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.Arrays;
import java.util.Scanner;
import java.util.function.IntPredicate;

public class B1144 {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);
        final int n = s.nextInt();
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = s.nextInt();
        }


        final long even = Arrays.stream(arr).filter(i -> i % 2 == 0).count();
        final long odd = n - even;

        if (Math.abs(even - odd) <= 1) {
            System.out.println(0);
            return;
        }

        Arrays.sort(arr);
        long diff = n - 2 * Math.min(even, odd) - 1;
        IntPredicate filter = even > odd ?
                i -> i % 2 == 0 :
                i -> i % 2 == 1;
        System.out.println(getMaxFiltredItems(arr, filter, diff));
    }

    private static long getMaxFiltredItems(int[] array, IntPredicate filter, long size) {
        long sum = 0;
        for (int i = 0; i < array.length; i++) {
            if (size == 0) break;
            if (filter.test(array[i])) {
                sum += array[i];
                size--;
            }
        }
        return sum;
    }
}
