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.*;
public class MyClass {
    public static void main(String args[]) {
      Scanner sc=new Scanner(System.in);
      ArrayList<Integer> even=new ArrayList<Integer>();
       ArrayList<Integer> odd=new ArrayList<Integer>();
      int n=sc.nextInt();
      int[] arr=new int[n];
      for(int i=0;i<n;i++)
      {arr[i]=sc.nextInt();
      }
    Arrays.sort(arr);
    for(int i=0;i<n;i++)
    {
        if(arr[i]%2==0)
      even.add(arr[i]);
      else
      odd.add(arr[i]);
    }
    if(even.size()==odd.size())
    System.out.println(0);
    else if(even.size()==odd.size()+1||odd.size()==even.size()+1)
    System.out.println(0);
    else
    {   int s=0;
        if(odd.size()>even.size())
        {
            int k=odd.size()-even.size();
            for(int i=k-2;i>=0;i--)
            s=s+odd.get(i);
        }
        else
        {
            int k=even.size()-odd.size();
            for(int i=k-2;i>=0;i--)
            s=s+even.get(i);
        }
        System.out.println(s);
    }
    }
}