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;

/**
 *
 * @author DELL
 */
public class Codechef {
    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();
            ArrayList<Integer> a=new ArrayList<>();
            for(int j=2;j<=Math.sqrt(n);j++)
            {  
               
                if(n%j==0)
                {
                if(n/j==j)
                {
                    a.add(j);
                }
                else
                {
                 a.add(j);
               a.add(n/j);
                }
            }
          }
            int flag=0;
  if(a.size()>=3)
  {
      for(int j=0;j<a.size()-2;j++)
      {
          for(int r=j+1;r<a.size()-1;r++)
          {
              for(int y=j+2;y<a.size();y++)
              {
                  if(a.get(j)*a.get(r)*a.get(y)==n&&(a.get(j)!=(a.get(r)))&&(a.get(j)!=(a.get(y)))&&(a.get(y)!=a.get(r)))
                  {
                      System.out.println("YES");
                      System.out.println(a.get(j)+" "+a.get(r)+" "+a.get(y));
                      flag=1;
                      break;
                  }
                }
              if(flag==1)
                  break;
          }
          if(flag==1)
              break;
      }
  }
 if(flag==0)
                System.out.println("NO");
      
}
}
}