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 Product_Of_Three_Numbers {

	public static void main(String args[]) {
		
		Scanner sc = new Scanner(System.in);
		//System.out.println("Enter the number of test cases :");
		int t=sc.nextInt();
		
		for(int i=0;i<t;i++) {
			int n=sc.nextInt();
			find(n);
		}
	}
	public static void find(int n) {
		
		int k = 0;
		int m=n;
		int res[] = new int[3];
		for(int i=2;i*i<=n;i++) {
			
			if(k==1 && n%i==0) {
				res[k] = i;
				k++;
				break;
			}
			if(k<1 && n%i==0) {
				res[k]=i;
				n=n/i;
				k++;
			}
			
		}
		int r=0;
		if(res[0]!=0 && res[1]!=0) {
			r=m/(res[0]*res[1]);
		
			if(r !=res[0] && r!=res[1] && r!=1) {
				System.out.println("YES");
				System.out.println(res[0]+" "+res[1]+" "+r);
			}
			else
				System.out.println("NO");
		}
		else 
			System.out.println("NO");		
	}
}