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.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;


public class Main
{
	static String s;
	public static void main(String[] args) throws NumberFormatException, IOException
	{
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw= new BufferedWriter(new OutputStreamWriter(System.out));
		String str= br.readLine();
		
		int t = Integer.parseInt(str);
		for(int h=0; h<t; h++)
		{
			int n= Integer.parseInt(br.readLine());
			String s="NO";
			int nn=0;
			int i=2;
			int m0=0;
			
			while(i*i<=n)
			{
				if(nn==0)
				{
					if(n%i==0)
					{
						n /= i;
						m0=i;
						nn++;
					}
				}
				else if(nn==1)
				{
					if(n%i==0 && n/i != i)
					{
						s = "YES\n" + m0  + " " + i + " " + n/i;
						break;
					}
				}
				i++;
			}
			
			System.out.println(s);
		}
	}
}