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.Scanner;

public class cfTaskC1{
	public static void main(String[] args) {
		Scanner input = new Scanner(System.in);
		int t = input.nextInt();
		int num;
		int[] arr = new int[3];
		arr[0] = 0;
		arr[1] = 0;
		arr[2] = 0;
		for(int i = 0; i < t; i++){
			num = input.nextInt();
			int realnum = num;
			int min = 2;
			for(int z = min; z*z <= num; z++){
				if(num%z == 0){
					arr[0] = z;
					min = z+1;
					num /= z;
					break;
				}
			}
			for(int z = min; z*z <= num; z++){
				if(num%z == 0){
					arr[1] = z;
					min = z+1;
					break;
				}
			}
			if(arr[0] != 0 && arr[1] != 0){
					if(realnum % (arr[0] * arr[1]) == 0 && realnum / (arr[0] * arr[1]) != arr[0] && realnum / (arr[0] * arr[1]) != arr[1]){
						arr[2] = realnum / (arr[0] * arr[1]);
						}
				}
			if(arr[2] != 0){
				System.out.println("YES");
				System.out.println(arr[0] + " " + arr[1] + " " + arr[2]);
			}
			else{
				System.out.println("NO");
			}
			arr[0] = 0;
			arr[1] = 0;
			arr[2] = 0;

		}

	}
}