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.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.AbstractCollection;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.AbstractQueue;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            int n = in.nextInt();
            PriorityQueue<Integer> odd = new PriorityQueue<>((p, q) -> q - p);
            PriorityQueue<Integer> even = new PriorityQueue<>((p, q) -> q - p);
            for (int i = 0; i < n; i++) {
                int num = in.nextInt();
                if (num % 2 == 0) even.add(num);
                else odd.add(num);
            }

            boolean evenFirst = even.size() > odd.size();
            while (!odd.isEmpty() && !even.isEmpty()) {
                if (evenFirst) {
                    even.remove();
                } else {
                    odd.remove();
                }
                evenFirst = !evenFirst;
            }

            if (evenFirst && !even.isEmpty()) even.remove();
            if (!evenFirst && !odd.isEmpty()) odd.remove();

            int res = 0;
            while (!odd.isEmpty()) res += odd.remove();
            while (!even.isEmpty()) res += even.remove();

            out.println(res);
        }

    }
}
