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.*;

public class Main {
	public static void main (String[] args) {
		Scanner s = new Scanner(System.in);
		int t = s.nextInt();
		for(int tt=0;tt<t;tt++)
		{
		    int n = s.nextInt();
		    int no = 0;
		    ArrayList<Integer> x = new ArrayList<>();
		    for(int i=2;i<=Math.sqrt(n);i++)
		    {
		        if( n%i==0 )
		        {
		            x.add(i);
		            no++;
		            n = n/i;
		            if(no==2)
		            break;
		        }
		    }
		    if(n!=1&&no==2 && n!=x.get(0) && n!=x.get(1)  )
		    {
		        System.out.println("YES");
		        System.out.println( x.get(0) + " " + x.get(1) + " " + n );
		    }
		    else
		    System.out.println("NO");
		}
	}
}