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.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;
import java.util.Vector;

public class Main
{
  static final int MAXN = 2000;
  static int n = 0;
  private static Vector<Integer> odd = new Vector<>();
  private static Vector<Integer> even = new Vector<>();
  private static long sum = 0;

  public static void main(String[] args)
  {
    int x = 0;
    Scanner scanner = new Scanner(System.in);
    n = scanner.nextInt();
    for(int i = 0; i < n; i++)
    {
      x = scanner.nextInt();
      if((x & 1) == 1)
        odd.add(x);
      else
        even.add(x);
      sum += x;
    }
    Comparator<Integer> comparator = new Comparator<Integer>(){
    @Override
    public int compare(Integer o1, Integer o2)
    {
      if(o1 < o2)
        return 1;
      else
        return -1;
    }
  };
    odd.sort(comparator);
    even.sort(comparator);
    int k = Math.min(odd.size(), even.size());
    long s1 = 0;
    long s2 = 0;
    for(int i = 0; i < k; i++)
    {
      s1 += odd.get(i);
      s2 += even.get(i);
    }
    long rem = sum;
    rem -= s1 + s2;
    if(odd.size() > k)
      rem -= odd.get(k);
    else if(even.size() > k)
      rem -= even.get(k);
    System.out.println(rem);
    scanner.close();
  }
}
