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.Comparator;
import java.util.Scanner;

public class Main {

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

        int n = reader.nextInt();

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

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

        even.sort(Comparator.reverseOrder());
        odd.sort(Comparator.reverseOrder());

        int evenLen = even.size();
        int oddLen = odd.size();

        int diff;
        int sum = 0;
        if (evenLen > oddLen) {
            diff = evenLen - oddLen - 1;

            if (diff >= 1) {
                for (int j = evenLen - 1; j >= evenLen - diff; j--) {
                    sum += even.get(j);
                }
            } else {
                sum = 0;
            }
        } else {
            diff = oddLen - evenLen - 1;
            if (diff >= 1) {
                for (int j = oddLen - 1; j >= oddLen - diff; j--) {
                    sum += odd.get(j);
                }
            } else {
                sum = 0;
            }
        }

        System.out.println(sum);
    }
}