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.Arrays;
import java.util.Scanner;

public class tEst {
    static int  a[] = new int[78498];
    static int count = 0;

    public static void main(String[] args) {
        for (int i = 2; i < 1000000; i++) {
            boolean prost = true;
            int sqrt_i = (int) Math.sqrt(i)+1;
            for (int j = 0; j < count && a[j] < sqrt_i; j++) {
                if (i%a[j]==0) {
                    prost = false;
                    break;
                }
            }
            if (prost) {
                a[count++] = i;
            }
        }


        try (Scanner scanner = new Scanner(System.in)) {
            int n = scanner.nextInt();
            for (int i = 0; i < n; i++) {
                long x = scanner.nextLong();
                long sqrt_x = (long) Math.sqrt(x);
                if (sqrt_x*sqrt_x == x && Arrays.binarySearch(a, (int)sqrt_x)>=0) {
                    System.out.println("YES");
                } else {
                    System.out.println("NO");
                }
            }
        }
    }
}