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:
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
    public static ArrayList<Long> primeFactors(long n) 
    { 
        ArrayList<Long> arr=new ArrayList<>();
        // Print the number of 2s that divide n 
        while (n%2==0) 
        { 
            arr.add(2l);
            n /= 2; 
        } 
  
        // n must be odd at this point.  So we can 
        // skip one element (Note i = i +2) 
        for (long i = 3; i <= Math.sqrt(n); i+= 2) 
        { 
            // While i divides n, print i and divide n 
            while (n%i == 0) 
            { 
                arr.add(i); 
                n /= i; 
            } 
        } 
  
        // This condition is to handle the case whien 
        // n is a prime number greater than 2 
        if (n > 2) 
            arr.add(n); 
            return arr;
    } 
	public static void main (String[] args) throws java.lang.Exception
	{
	    
		Scanner sc=new Scanner(System.in);
		int t=sc.nextInt();
		for(int y=0;y<t;++y)
		{
		    long n=sc.nextLong();
		   ArrayList<Long> arr = primeFactors(n);
		    if(arr.size()<3)
		    {
		        System.out.println("NO");
		        continue;
		    }
		    
		    if(arr.size()==3)
		    { long a=arr.get(0);
		      long b=arr.get(1);
		      long c=arr.get(2);
		      
		         if(a==b || b==c || a==c)
		    {
		        System.out.println("NO");
		        continue;
		    }
		    else{
		        System.out.println("YES");
		        System.out.println(a+" "+b+" "+c);
		        continue;
		    }
		    }
		    long a=arr.get(0);
		    long b=0;
		    if(arr.get(0)==arr.get(1))
		    {
		        b=arr.get(1)*arr.get(2);
		    }
		    else{
		        b=arr.get(1);
		    }
		    long c=n/(a*b);
		    //System.out.println(a+" akshay  "+b+" "+c);
		    if(a==b || b==c || a==c)
		    {
		        System.out.println("NO");
		        continue;
		    }
		    else{
		        System.out.println("YES");
		        System.out.println(a+" "+b+" "+c);
		        continue;
		    }
		   
		}
	}
}