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 CodeForces1294C{
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int t = input.nextInt();
		for(int j = 0;j<t;j++){
			int n = input.nextInt();
			ArrayList<Integer> arr = new ArrayList<>();
			int m = n;
			for(int i = 2;i<=Math.sqrt(m);i++){
				if(n%i == 0){
					if(arr.size() == 2){
						break;
					}
					arr.add(i);
					n/= i;
				}
			}

			if(arr.size() < 2 || arr.contains(n)){
				System.out.println("NO");
			}
			else{
				System.out.println("YES");
				System.out.println(arr.get(0) + " " + arr.get(1) + " " + n);
			}
		}
	}
}