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.*;

public class _1144B {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);

        int n=sc.nextInt();
        ArrayList<Integer> ar_ji=new ArrayList<>();
        ArrayList<Integer> ar_ou=new ArrayList<>();

        for (int i=0;i<n;i++){
            int number=sc.nextInt();
            if (number%2!=0){
                ar_ji.add(number);
            }else {
                ar_ou.add(number);
            }
        }

        if (ar_ji.size()-ar_ou.size()==1||ar_ou.size()-ar_ji.size()==1||ar_ji.size()==ar_ou.size()){
            System.out.println(0);
        }else {
            Collections.sort(ar_ji);
            Collections.sort(ar_ou);

            if (ar_ji.size()>ar_ou.size()){
                int x=ar_ji.size()-ar_ou.size();
                int sum=0;
                for (int i=0;i<x-1;i++){
                    sum+=ar_ji.get(i);

                }
                System.out.println(sum);
            }else{
                int x=ar_ou.size()-ar_ji.size();
                int sum=0;
                for (int i=0;i<x-1;i++){
                    sum+=ar_ou.get(i);
                }
                System.out.println(sum);
            }

        }




    }
}
