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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

/*
 * To change this license header, choose License Headers in Project Properties.
 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
/**
 *
 * @author ali
 */
public class ParityDeletions {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        short n = in.nextShort();
        int[] numbers = new int[n];
        short odd = 0;
        short even = 0;
                int result = 0;

        List<Integer> oddNumbers = new ArrayList<>();
        List<Integer> evenNumbers = new ArrayList<>();
        for (short i = 0; i < n; i++) {
            int a = in.nextInt();
            numbers[i] = a;

        }

        for (int f : numbers) {
            if (f % 2 == 0) {
                even++;
                evenNumbers.add(f);
            } else {
                odd++;
                oddNumbers.add(f);
            }
        }

        if (odd > even) {
            Collections.sort(oddNumbers);
            for(int i = 0; i < (odd - even -1); i++)
            {
               result += oddNumbers.get(i);
            }
            

        }
        
              else {
            Collections.sort(evenNumbers);
            for(int i = 0; i < (even - odd -1); i++)
            {
               result += evenNumbers.get(i);
            }
            

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