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.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;

public class Tprimes {
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter pw = new PrintWriter(System.out);
        boolean[] primes = new boolean[1_000_001];
        int sqrt = (int) Math.sqrt(1_000_001);
        for (int i = 0; i < 1_000_001; i++) {
            if (i % 2 == 0 && i != 2)
                primes[i] = false;
            else
                primes[i] = true;
        }
        primes[0] = primes[1] = false;
        for (int i = 3; i <= sqrt; i++) {
            if (primes[i]) {
                for (int j = i * i; j <= 1_000_000; j += i){
                    primes[j] = false;
                }
            }
        }
        br.readLine();
        String[] in =  br.readLine().split(" ");
        StringBuilder sb = new StringBuilder();
        for (int i = 0; i < in.length; i++) {
            long temp1 = Long.parseLong(in[i]);
            long temp2 = (long) Math.sqrt(temp1);
            if (temp2 * temp2 == temp1 && primes[(int) temp2])
                sb.append("YES\n");
            else
                sb.append("NO\n");
        }
        pw.println(sb);
        pw.close();
    }
}