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.Collections;
import java.util.HashMap;
import java.util.Scanner;

/**
 *
 * @author arabtech
 */
public class Nnn {

    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        ArrayList<Integer> even=new ArrayList<Integer>();
        ArrayList<Integer> odd=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            int num=sc.nextInt();
            if(num%2==0){
                even.add(num);
            }
            else{
                odd.add(num);
            }
        }
        if(n%2==0&&even.size()==odd.size()){
            System.out.println(0);
        }
        else if(n%2==1&&Math.abs(even.size()-odd.size())==1){
            System.out.println(0);
        }
        else{
            int sum=0;
            if(odd.size()<even.size()){
                Collections.sort(even);
                for(int i=even.size()-odd.size()-2;i>=0;i--){
                    sum+=even.get(i);
                }
            }
            else{
                Collections.sort(odd);
                 for(int i=odd.size()-even.size()-2;i>=0;i--){
                    sum+=odd.get(i);
                }
            } 
            System.out.println(sum);
        }
    }
}
