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.ArrayList;
import java.util.List;
import java.util.Scanner;

import static java.lang.Math.sqrt;

public class Main {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int n = scanner.nextInt();
        //int n = 100;
        List<Long> set = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            set.add(scanner.nextLong());
            //set.add((long)999999901 + i);
        }

        set.forEach(number -> {
            int a = 0;
            int b = 0;
            int c = 0;

            long t = 0;

            int g =(int) sqrt(number);
            for (int i = 2; i < number / i; i++) {
                if (number % i == 0) {
                    a = i;
                    t = number / a;
                    break;
                }
            }

            if (t != 0) {
                int h = (int)(number / a);
                for (int i = a + 1; i < h / i; i++) {
                    if (t % i == 0) {
                        b = i;
                        break;
                    }
                }
            }

            if (a != 0 && b != 0) {
                c = (int) (number / a) / b;
                if (c == a || c == b || c < 2) {
                    System.out.println("NO");
                    return;
                }
            }


            if (a != 0 && b != 0 && c != 0) {
                System.out.println("YES");
                System.out.println(a + " " + b + " " + c);
            } else {
                System.out.println("NO");
            }

        });

    }






}