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 C615
{
	public static void main(String[] args) 
	{
		// TODO Auto-generated method stub
		Scanner obj=new Scanner(System.in);
		int t=obj.nextInt();
		while (t-->0)
		{
			int n=obj.nextInt();
			int k=n;
			int c=0;
			ArrayList<Integer> arr=new ArrayList<>();
			for(int i=2;i<=Math.sqrt(k);i++)
			{
				if(n%i==0)
				{
					n=n/i;
					c++;
					arr.add(i);
					if(c==2)
					{
						break;
					}
				}
			}
			if(c>=2)
			{
				if(k%(arr.get(0)*arr.get(1))==0)
				{
					if(((k/(arr.get(0)*arr.get(1)))!=arr.get(0))&&(k/(arr.get(0)*arr.get(1)))!=arr.get(1))
					{
						System.out.println("YES");
						System.out.println(arr.get(0)+" "+arr.get(1)+" "+(k/(arr.get(0)*arr.get(1))));
					}
					else 
						System.out.println("NO");
				}
			}
			else System.out.println("NO");

		}

	}
}