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.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Solution {
    private static Scanner sc = new Scanner(System.in);

    public static void main(String[] args) {
        boolean[] pre = new boolean[1000001];
        Arrays.fill(pre, true);
        pre[0] = false;
        pre[1] = false;
        for (int p = 2; p * p < pre.length; p++) {
            if (pre[p]) {
                for (int i = p * p; i < pre.length; i += p)
                    pre[i] = false;
            }
        }
        int t = 0;
        if (sc.hasNext())
            t = sc.nextInt();
        while (t-- > 0) {
            long n = sc.nextLong();
            solve(n, pre);
        }
    }
    //   }

    private static void solve(long n, boolean[] pre) {
        double m = Math.sqrt(n);
        int check = (int) m;
        if (pre[(int) m] && m == check)
            System.out.println("YES");
        else
            System.out.println("NO");
    }
}