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 {
	static final long M = 1000000007;
		static FastReader in = new FastReader();
		static PrintWriter out = new PrintWriter(System.out);
//		static Scanner in = new Scanner(System.in);
//        File file = new File("input.txt");
//        Scanner in = new Scanner(file);
//        PrintWriter out = new PrintWriter(new FileWriter("output.txt"));
    public static void main(String[] args) {
    	
    	int t = in.nextInt();
    	while(t-- > 0) {
    		long n = in.nextLong();
    		int a = -1, b = -1;
    		for(int i = 2; i*i<=n; i++) {
    			if(n%i == 0) {
    				a = i;
    				n/=i;
    				break;
    			}
    		}
    		for(int i = 2; i*i<=n; i++) {
    			if(n%i==0 && i!=a) {
    				b = i;
    				n/=i;
    				break;
    			}
    		}
    		if(n==a || n==b || n<2 || b==-1 || a==-1) {
    			System.out.println("NO");
    		}else {
    			System.out.println("YES");
    			System.out.println(a+" "+b+" "+n);
    		}
    		
    	}

    	
    	
    	
    	out.close();   	
    }
    
    private static int gcd(int a, int b) {
    	if(b==0) return a;
    	return gcd(b, a%b);
    }

	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;
        }
    }
}