
        while(max - min > 1)
        {
            med = (max+min)/2l;
            if(med*med < x)
                min = med;
            else if(med*med > x)
                max = med;
            else
                return med;
            
        }
        //sysout
        return max;
        
    }

}