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.Comparator;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();

        ArrayList<Integer> odds = new ArrayList<Integer>();
        ArrayList<Integer> evens = new ArrayList<Integer>();
        int totalSum = 0;

        for (int i = 0; i < n; i += 1) {
            int num = in.nextInt();
            totalSum += num;

            if (num % 2 == 1) {
                odds.add(num);
            } else {
                evens.add(num);
            }
        }

        Comparator<Integer> revComp = new Comparator<Integer>() {
            @Override
            public int compare(Integer a, Integer b) {
                return b.compareTo(a);
            }
        };

        Collections.sort(odds, revComp);
        Collections.sort(evens, revComp);

        int commonSize = Math.min(odds.size(), evens.size());
        int res = totalSum
                - prefixSum(odds, commonSize)
                - prefixSum(evens, commonSize);

        System.out.println(res);

    }

    private static int prefixSum(final ArrayList<Integer> arr, int commonSize) {
        int sum = 0;
        for (int i = 0; i < Math.min(commonSize + 1, arr.size()); i += 1) {
            sum += arr.get(i);
        }
        return sum;
    }
}
