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.*;
public class Main
{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long t = sc.nextLong();
		while(t>0){
		   long n = sc.nextLong();
		   long a[] = new long[3];
		   int cnt = 0;
		   for(long i=2;i*i<n;i++){
            if(n%i==0){
	           a[0] = i;
		        cnt++;
		         n /= i;
		         break;
		      }
		   }
		    for(long i=a[0]+1;i*i<n;i++){
		       if(n%i==0){
		           a[1] = i;
		           cnt++;
		           n /= i;
		           break;
		       }
		    }
		     
		    if((n<a[1] && a[1]>0)|| (n<a[0] && a[0]>0) || cnt<2){
                System.out.println("NO");		        
		    }
		    else{
		        System.out.println("YES\n"+a[0]+" "+a[1]+" "+n);    
		    }

		    
            
            t--;
		}
	}
}