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 q = in.nextInt();

            while (q > 0) {

                int n = in.nextInt();
                int a = -1;
                int b = -1;
                int c = -1;
                boolean flag = false;
                for (int i = 2; i <= Math.sqrt(n); i++) {
                    int temp = n;
                    if (temp % i == 0) {
                        a = i;
                        temp /= i;
                        boolean f = false;
                        for (int j = i + 1; j <= Math.sqrt(temp); j++) {
                            if (temp % j == 0 && temp / j != j) {
                                b = j;
                                c = (n / b) / a;
                                flag = true;
                                f = true;
                                break;
                            }
                        }
                        if (f) break;
                    }
                }

                if (flag) {
                    out.println("YES");
                    out.println(a + " " + b + " " + c);
                } else {
                    out.println("NO");
                }
                q--;
            }
        }

    }
}