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.io.*;
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class JavaApplication1 {
	public static void main(String args[]) throws IOException {
        
Scanner sc  = new Scanner(System.in);
int t = sc.nextInt();

for (int i = 0; i < t; i++) {
int x = sc.nextInt();
List<Integer> list = new ArrayList();
int factor = 2;
    for (int j = 2; j*j < x; j++) {
        
        if (list.size()>=3) {
           break;
        }
        if (x%factor ==0) {
            if (!list.isEmpty()) {
                 list.add(x/factor);    
            }
            list.add(factor);
            x = x/ factor;
       
        }
           factor++;
    }
    
    if (list.size() < 3) {
         System.out.println("NO");
    }else
    {
     System.out.println("YES");
     System.out.println(list.get(0)+" "+list.get(1)+" "+list.get(2));
    }
}


           
            
           






}}