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 Question1144B {
    public static void main(String[] args) {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        List<Integer> evenList=new ArrayList<>();
        List<Integer> oddList=new ArrayList<>();
        int[] arr=new int[n];
        for(int i=0;i<n;i++){
            arr[i]=sc.nextInt();
            if(arr[i]%2==0){
                evenList.add(arr[i]);
            }
            else {
                oddList.add(arr[i]);
            }
        }

        if(evenList.size()==oddList.size()){
            System.out.println("0");
        }
        else if(evenList.size()-1==oddList.size()||oddList.size()-1==evenList.size()){
            System.out.println("0");
        }
        else {
            Collections.sort(evenList, new Comparator<Integer>() {
                @Override
                public int compare(Integer o1, Integer o2) {
                    return Integer.compare(o2,o1);
                }
            });
            Collections.sort(oddList, new Comparator<Integer>() {
                @Override
                public int compare(Integer o1, Integer o2) {
                    return Integer.compare(o2,o1);
                }
            });
            long sum=0;

//            System.out.println(evenList);
//            System.out.println(oddList);
            if(evenList.size()>oddList.size()){
                int count=evenList.size()-oddList.size();
                int i=evenList.size()-1;
                int x=0;
                while (i>0){
                    sum+=evenList.get(i);
                    i--;
                    x++;
                    if(x==count-1){
                        break;
                    }
                }

            }else {
                int count=oddList.size()-evenList.size();
                //System.out.println(count);
                int i=oddList.size()-1;
                int x=0;
                while (i>0){
                    sum+=oddList.get(i);
                    i--;
                    x++;
                    if(x==count-1){
                        break;
                    }
                }

            }
            System.out.println(sum);
        }
    }
}
