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.HashSet;
import java.util.Iterator;
import java.util.Scanner;

public class Solution {

    private static HashSet<Integer> set = new HashSet<>();

    private static void process(int num, int init){

        for(int i = init; i * i <= num; i++){
            if(num % i == 0){
                if(set.size() == 1){
                    if(i != num){
                        set.add(i);
                        set.add(num/ i);
                        break;
                    }
                }
                set.add(i);
                process(num / i, i + 1);
                break;
            }
        }

    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();

        for(int i = 0; i < n; i++){ //test cases

            int num = sc.nextInt();

            process(num, 2);

            if(set.size() >= 3){
                System.out.println("YES");
                Iterator<Integer> it = set.iterator();
                while(it.hasNext()){
                    System.out.print(it.next() + " ");
                }
            } else {
                System.out.println("NO");
            }

            set.clear();

        }


    }
}