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.*;
import java.io.*;

public class CodeForces {

    private Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

    public static void main(String[] args) {
        new CodeForces().solve();
    }

    private void solve(){
        int n = in.nextInt();

        List<Integer> odd = new ArrayList<>();
        List<Integer> even = new ArrayList<>();

        for(int i = 0; i < n; i++){
            int t = in.nextInt();
            if(t % 2 == 0)
                even.add(t);
            else
                odd.add(t);
        }

        Collections.sort(odd, Collections.<Integer>reverseOrder());
        Collections.sort(even, Collections.<Integer>reverseOrder());

        int index = odd.size() < even.size() ? odd.size() + 1 : even.size() + 1;
        List<Integer> fin = odd.size() > even.size() ? odd : even;

        long res = 0;
        for(int i = index; i < fin.size(); i++){
            res += fin.get(i);
        }

        System.out.println(res);

    }

    String get(String s){
        char[] chars = s.toCharArray();
        Arrays.sort(chars);

        for(int i = 1; i < chars.length; i++){
            if(chars[i] != chars[i-1] + 1){
                return "No";
            }
        }
        return "Yes";
    }






}