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.Arrays;
import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int t=sc.nextInt();	
		int a[]=new int[3];
		while(t-->0) {
			Arrays.fill(a,0);
			int cnt=0;
			int n=sc.nextInt();
			for(int i=2;i<=Math.sqrt(n);i++) {
				if(n%i==0) {
					a[cnt++]=i;
					n/=i;
					if(cnt==2) {a[cnt]=n;break;}
				}
			}
			if(cnt==2&&a[2]>a[1]) {
				System.out.println("YES\n"+a[0]+" "+a[1]+" "+a[2]);
			}
			else System.out.println("NO");
		}
		sc.close();
	}
}