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 code {
	static int sqrt(int x) {
		for(int i=2; true; i++) {
			if(i*i==x) {
				return i;
			}
			if(i*i>x) {
				return i-1;
			}
		}
	}
 
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		for(int i=0; i<n; i++) {
			int a= sc.nextInt();
			int b= sqrt(a);
			int c=0;
			double[] arr= new double[2];
			for(double j=2; j<=b; j++) {
				if((a/j)%1==0) {
					arr[c]=j;
					c++;
				}
				if(c==2) {
					double z=((a/arr[0])/arr[1]);
					if(z%1==0 && z!=arr[1] && z!=arr[0]) {
						break;
					}
					else {
						c--;
					}
				}
			}
			if(c==2) {
				System.out.println("YES");
				System.out.println((int)arr[0]+" "+(int)arr[1]+" "+(int)((a/arr[0])/arr[1]));
			}
			else {
				System.out.println("NO");
			}
		}
	}
}