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.Scanner;


public class Main {

	/**
	 * @param args
	 */
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t-->0){
			int n = sc.nextInt();
			doTheTask(n);
		}
	}
	static void doTheTask (int n)
	{
	    for (int i=2; i*i<=n; i++)
	    {
	        if (n % i == 0)
	        {
	            int d = n/i;

	            for (int j=i+1; j*j<d; j++)
	            {
	                if (d % j == 0)
	                {
	                    System.out.printf ("YES\n%d %d %d\n",i,j,d/j);
	                    return;
	                }
	            }
	        }
	    }

	    System.out.println ("NO\n");
	}

}