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.*;
import java.lang.Math;

public class hello
{
    public static void main (String[] args) throws java.lang.Exception
    {
        
        boolean[] isPrime = new boolean[1000010];
        for(int i = 1; i <= 1000000; i++)
            isPrime[i] = true;
        isPrime[1] = false;
        for(int p = 2; p <= 1000000; p++)
            if(isPrime[p])
                for(int k = 2; k*p <= 1000000; k++)
                    isPrime[k*p] = false;
        Scanner scan = new Scanner(System.in);
        int ans = 0;
        int a = scan.nextInt();
        scan.nextLine();
        int[] nums = new int[a];
        for(int i = 0; i < a; i++) {
            long b = scan.nextLong();
            double sqrt = Math.sqrt(b);
            if(sqrt == Math.ceil(sqrt)) {
                if(isPrime[(int)sqrt]) {
                    System.out.println("YES");
                    continue;
                }
            }
            System.out.println("NO");
        }
        //System.out.println(ans);
    }
    
    /*private static boolean checkPrime(long n) {
        if (n%2==0 && n != 2) return false;
        //if not, then just check the odds
        for(long i=3;i*i<=n;i+=2) {
            if(n%i==0)
                return false;
        }
        return true;
    }*/
}