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.Arrays;
import java.util.Scanner;

/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */

/**
 *
 * @author ahmadla
 */
public class ll {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        // TODO code application logic here
        Scanner in =new Scanner (System.in);
      
        boolean f=false,f1;
        int n =in.nextInt();
          int arr[]=new int [n];
          long co=0;long ce=0;
        for (int k= 0; k< n; k++) {
         arr[k] =in.nextInt();
         if(arr[k]%2!=0)
             co++;
         else
             ce++;
        }
        boolean f3=true;
        long c=0;
        long sum=0;
   
         if(co>ce)
         {
         f3=false;
         c=co-ce;
         }else
             c=ce-co;
       
          
    
        c-=1;
        Arrays.sort(arr);
    
         for (int i = 0; i < n; i++) {
             
             if(c<=0)
                break;    
   
             if(f3)
            {
            if(arr[i]%2==0)
            {  sum+=arr[i] ;
            c--;
            }
    
            }
            else
            {
             if(arr[i]%2!=0)
             { sum+=arr[i] ;
             c--;  }
            }
                  
           
        }
       
          System.out.println(sum);
    }
}
