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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Scanner;

public class ParityAlternatedDeletions {
    public static void main(String[] args) {
        Scanner s = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int n=s.nextInt();
        ArrayList<Integer>even=new ArrayList<>();
        ArrayList<Integer>odd=new ArrayList<>();
        for(int i=0;i<n;i++){
            int el=s.nextInt();
            if(el%2==0)
                even.add(el);
            else
                odd.add(el);
        }
        Collections.sort(even);
        Collections.sort(odd);
        int diff=0;
        if(even.size()>odd.size()){
            diff=even.size()-odd.size()-1;
            if(diff==0||even.size()==odd.size())
                System.out.println(0);
            else{
                long sum=0;
                for(int i=0;i<diff;i++){
                    sum+=even.get(i);
                }
                System.out.println(sum);
            }
        }else{
            diff=odd.size()-even.size()-1;
            if(diff==0)
                System.out.println(0);
            else{
                long sum=0;
                for(int i=0;i<diff;i++){
                    sum+=odd.get(i);
                }
                System.out.println(sum);
            }
        }
    }
    }
