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.*;
import java.util.*;  
public class main {	

	public static void main(String[] args) throws NumberFormatException, IOException
	{
		BufferedReader br= new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw= new PrintWriter(System.out);
		int t= Integer.parseInt(br.readLine());
		for (int i = 0; i < t; i++) {
			int n = Integer.parseInt(br.readLine());
			boolean possible=false;
			o:for (int j = 2; j <= Math.sqrt(n); j++) {
				if(n%j==0)
				{
					int temp=n/j;
					for (int k = j+1; k <= Math.sqrt(temp); k++) {
						if(temp%k==0)
						{
							if(j!= k && k!=temp/k && j!=temp/k)
							{
								pw.println("YES");
								pw.println(temp/k + " " + k + " " + j);
								possible=true;
							}
							break o;
						}
					}
				}
			}
			if(!possible)pw.println("NO");
		}
		pw.close();
	}
}