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 Main
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc=new Scanner(System.in);
		
		int t=sc.nextInt();
		for(int k=0;k<t;k++){
			
		int n=sc.nextInt();
		int n1=n;
		int[] a1=new int[3];
		int count=0;
		
		for(int i=2;i*i<=n;i++)
		{
			if(n%i==0 && (i!=a1[0] || i!=a1[1]))
			{
				a1[count]=i;
				count++;
				n=n/i;
				if(count==2 && n>1 && (n!=a1[0] && n!=a1[1]))
				{
					a1[2]=n;
					count++;
				}
			}
			
			if(count==3)
			{
				System.out.println("YES");
				
					System.out.print(a1[0]+" "+a1[1]+" "+a1[2]);
				
				System.out.println();
				break;
			}
				
		}
			if(count!=3)
			{
				System.out.println("NO");
			}
		}
		
	
	}
}