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);
		//System.out.println("Enter T: ");
		int T=sc.nextInt();
		for(int t=0;t<T;t++){
			int n=sc.nextInt();
			solve(n);
		}
        }
    	public static void solve(int n) {
		int n_copy=n;
		ArrayList<Integer>list=new ArrayList<>();
		for(int i=2;i<=Math.sqrt(n);i++){
			if(n_copy%i==0){
				list.add(n/i);
			}
		}
		int a=0,b=0,c=0;
		boolean flag=false;
		String res="NO";
		for(int i=0;i<list.size();i++){
			int num=list.get(i);
			for(int j=2;j<=Math.sqrt(num);j++){
				if(num%j==0){
					int num2=num/j;
					int third=n/num;
					if(num2!=j&&num2!=third&&j!=third){
						a=num2;
						b=j;
						c=n/num;
						res="YES";
						flag=true;
						break;
					}
				}
			}
			if(flag==true){break;}
			
		}
		System.out.println(res);
		if(res.equals("YES")){
			System.out.println(a+" "+b+" "+c);
		}
	}
    
    
}