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.io.*;
import java.util.*;

public class Main
{

    public static void main(String[] args) throws IOException
    {
        BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
        String[] line = sc.readLine().split(" ");
        int cases = Integer.parseInt(line[0]);

        top:
        for (int l = 0; l < cases; l++)
        {
            line = sc.readLine().split(" ");
            int num = Integer.parseInt(line[0]);
            int nums[] = new int[3];
            int loc = 0;

            for (int i = 2; i * i < num; i++)
            {
                if (num % i == 0)
                {
                    nums[loc] = i;
                    num = num / i;
                    loc++;

                }
                if (loc == 2)
                {
                    nums[2] = num;
                    System.out.println("YES");
                    System.out.println(nums[0] + " " + nums[1] + " " + nums[2] + " ");
                    continue top;
                }
            }
            System.out.println("NO");
        }
    }
}