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.Scanner;

public class ProductofThreeNumbers {
    
    public static int findDiv(int last, int n){
        for(int i=last+1; i<Math.sqrt(n) ;i++){
            if(n%i==0)
                return i;
        }
        return -1;
    }
    
    public static void main(String[] args) {

        Scanner s = new Scanner(System.in);

        int t = s.nextInt();

        while (t-- > 0) {

            int n = s.nextInt();

            int a=findDiv(1, n);
            int b=findDiv(a, n/a);
            int c=n/(a*b);
            
            if(a<0 || b<0 || a==c || b==c)
                System.out.println("NO");
            else{
                System.out.println("YES");
                System.out.print(a+ " "+ b+ " "+c);
                System.out.println();
            }
            
        }
    }
}