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.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Jaynil
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        CProductOfThreeNumbers solver = new CProductOfThreeNumbers();
        int testCount = Integer.parseInt(in.next());
        for (int i = 1; i <= testCount; i++)
            solver.solve(i, in, out);
        out.close();
    }

    static class CProductOfThreeNumbers {
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            if (n % 2 == 0) {
                n = n / 2;
                for (int i = 3; i * i < n; i++) {
                    if (n % i == 0 && n / i != 2) {
                        out.println("YES");
                        out.println(2 + " " + (n / i) + " " + i);
                        return;
                    }
                }
                out.println("NO");
                return;
            }
            if (Maths.isPrime(n)) {
                out.println("NO");
                return;
            }
            int x = 0;
            for (int i = 2; i * i <= n; i++) {
                if (n % i == 0) {
                    x = i;
                    break;
                }
            }
            n = n / x;
            if (Maths.isPrime(n)) {
                out.println("NO");
                return;
            }
            for (int i = 2; i * i < n; i++) {
                if (n % i == 0 && i != x && n / i != x) {
                    out.println("YES");
                    out.println(x + " " + (n / i) + " " + i);
                    return;
                }
            }
            out.println("NO");
        }

    }

    static class Maths {
        static boolean isPrime(int n) {
            if (n <= 1) return false;
            if (n <= 3) return true;
            if (n % 2 == 0 || n % 3 == 0) return false;
            for (int i = 5; i * i <= n; i = i + 6)
                if (n % i == 0 || n % (i + 2) == 0)
                    return false;
            return true;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}