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.io.*;
import java.lang.*;
import java.math.BigInteger;
import java.util.*;
public class Main{
	static Scanner scanner=new Scanner(System.in);
	public static void main(String[] args) {
		int q=scanner.nextInt();
		while(q-->0) {
			int n=scanner.nextInt();
			Set<Integer>set=new HashSet<Integer>();
			for(int i=2;i<=Math.sqrt(n);i++) {
				if(n%i==0) {
					set.add(i);
					n/=i;
					if(set.size()==2) {
						set.add(n);
						break;
					}
				}
			}
			if(set.size()==3) {
				System.out.println("YES");
				for(int i:set) {
					System.out.print(i+" ");
				}
				System.out.println();
			}else System.out.println("No");
		}
	}
}