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 Main {


    public static int calcSum(int[] ar, int n) {
        int sum = 0;

        for (int i = 0; i < n; i++) {
            sum += ar[i];
        }

        return sum;
    }


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

        int n = sc.nextInt();
        int a;

        int arr0[] = new int[n];
        int arr1[] = new int[n];

        int i0 = 0, i1 = 0;

        for (int i = 0; i < n; i++) {
            a = sc.nextInt();

            if ((a & 1) == 0) arr0[i0++] = a;
            else arr1[i1++] = a;
        }

        Arrays.sort(arr0, 0, i0);
        Arrays.sort(arr1, 0, i1);

        if (i0 >= i1) {
            int d = i0 - i1 - 1;
            System.out.println(calcSum(arr0, d));
        }
        else {
            int d = i1 - i0 - 1;
            System.out.println(calcSum(arr1, d));
        }
    }
}
