Polycarp has an array a consisting of n integers.

He wants to play a game with this array. The game consists of several moves. On the first move he chooses any element and deletes it (after the first move the array contains n-1 elements). For each of the next moves he chooses any element with the only restriction: its parity should differ from the parity of the element deleted on the previous move. In other words, he alternates parities (even-odd-even-odd-... or odd-even-odd-even-...) of the removed elements. Polycarp stops if he can't make a move.

Formally: 

  * If it is the first move, he chooses any element and deletes it; 
  * If it is the second or any next move: 
    * if the last deleted element was odd, Polycarp chooses any even element and deletes it; 
    * if the last deleted element was even, Polycarp chooses any odd element and deletes it. 
  * If after some move Polycarp cannot make a move, the game ends. 



Polycarp's goal is to minimize the sum of non-deleted elements of the array after end of the game. If Polycarp can delete the whole array, then the sum of non-deleted elements is zero.

Help Polycarp find this value.

Input

The first line of the input contains one integer n (1 ≤ n ≤ 2000) — the number of elements of a.

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^6), where a_i is the i-th element of a.

Output

Print one integer — the minimum possible sum of non-deleted elements of the array after end of the game.

Examples

Input


5
1 5 7 8 2


Output


0


Input


6
5 1 2 4 6 3


Output


0


Input


2
1000000 1000000


Output


1000000


import java.util.ArrayList;
import java.util.Arrays;
import java.util.Queue;
import java.util.Scanner;
import java.util.Stack;


public class JavaApplication2 {
  
        
 
       public static void main(String[] args) {
           Scanner ss=new Scanner(System.in);
           int n=ss.nextInt();
            int[] arr= new int[n];
            int odd=0;
            int even=0;
            int sum=0;
            for (int i = 0; i < n; i++) {
                arr[i]=ss.nextInt();
                if(arr[i]%2==0)
                    even++;
                else odd++;
           }
            Arrays.sort(arr);
            if(odd==even)
                System.out.print(sum);
            else if(Math.abs(odd-even)==1)
                System.out.print(sum);
            
            else{
                if(even>odd+1)
                {
                   even=even-odd-1;
                    for (int i = 0; i < even; i++) {
                        if(arr[i]%2==0)
                            sum+=arr[i];
                        else even++;
                        
                    }
                }
                else{
                     odd=odd-even-1;
                    for (int i = 0; i < odd; i++) {
                        if(arr[i]%2==1)
                            sum+=arr[i];
                        else odd++;
                        
                    }
                    
                    
                }
                
           System.out.print(sum);
               
           }
        
             
                     
                     
                     
                 
                 
                
                     
                 
                    
          
           
        
  
       
        
     
        
            
       
       
        
        
        
        
           
          


        
    }

   
}
