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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int t = in.nextInt();
            while (t-- > 0)
            {
                solve(in, out);
            }
        }

        private void solve(Scanner in, PrintWriter out)
        {
            int n = in.nextInt();
            int N = n;
            int a = 1;
            int b = 1;
            int c = 1;

            int sqrt = (int) Math.sqrt(1_000_000_000) + 1;
            for (int i = 2; i <= sqrt; i++)
            {
                if (n % i == 0)
                {
                    a = i;
                    n /= i;
                    break;
                }
            }
            if (a == 1)
            {
                out.println("NO");
                return;
            }

            for (int i = 2; i <= sqrt; i++)
            {
                if (i != a)
                {
                    if (n % i == 0)
                    {
                        b = i;
                        n /= i;
                        break;
                    }
                }
            }

            if (b == 1)
            {
                out.println("NO");
                return;
            }

            c = n;

            if (c == 1)
            {
                out.println("NO");
                return;
            }

            if (a == b || b == c || a == c)
            {
                out.println("NO");
                return;
            }

            if (a * b * c == N)
            {
                out.println("YES");
                out.println(a + " " + b + " " + c);
                return;
            }
            out.println("NO");
        }

    }
}