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.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int a[]=new int [(int)5e4+10];
		ArrayList<Integer> al=new ArrayList<Integer>();
		Arrays.fill(a,1);
		for(int i=2;i<a.length;i++) {
			if(a[i]==1) {
				for(int j=2*i;j<a.length;j+=i) a[j]=0;
				al.add(i);
			}
		}
		int t=sc.nextInt();
		while(t-->0) {
			int n=sc.nextInt();
			int g=0,ans=0;
			for(int i=0;al.get(i)<=Math.sqrt(n);i++) {
				if(n%al.get(i)==0) {ans=al.get(i);n/=ans;break;}
			}
			if(ans==0) {System.out.println("NO");continue;}
			for(int i=2;i<=Math.sqrt(n);i++) {
				if(i==ans) continue;
				if(n%i==0&&n/i!=i&&n/i!=ans) {
					System.out.println("YES\n"+ans+" "+i+" "+(n/i));
					g=1;
					break;
				}
			}
			if(g==0)
				System.out.println("NO");
		}
		sc.close();
	}
}