Problem: You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 

Solution (in JAVA):

Solution:
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;




public class App{
    
    public static void main(String[] args) {
          Scanner in =  new Scanner(System.in);
     
          int t = in.nextInt();

          while(t-- > 0){
              int n = in.nextInt();

              boolean flag = true;
              for(int i = 2;i*i < n;i++){
                   if(n%i == 0){
                     for(int j = i+1;j*j < n/i;j++){
                      
                         if((n/i)%j == 0){
                          flag = false;
                           System.out.println("YES");
                           System.out.println(i + " " + j + " " + n/i/j);                      
                           i = n;
                          break;
                          }
                     }
                   }

              }

              if(flag){
                System.out.println("NO");
              }
          }
    }
  }