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 Main{
  public static void main(String[] args)throws IOException{
    Scanner sc = new Scanner(System.in);
    long a,b,c,d,e,f,g,h,i,j,k;
    a = sc.nextLong();
    for(b = 0;b < a;b++){
      c = sc.nextLong();
      d = (long)Math.sqrt(c);
      if(c % 2 == 0){
        e = c/2;
        i = 0;
        g = 0;
        h = 0;
        for(f = 3;f <= d;f++){
          if(e % f == 0 && e % (e/f) == 0 && (e/f) > 2 && (e/f) != f){
            g = f;
            h = e/f;
            i = 1;
            break;
          }
        }
        if(i == 1){
          System.out.println("YES");
          System.out.println(2+" "+g+" "+h);
        }else{
          System.out.println("NO");
        }
      }else{
        e  =c;
        i = 0;
        j = 0;
        k = 0;
        g = 0;
        h = 0;
        
        for(f = 3;f <= d;f++){
          if(c % f == 0){
            e = c/f;
            k = f;
            i = 1;
            break;
          }
        }
        if(i == 1){
          for(f = 2;f <= d;f++){
            
            if(e % f == 0 && e % (e/f) == 0 && (e/f) >= 2 && (e/f) != f && (e/f) != k && f != k){
              g = f;
              h = e/f;
              j = 1;
              break;
            }
          }
          if(j == 1){
            System.out.println("YES");
            System.out.println(k+" "+g+" "+h);
          }else{
          System.out.println("NO");
        }
        }else{
          System.out.println("NO");
        }
      }
    }
  }
}