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;

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

        BufferedReader br = new BufferedReader(new InputStreamReader(System.in), 1024 * 1024 * 2);

        int n = Integer.valueOf(br.readLine());
        int v[] = readArrayLine(br.readLine(), n);
        Arrays.sort(v);

        int countOdd = 0;
        int countEven = 0;
        for (int i = 0; i < n; i++) {
            if (v[i] % 2 == 1) {
                countOdd++;
            } else {
                countEven++;
            }
        }

        if (Math.abs(countEven - countOdd) <= 1) {
            System.out.println(0);
        } else {
            long sum = 0;
            if (countEven > countOdd) {
                int diff = countEven - countOdd - 1;
                for (int i = 0; i < n; i++) {
                    if (v[i] % 2 == 0) {
                        sum += v[i];
                        diff--;
                    }
                    if (diff == 0) {
                        break;
                    }
                }
            } else {
                int diff = countOdd - countEven - 1;
                for (int i = 0; i < n; i++) {
                    if (v[i] % 2 == 1) {
                        sum += v[i];
                        diff--;
                    }
                    if (diff == 0) {
                        break;
                    }
                }
            }
            System.out.println(sum);
        }
    }

    public static int[] readArrayLine(String line, int n) {
        return readArrayLine(line, n, null, 0);
    }

    private static int[] readArrayLine(String line, int n, int array[], int pos) {
        int[] ret = array == null ? new int[n] : array;
        int start = 0;
        int end = line.indexOf(' ', start);
        for (int i = pos; i < pos + n; i++) {
            if (end > 0)
                ret[i] = Integer.parseInt(line.substring(start, end));
            else
                ret[i] = Integer.parseInt(line.substring(start));
            start = end + 1;
            end = line.indexOf(' ', start);
        }
        return ret;
    }
}
