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.ArrayList;
import java.util.HashSet;
import java.util.StringTokenizer;
// نورت الكود يا كبير اتفضل

// يا رب Accepted
public class ProductOfThreeNumbers {

    static ArrayList<Integer> primes;

    public static void primeFactors(int n) {
        while (n % 2 == 0) {
            primes.add(2);
            n /= 2;
        }
        for (int i = 3; i <= Math.sqrt(n); i += 2) {
            while (n % i == 0) {
                primes.add(i);
                n /= i;
            }
        }
        if (n > 1)
            primes.add(n);
    }

    public static void main(String[] args) {
        FastReader in = new FastReader();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));


        int t = in.nextInt();
        while (t-- > 0) {
            primes = new ArrayList<>();
            int x = in.nextInt();
            primeFactors(x);
            

            if (primes.size() < 3)
                out.println("NO");
            else {
                HashSet<Integer> set = new HashSet<>();
                int sum = 1, size = 0;
                for (Integer i : primes) {
                    if (size < 3)
                        if (!set.contains(i)) {
                            set.add(i);
                            size++;
                        } else if (!set.contains(sum * i)) {
                            set.add(sum * i);
                            sum = 1;
                            size++;
                        } else
                            sum *= i;
                    else
                        sum *= i;
                }
                if (sum != 1)
                    for (Integer i : set) {
                        if (!set.contains(i * sum)) {
                            set.remove(i);
                            set.add(i * sum);
                            sum = 1;
                            break;
                        }
                    }

                if (set.size() < 3 || sum != 1)
                    out.println("NO");
                if (set.size() == 3) {
                    out.println("YES");
                    for (Integer i : set) {
                        out.print(i + " ");
                    }
                    out.println();
                }
            }
        }

        out.close();
    }

    private static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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