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.Scanner;

public class ewtry {
public static void main(String[] args) {
   Scanner sc=new Scanner (System.in);
   int t=sc.nextInt();
   
   while(t-->0)
   {
       int n=sc.nextInt();
       ArrayList <Integer> l1=new ArrayList<Integer>();
       
       
       for(int i=2;i<=Math.sqrt(n);i++)
       {
           if(n%i==0)
           {
               n=n/i;
               l1.add(i);
               if(l1.size()==2&&n>1&&n!=i)
               {
                   l1.add(n);
                   break;
               }
           }
           
           
       }
     if(l1.size()==3)
     {
         System.out.println("YES");
         String s="";
         
         for(int i=0;i<3;i++)
         {
            s=s+l1.get(i)+" ";
         }
         System.out.println(s);
     }
     else{
         System.out.println("NO");
     }
    }
}
    
}