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.BufferedReader;
import java.util.ArrayList;
//import java.util.HashMap;
import java.io.InputStreamReader;
public class TEMP1
{
	static boolean isp(int n)
	{
		for(int i=2;i<=(int)Math.sqrt(n);i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static void main(String args[])throws Exception
	{
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		int t=Integer.parseInt(br.readLine());
		for(int i=0;i<t;i++)
		{
			int n=Integer.parseInt(br.readLine());
			int copy=n;
			if(n<24)
			{
				System.out.println("NO");
				continue;
			}
			String ans="";
			int temp=(int)Math.sqrt(n);
			int cou=0,ls=0;
			int arr[]=new int[2];
			for(int j=2;j<=temp;j++)
			{
				if(n%j==0)
				{
					ans=ans+(j+" ");
					n/=j;
					cou++;
					arr[ls]=j;
					ls++;
					if(cou==2)
						break;
				}
			}
			if(n==1||arr[0]==n||arr[1]==n||cou<2)
				System.out.println("NO");
			else
				System.out.println("YES\n"+ans+n);
		}
	}
}