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.*;
import java.lang.*;
import java.io.*;
 
 
public class Main
{
   
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int t = sc.nextInt();
		while(t>0){
		int n = sc.nextInt();
		int num = n;
		final int MAX = 100000;
		int[] arr = new int[MAX];
		int id = 0;
		for(int i=2;i*i<=num;i++) {
			if(num%i==0) {
			    while(num%i==0) {
			       	arr[id++] = i;
					num = num/i;
				
				}
			
			}
		}
		if(num>1) arr[id++] = num;
		if(id<3){
		    System.out.println("NO"); t--;continue;
		}
	
		int a = arr[0];
		int b = 1;
		int c = 1;
		int st = 1;
		if(arr[0]!=arr[1]){
		     b = arr[1];
		     st = 2;
		}
		else{
		     b = arr[1]*arr[2];
		     st = 3;
		}
		
		if(a*b==n){
		    System.out.println("NO");
		    t--;
		   continue;
		}
		for(int i=st;i<id;i++){
		    c = c*arr[i];
		}
		if(a!= b && b!=c && c!=a){
		System.out.println("YES");
    	System.out.print(a + " " + b + " " + c);
    	System.out.println();}
    	else System.out.println("NO");
    	t--;
		}
	}
}