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.math.*;
import java.util.*;

public class A {
	
	
	
	public static void main(String[] agrs) throws IOException {
		

//		PrintWriter pw = new PrintWriter(System.out);
		FastScanner sc = new FastScanner();
		

		int yo = sc.nextInt();
		while(yo-->0) {
			int n = sc.nextInt();
			if(n < 8) {
				System.out.println("NO");
				continue;
			}
			Set<Integer> set = new HashSet<>();
			for(int i = 2; i*i <= n; i++) {
				if(n%i == 0 && !set.contains(i)) {
					n /= i;
					set.add(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 e : set) {
					System.out.print(e + " ");
				}
				System.out.print(n + " ");
				System.out.println();
			}
			
		}
		
		
	}
	
	

	static class Pair{
		int x;
		int y;
		public Pair(int x, int y) {
			this.x = x;
			this.y = y;
		}
	}
	static int gcd(int a, int b) {
		return a%b == 0 ? b : gcd(b,a%b);
	}
	
	static int mod = 1000000007;
	
	static long pow(int a, int b) {
		if(b == 0) {
			return 1;
		}
		if(b == 1) {
			return a;
		}
		if(b%2 == 0) {
		
			long ans = pow(a,b/2);
			return ans*ans;
		}
		else {
			long ans = pow(a,(b-1)/2);
			return a * ans * ans;
		}
		
	}
	
	static boolean[] sieve(int n) {
		
		boolean isPrime[] = new boolean[n+1];
		for(int i = 2; i <= n; i++) {
			if(isPrime[i]) continue;
			for(int j = 2*i; j <= n; j+=i) {
				isPrime[j] = true;
			}
		
		}
		return isPrime;
		
	}


	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	
//	For Input.txt and Output.txt
	
//	FileInputStream in = new FileInputStream("input.txt");
//	FileOutputStream out = new FileOutputStream("output.txt");
//	PrintWriter pw = new PrintWriter(out);
//	Scanner sc = new Scanner(in);
 
}