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:
//package codeforces;
import java.util.*;
public class Main {

    public static boolean isprime(long x){
        if (x == 1)
            return false;
        for (int i = 2; i <= Math.sqrt(x); i++) {
            if (x%i == 0)
                return false;
        }
        return true;
    }
    public static void main(String[] args) {
        int[] p = new int[1000001];
        for (int i = 2; i < 1000; i++) {
            int j = i*2;
            while (j<1000001){
                p[j] = 1;
                j += i;
            }
        }
        
        long x,n;
        Scanner l = new Scanner(System.in);
        n = l.nextLong();
        for (int i = 0; i < n; i++) {
            x = l.nextLong();
            long temp = (long)Math.sqrt(x);
            if (temp*temp == x && temp != 1 && p[(int)temp] == 0)
                System.out.println("YES");
            else
                System.out.println("NO");
        }
    }
}