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.InputStreamReader;
import java.util.ArrayList;

public class PolyCarpParity {

    public static void main(String [] args) throws Exception {
        BufferedReader bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        int lines = Integer.parseInt(bufferedReader.readLine());
        String val = bufferedReader.readLine();
        String[] split = val.split(" ");
        int parity = parity(split);
        System.out.println(parity);
    }

    public static int parity(String [] input) {
        if(input.length <= 1) {
            return 0;
        }
        ArrayList<Integer> evens = new ArrayList<>();
        ArrayList<Integer> odds = new ArrayList<>();
        for(int i=0; i< input.length; i++) {
            int value = Integer.parseInt(input[i]);
            if(value % 2 == 0) {
                evens.add(value);
            }
            else odds.add(value);
        }
        if(Math.abs(evens.size() - odds.size()) <= 1) {
            return 0;
        }
        if(evens.size() > odds.size()) {
            return getOverflow(evens, odds);
        }
        else return getOverflow(odds, evens);
    }

    public static int getOverflow(ArrayList<Integer> largerVal, ArrayList<Integer> lowerval) {
        largerVal.sort(Integer::compareTo);
        int sum = 0;
        for(int i=0; i<largerVal.size() - lowerval.size() - 1; i++) {
            sum += largerVal.get(i);
        }
        return sum;
    }
}
