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.*;
import java.io.*;

public class Main{
     public static void main(String[] args) {
          MyScanner kb = new MyScanner();
          out = new PrintWriter(new BufferedOutputStream(System.out));
          int i, j, T;
          double N;
          
          boolean[] primeNaki = new boolean[1000001];
          
          Arrays.fill(primeNaki, true);
          primeNaki[0] = primeNaki[1] = false;
          
          for (i = 2 ; i * i <= primeNaki.length ; i++) {
               for (j = i * i ; j < primeNaki.length ; j = j + i){
                    primeNaki[j] = false;
               }
          }
          
          T = kb.nextInt();
          
          for(i = 1 ; i <= T ; i++){
               N = kb.nextDouble();
               
               
               if ((int)Math.sqrt(N) == Math.sqrt(N) && primeNaki[(int)Math.sqrt(N)]){
                    out.println("YES");
               }
               else {
                    out.println("NO");
               }
          }
          
          out.close();
     }
     
     
     //-----------PrintWriter for faster output---------------------------------
     public static PrintWriter out;
     
     //-----------MyScanner class for faster input----------
     public static class MyScanner {
          BufferedReader br;
          StringTokenizer st;
          
          public MyScanner() {
               br = new BufferedReader(new InputStreamReader(System.in));
          }
          
          String next() {
               while (st == null || !st.hasMoreElements()) {
                    try {
                         st = new StringTokenizer(br.readLine());
                    } catch (IOException e) {
                         e.printStackTrace();
                    }
               }
               return st.nextToken();
          }
          
          int nextInt() {
               return Integer.parseInt(next());
          }
          
          long nextLong() {
               return Long.parseLong(next());
          }
          
          double nextDouble() {
               return Double.parseDouble(next());
          }
          
          String nextLine(){
               String str = "";
               try {
                    str = br.readLine();
               } catch (IOException e) {
                    e.printStackTrace();
               }
               return str;
          }
          
     }
     //--------------------------------------------------------
}