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 Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        sc.nextLine();
        int minEven = Integer.MAX_VALUE;
        int minOdd = Integer.MAX_VALUE;
        int sE=0;
        int sO=0;
        ArrayList<Integer>even = new ArrayList<>();
        ArrayList<Integer>odd = new ArrayList<>();
        for(int i=0;i<n;i++){
           int m = sc.nextInt();
            if(m%2==0){
                even.add(m);
                minEven = Math.min(minEven,m);
                sE+=m;
            }else{
                odd.add(m);
                minOdd = Math.min(minOdd,m);
                sO+=m;
            }
        }
        int sum=sO+sE;
        int res=0;
        if(even.size()>odd.size()){
            Collections.sort(even);
             for(int i=0;i<even.size()-odd.size()-1;i++){
                 res+=even.get(i);
             }
        }else{
            Collections.sort(odd);
            for(int i=0;i<odd.size()-even.size()-1;i++){
                res+=odd.get(i);
            }
        }

        System.out.println(res);
       // System.out.println(even+" "+sE+" "+minEven);
        //System.out.println(odd+" "+sO+" "+minOdd);


    }
}