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 Solution{
    
    public static void main(String[] args) throws Exception{
        
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(buffer.readLine());
        while(t-- > 0){
            long num = Long.parseLong(buffer.readLine());
            int a=-1,b= -1, c=-1;
            boolean check = false;
            for(int i=2; i*i<=num; i++){
                if(num % i == 0){
                    a = i;
                    int n = (int)num/a;
                    
                    for(int j=2; j*j<=n && j!= a && n/j != a; j++){
                        if(n % j == 0){
                            if(j != n/j){
                                b = j;
                                c = n/j;
                                check = true;
                                break;
                            }
                            
                        }
                    }
                    if(check)
                        break;
                }
            }
            if(check){
                System.out.println("YES");
                System.out.println(a + " " + b + " " + c);
            }
            else
                System.out.println("NO");
        }
            
}
}