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.*;
public class ProductOf3Numbers {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		int arr[] = new int[t];
		for(int i=0; i<t; i++) {
			arr[i] = sc.nextInt();
		}
		sc.close();
		for(int i=0; i<t; i++) {
			if(isPossible(arr[i]) == "NO")
			System.out.println(isPossible(arr[i]));
			else {
				System.out.println("YES");
				System.out.println(isPossible(arr[i]));
			}
		}
		
	}
	static String isPossible(int n) {
		int sqrt = (int)Math.floor(Math.pow(n,0.5));
		ArrayList<Integer> arr = new ArrayList<>();
		int i;
		for(i=2; i<= sqrt; i++) {
			if(n%i == 0 && arr.size() < 2) {
				n = n/i;
				arr.add(i);
			}
		}
		if(arr.size() < 2) {
			return "NO";
		}
		else {
			if(arr.get(0) != n && arr.get(1) != n)
				return arr.get(0) + " " + arr.get(1) + " " + n;
		}
		return "NO";
	}
}