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 MyClass {
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      int t=sc.nextInt();
      for(int i=0;i<t;i++)
      {
          int n=sc.nextInt();
          int b=0;
          int arr[]=new int[3];
          for(int j=2;j*j<n;j++)
          {
              if(n%j==0)
              {
                  arr[0]=j;
                  int h=n/j;
                for(int k=j+1;k*k<h;k++)
                {
                  if(h%k==0)
                  {
                      arr[1]=k;
                      arr[2]=h/k;
                      break;
                  }
              }
              break;
              }
          }
              int g=0;
              Arrays.sort(arr);
              for(int j=0;j<2;j++)
              {
                 if(arr[j]==arr[j+1]||arr[j]==0||arr[j+1]==0)
                    g=1;
              }
              if(g==0)
              {
                  System.out.println("YES");
                  System.out.println(arr[0]+" "+arr[1]+" "+arr[2]);
              }
              else
                System.out.println("NO");
      
    }
}
}