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.B;

import java.util.*;

public class cf230B {

    private static int MAX_N = (int) 1e6;
    private static boolean[] primes = new boolean[MAX_N+1];

    private static void seive() {
        primes[0] = primes[1] = true;
        for (int i = 2; i*i < MAX_N; i++) {
            if (!primes[i]) {
                for (int j = i*i; j <= MAX_N; j += i) {
                    if (j < 0) {
                        break;
                    }
                    primes[j] = true;
                }
            }
        }
    }

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

        int n = in.nextInt();
        ArrayList<Long> list = new ArrayList<>(n);

        for (int i = 0; i < n; i++) {
            list.add(in.nextLong());
        }

        for (long j: list) {
            double root = Math.sqrt(j);
            if ((int) root == root && !primes[(int) root]) {
                System.out.println("YES");
            }
            else {
                System.out.println("NO");
            }
        }
    }
}