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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class ProductOfThreeNumbers {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner s=new Scanner(System.in);
		int t=s.nextInt();
		while(t--!=0){
			int n=s.nextInt();
			int v=n;
			Set<Integer> st=new HashSet<>();
			for(int i=2;i<=Math.sqrt(v);i++){
				if(v%i==0){
					st.add(i);
					v=v/i;
					break;
				}
			}
			for(int i=2;i<=Math.sqrt(v);i++){
				if(v%i==0){
					if(!st.contains(i)){
					st.add(i);
					v=v/i;
					break;
					}
				}
			}
			if(st.size()!=2){
				System.out.println("NO");
				continue;
			}
			int r=1;
			for(Integer i:st){
				r*=i;
			}
			if(n%r==0){
				int y=n/r;
				st.add(y);
				if(st.size()==3){
				System.out.println("YES");
				for(Integer i:st){
					System.out.print(i+" ");
				}
				System.out.println();
				}else{
					System.out.println("NO");
				}
			}else{
				System.out.println("NO");
			}
		}
	}

}