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.*;
import java.math.*;
import javafx.util.Pair;
public class Fff {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) throws IOException {
   
    BufferedReader bf=new BufferedReader(new InputStreamReader(System.in));
     StringBuffer out = new StringBuffer();
    int t=Integer.parseInt(bf.readLine());
        while (t-- > 0) {
            int n = Integer.parseInt(bf.readLine());
            ArrayList<Integer> al = new ArrayList();
            StringBuffer out1 = new StringBuffer();
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    al.add(i);
                    al.add(n / i);
                }
            }
            Collections.sort(al);
            boolean tf=false;
            for (int k = 0; k < al.size(); k++) {
                int x = al.get(k);
                for (int j = 2; j*j <= x; j++) {
                    if (x % j == 0) {
                        if (x / j != j&& x / j != al.get(al.size()-k-1)&&al.get(al.size()-k-1)!=j) {
                            out1.append((x/j)+" "+ j +" "+ al.get(al.size()-k-1));
                        tf=true;break;}
                    }
                }if(tf){break;}
            }
            if(!tf){out.append("NO\n");}
            else{out.append("YES\n"+out1+"\n");}
        }
        System.out.print(out);
    }
 
    
}