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.*;
// scanner.nextInt();
public class Solution {
    public static void main(String[] args) {
        
        Scanner scanner = new Scanner(System.in);
        int test_case = scanner.nextInt();
            for(int z = 0; z < test_case; ++z)
            {
                int n = scanner.nextInt();
		
                int[] divisores = new int[3];
                
                int size = 0;
                boolean done = false;
                for(int i = 2; i*i <= n; ++i)
                {
                    if(n % i == 0)
                    {
                        divisores[size] = i;
                        ++size;
                        n /= i;
                        if(size == 2 && n > i)
                        {          
                            divisores[2] = n;
                            done = true;
                            break;
                            
                        }
                        else if(size == 2) break;
                        
                    }             
                }
                if(done)
                    {
                        System.out.println("Yes");
                        System.out.println(divisores[0] + " " + divisores[1] + " " + divisores[2]);
                    }
                    else System.out.println("No");
                        
            }
                    
    }
    
}