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:
/*package whatever //do not write package name here */

import java.io.*;
import java.util.*;

public class GFG {
   
   static String solve(ArrayList<Integer> div,int n)
   {
       HashSet<Integer> set=new HashSet<>();
       int sz=div.size();
       for(int i=0;i<sz;i++)
           set.add(div.get(i));
       
       for(int i=0;i<sz;i++)
       {
           for(int j=i+1;j<sz;j++)
           {
               int a=div.get(i);
               int b=div.get(j);
               if(a!=b){
               int ab=a*b;
               if(n%ab==0)
               {
                   int c=n/ab;
                   if(set.contains(c)&&(a!=c)&&(b!=c))
                   {
                       return "YES\n"+c+" "+a+" "+" "+b;
                   }
               }
                  }
           }
       }
      return "NO";
   }
   static void findDiv(int n,ArrayList<Integer> div)
   {
       int p=(int)Math.sqrt(n);
       for(int i=2;i<=p;i++)
       {
           if(n%i==0)
           {
               if(n/i==i)
               {
                   div.add(i);
               }
               else
               {
                   div.add(n/i);
                   div.add(i);
               }
           }
       }
   }
	public static void main (String[] args) throws Exception{
		 BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
		 int t=Integer.parseInt(bf.readLine());
		 StringBuffer str=new StringBuffer("");
		 while(t-->0)
		 {
		     int n=Integer.parseInt(bf.readLine());
		     ArrayList<Integer> div=new ArrayList<>();
		     findDiv(n,div);
		     Collections.sort(div);
		     str.append(solve(div,n)+"\n");
		 }
		 System.out.println(str);
	}
}