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.Collections;
import java.util.Scanner;
import java.util.Vector;


public class JavaApplication168<T> {

    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        int n = sc.nextInt();
        Vector<Integer> odd = new Vector();
        Vector<Integer> even = new Vector();
        int sum = 0;
        int index_odd =0 , index_even = 0;
        for(int i=0; i<n; i++){
            int num = sc.nextInt();
            sum += num;
            if(num % 2 != 0){
                odd.add(num);
            }else{
                even.add(num);
            }
        }
        
        
        Collections.sort(odd,Collections.reverseOrder());
        Collections.sort(even,Collections.reverseOrder());
        int k = Math.min(odd.size(), even.size());
        int rem = sum;
        for(int i=0; i<k; i++){
            rem -= odd.get(i);
        }
        for(int i=0; i<k; i++){
            rem -= even.get(i);
        }
        if(odd.size() > k){
            rem -= odd.get(k);
        }
        if(even.size() > k){
            rem -= even.get(k);
        }
        System.out.println(rem);
        
        
        
        
        

        
    }
}
