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

public class GFG {
	public static void main (String[] args) {
	   
        Scanner sc=new Scanner(System.in);
        int t=sc.nextInt();
        for(int i=0;i<t;i++)
         {int n=sc.nextInt();mm(n);}
         
    }
    static int mm (int n){
        int nsqr=(int)Math.sqrt(n);
             for(int j=2;j<=nsqr;j++)
         {
             if(n%j==0)
              {int nbyjsqr=(int)Math.sqrt(n/j);
                  for(int k=j+1;k<=nbyjsqr;k++)
              {
                  if((n/j)%k==0)
                   {if(j!=k&&k!=(n/(j*k))&&(n/(j*k))!=j)
                   {System.out.println("YES");
                    System.out.println(j+" "+k+" "+n/(k*j));
                    return 1;
                   }}
              }
              }
            
         }
         System.out.println("NO");
                    
                    return -1;  
   
    }
	}