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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import javafx.print.Collation;

public class ParityAlternatedDeletions {

    public static int nextInt(BufferedReader in) throws IOException {
        int neg = 1;
        int ch = in.read();
        while (ch != '-' && (ch < '0' || ch > '9')) {
            ch = in.read();
        }
        if (ch == '-') {
            neg = -1;
            ch = in.read();
        }
        int c = ch - '0';
        ch = in.read();
        while (ch >= '0' && ch <= '9') {
            c = c * 10 + ch - '0';
            ch = in.read();
        }
        return c * neg;
    }

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = nextInt(in);

        ArrayList<Integer> listEven = new ArrayList<>();
        ArrayList<Integer> listOdd = new ArrayList<>();
        int sum = 0;
        int even = 0;
        int odd = 0;
        for (int i = 0; i < n; i++) {
            int num = nextInt(in);
            if (num % 2 == 0) {
                listEven.add(num);
                even++;
            } else {
                listOdd.add(num);
                odd++;
            }
            sum += num;
        }
        Collections.sort(listOdd);
        Collections.sort(listEven);
        boolean last;
        int t;
        if (even > odd) {
            t = listEven.remove(even - 1);
            even--;
            last = true;
            sum -= t;
        } else {
            t = listOdd.remove(odd - 1);
            odd--;
            last = false;
            sum -= t;
        }
        boolean deleted = true;
        while (deleted) {
            deleted = false;
            if (last) {
                if (odd != 0) {
                    t = listOdd.remove(odd - 1);
                    sum -= t;
                    odd--;
                    deleted = true;
                    last = false;
                }
            } else {
                if (even != 0) {
                    t = listEven.remove(even - 1);
                    sum -= t;
                    even--;
                    deleted = true;
                    last = true;
                }
            }
        }

        System.out.println(sum);

    }

}
