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.Collections;
import java.util.List;
import java.util.Scanner;

public class B1144 {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        int[] A = new int[N];
        for (int n=0; n<N; n++) {
            A[n] = in.nextInt();
        }
        int answer = Math.min(answer(A, true), answer(A, false));
        System.out.println(answer);
    }

    private static int answer(int[] A, boolean odd) {
        List<Integer> oddList = new ArrayList<Integer>();
        List<Integer> evenList = new ArrayList<Integer>();
        for (int a : A) {
            if (a%2 == 0) {
                evenList.add(a);
            } else {
                oddList.add(a);
            }
        }
        Collections.sort(oddList);
        Collections.sort(evenList);
        Collections.reverse(oddList);
        Collections.reverse(evenList);
        while (true) {
            if (odd) {
                if (oddList.isEmpty()) break;
                oddList.remove(0);
            } else {
                if (evenList.isEmpty()) break;
                evenList.remove(0);
            }
            odd = !odd;
        }
        int sum = 0;
        for (int x : oddList) sum += x;
        for (int x : evenList) sum += x;
        return sum;
    }

}
