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 static java.lang.System.*;
import java.util.*;
import java.io.*;

public class Main{
    public static void main(String[] args) throws IOException{
        Scanner sc = new Scanner (in);
        BufferedWriter writer = new BufferedWriter(new OutputStreamWriter(out));
        
        int n = sc.nextInt();
        int[] odd = new int[n];
        int[] even = new int[n];
        int oddIndex = 0, evenIndex = 0;
        for (int i = 0; i < n; i++) {
            int input = sc.nextInt();
            if (input % 2 == 0) {
                even[evenIndex++] = input;
            } else {
                odd[oddIndex++] = input;
            }
        }
        
        Arrays.sort(odd, 0, oddIndex);
        Arrays.sort(even, 0, evenIndex);
        long sum = 0;
        if (oddIndex - 1> evenIndex) {
            int index = 0;
            while (oddIndex - 1 - index> evenIndex) sum += odd[index++];
        } else if (evenIndex - 1> oddIndex) {
            int index = 0;
            while (evenIndex - 1 - index> oddIndex) sum += even[index++];
        }
        
        writer.write(String.valueOf(sum));
        writer.write(lineSeparator());
        writer.flush();
    }
}