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;

public class Main {

	public static void main(String[] args){
		
		int t;
		Scanner sc = new Scanner(System.in);
		t = sc.nextInt();
		for(int i=0;i<t;i++)
		{
			int n = sc.nextInt();
			ArrayList<Integer> ans = new ArrayList<>();
			int count=0;
			
			int cuberoot = (int)Math.pow(n, 0.33)+1;
			int j=2;
			int temp = n;
			while(j*j<n)
			{
				if(temp%j==0)
				{
					temp = temp/j;
					ans.add(j);
					count++;
					if(count==2)
						break;
				}
				
				j++;
			}
			
	
			
			if(count!=2)
			{
				System.out.println("NO");
				continue;
			}
			else
			{
				if(temp!=ans.get(1) && temp!=ans.get(0) && temp>2)
				{
				System.out.println("YES");
				System.out.println(ans.get(0)+" "+ans.get(1)+" "+n/(ans.get(0)*ans.get(1)));
				}
				else
					System.out.println("NO");
				
					
			}
		}
		
    } 

}