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 Aman {
    public static void main(String args[]) {
        Scanner in = new Scanner(System.in);
        int t = in.nextInt();
        
        for(int i = 0; i < t; i++) {
            int n = in.nextInt();
            int ans[] = new int[3];
            int m = 0;
            int temp = (int) Math.sqrt(n);
            
            for(int j = 2; j < temp && m < 2; j++) {
                if(n%j == 0) {
                    ans[m++] = j;
                    n = n/j;
                }
            }
            if(m == 2) {
                ans[m] = n;
                if(ans[1] != ans[2] && ans[0] != ans[2] && n != 1) {
                   System.out.println("YES"); 
                    System.out.print(ans[0] + " " + ans[1] + " " + ans[2] + "\n");
                } else
                System.out.println("NO");
            } else {
                System.out.println("NO"); 
            }
        }  
    }
}