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 in = new Scanner(System.in);
		int t = in.nextInt();
		while(t-->0){
		
		int n = in.nextInt();
		int count=0;
		
		int a=0,b=0;
		
		for(int i=2;i<=Math.sqrt(n);i++){
		    
		    if(n%i==0){
		        n=n/i;
		        if(a==0){
		            count++;
		            a=i;
		        }else if(b==0 && i!=n){
		            b=i;
		            count++;
		            break;
		        }
		    }
		    
		}
		
		if(count==2){
		        System.out.println("YES");
		        System.out.println(a+" "+b+" "+n);
		    }else{
		        System.out.println("NO");
		    }
 
		
	  }
	    
	}
}