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

public class Main {

    /**
     *
     * k = 1
     *
     * 2^17+1  2^17     0
     * 1      2^17+1   1
     *
     * dp[2][2] = max(
     */


    public static void main(String[] args) {
        FastReader sc = new FastReader();
        int t = sc.nextInt();
        outer: while (t-->0) {
            int n = sc.nextInt();
            Set<Integer> set = new HashSet<>();
            for (int i = 2; i*i<=n;i++) {
                if (n % i == 0) {
                    set.add(i);
                    n /= i;
                    break;
                }
            }
            for (int i = 2; i*i <= n; i++) {
                if (n % i == 0 && !set.contains(i)) {
                    n /= i;
                    set.add(i);
                    break;
                }
            }
            if (set.size() < 2 || set.contains(n)) {
                System.out.println("NO");
            } else {
                System.out.println("YES");
                for (int k : set) {
                    System.out.print(k+ " ");
                }
                System.out.println(n);
            }
        }


        // 2 <= a * b * c = n
        //

    }

    private static int[] isPrime(int num) {
        for (int i = 2; i <= (int)Math.sqrt(num); i++) {
            if (num % i == 0) return new int[]{i, num/i};
        }
        return null;
    }

    private static int sign(long num) {
        if (num < 0) return -1;
        return 1;
    }

    private static class Pair {
        int x;
        int y;
        public Pair(int x, int y) {
            this.x=x;
            this.y=y;
        }
    }




    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public 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());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }


    }

}

/**
 * 7 3
 * 3 1 5
 * 9 6 5
 *
 * i = 1: 1
 * i = 2: 2
 * i = 3: 3
 *
 *
 * 1 2 3 3 3 3 3
 */


/**
 *
 *  1+1
 **/