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; // don't place package name! */

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

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{

	public static void main (String[] args) 
	{
		// your code goes here
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		
		while(t-->0)
		{
		  int n=s.nextInt();
		  int jo=0;
		  for(int i=2;i<=Math.sqrt(n);i++)
		  {
		      if(n%i==0)
		      {
		          int r=n/i;
		          for(int j=2;j<=Math.sqrt(r);j++)
		          {
		              if(r%j==0&&j!=i&&r/j!=i&&j!=r/j)
		              {
		                  System.out.println("YES");
		                  System.out.println(i+" "+j+" "+r/j);
		                  jo=1;
		                  break;
		              }
		          }
		          if(jo==1)
		          break;
		      }
		  }
		  if(jo==0)
		  System.out.println("NO");
		      
		}
	}
}