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 Main {
    public static void main(String[] args){
        Scanner s = new Scanner(System.in);
        int t = s.nextInt();
        while(t>0){
        int a=0;
        int b=0;
        int c=0;
        int n = s.nextInt();
        for(int i =2; i*i<=n;i++ ){
            a=0;
            if(n%i==0){
                a=i;
                n=n/i;
                for(int j=i+1;j*j<=n;j++){
                b=0;
                c=0;
                if(n%j==0){
                    b=j;
                    c=n/j;
                    if(c!=b)
                    break;
                }
                b=0;
                }
                if(b!=0){
                    break;
                }
            }
         
        }
        if(b==0){
            System.out.println("NO");
        }else{
            System.out.println("YES");
            System.out.println(a+" "+b+" "+c);
        }
        t--;
        }
    }
}