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.*;
import java.util.Arrays;
import java.util.Stack;
import java.util.StringTokenizer;

public class Z {
    public static void main(String[] args) {
        int[] inputs = io.nextIntArray(io.nextInt());
        Arrays.sort(inputs);

        Stack<Integer> even = new Stack<>();
        Stack<Integer> odd = new Stack<>();
        for (int i : inputs) {
            if (i % 2 == 0) even.push(i);
            else odd.push(i);
        }
        if(even.size() > odd.size()) even.pop();
        else if(odd.size() > even.size()) odd.pop();

        while (even.size() != 0 && odd.size() != 0) {
            even.pop();
            odd.pop();
        }
        int answer = 0;
        Stack<Integer> rem = even.size() > 0 ? even : odd;
        while (!rem.isEmpty())
            answer += rem.pop();

        io.println(answer);
        io.flush(); io.close();
    }
    static FastIO io = new FastIO(System.in);

    static class FastIO extends PrintWriter {
        private BufferedReader br;
        private StringTokenizer tk;
        private FileReader fr;

        FastIO(InputStream in) {
            this();
            br = new BufferedReader(new InputStreamReader(in));
        }

        FastIO(String location) {
            this();
            try {br = new BufferedReader(new FileReader(location));}
            catch (IOException e) {println(e); flush();}
        }

        private FastIO() {
            super(System.out);
            tk = new StringTokenizer("");
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (IOException ignored) { }

            return nextLine();
        }

        String next() {
            if (hasNext())
                return tk.nextToken();
            else
                tk = new StringTokenizer(nextLine());

            return next();
        }

        boolean hasNext() {
            return tk.hasMoreTokens();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        int[] nextIntArray(int length) {
            int[] array = new int[length];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        void exit() {
            try {
                super.close();
                br.close();
            } catch (IOException ignored) { }
        }
    }
}