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.InputStream;
import java.io.PrintWriter;
import java.util.function.Supplier;
import java.util.*;

public class Alternating {
    static Supplier<InputStream> inputSupplier = () -> System.in;
    static Supplier<PrintWriter> outSupplier = () -> new PrintWriter(System.out);

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(inputSupplier.get());
        PrintWriter out = outSupplier.get();
        int n = sc.nextInt();
        List<Integer> even = new ArrayList<>();
        List<Integer> odd = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            if(a%2==0) even.add(a);
            else odd.add(a);
        }
        Collections.sort(even);
        Collections.sort(odd);
        int nEven = even.size();
        int nOdd = odd.size();
        long result = 0;
        if (Math.abs(nEven - nOdd) <= 1) {
            result = 0;
        } else if(nEven>nOdd) {
            for (int i = 0; i < nEven-nOdd-1; i++) {
                result += even.get(i);
            }
        } else {
            for (int i = 0; i < nOdd-nEven-1; i++) {
                result += odd.get(i);
            }
        }
        out.print(result);

        sc.close();
        out.close();
    }
}
