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.BufferedReader;
        import java.io.IOException;
        import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

import static java.lang.Integer.MAX_VALUE;
import static java.lang.Integer.parseInt;
public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = parseInt(in.readLine());
        int even,odd;
        even = 0; odd = 0;
        PriorityQueue<Integer> e = new PriorityQueue<Integer>(new Comparator<Integer>() {
            @Override
            public int compare(Integer integer, Integer t1) {
                if (integer >= t1)
                {
                    return -1;
                }
                return 1;
            }
        });
        PriorityQueue<Integer> o = new PriorityQueue<Integer>(new Comparator<Integer>() {
            @Override
            public int compare(Integer integer, Integer t1) {
                if (integer >= t1)
                {
                    return -1;
                }
                return 1;
            }
        });
        StringTokenizer st = new StringTokenizer(in.readLine());
        long counter = 0;
        for (int i = 0; st.hasMoreElements(); i++) {
            int tmp = parseInt(st.nextToken());
            if (tmp %2 == 0 && tmp != 0)
            {
                e.add(tmp);
                even++ ;
            }
            else if(tmp %2 ==1)
            {
                o.add(tmp);
                odd++ ;
            }
            counter += tmp;
        }
        int y = Math.min(e.size(),o.size());
        for (int i = 0; i < y; i++) {
            counter -= (e.poll()+o.poll());
        }
        if (!e.isEmpty())
        {
            counter -= e.poll();
        }
        else if (!o.isEmpty())
        {
            counter -= o.poll();
        }
        System.out.println(counter);
        


    }
}
