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.*;
import java.io.*;
 
public class CodeForces
{
	public static void main(String[] args)throws IOException
	{
		Scanner sc=new Scanner(System.in);
		//Scanner sc=new Scanner(new File("ip.txt"));
		int tc,n,a,b,i,sq;
		boolean flag;

		
		tc=sc.nextInt();
		while(tc-->0)
		{
			n=sc.nextInt();
			sq=(int)Math.sqrt(n);

			for(i=2;i<=sq;i++)
				if(n%i==0)
					break;

			if(i==sq+1)
			{
				System.out.println("NO");
				continue;
			}

			a=i;
			n=n/i;
			sq=(int)Math.sqrt(n);

			for(i=2;i<=sq;i++)
				if(n%i==0&&i!=a)
					break;

			if(i==sq+1)
			{
				System.out.println("NO");
				continue;
			}

			b=i;
			n=n/i;
			if(n!=b&&n!=a)
			{
				System.out.println("YES");
				System.out.println(a+" "+b+" "+n);
			}
			else
				System.out.println("NO");
		}		
	}
}