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 input = new Scanner(System.in);
        int n, po, ne, i, j, k;
        n = input.nextInt();
        int[] a1 = new int[n];
        int[] a2 = new int[n];
        for (i = 0, j = 0, k = 0; k < n; k++) {
            int tem = input.nextInt();
            if (tem % 2 == 0) a1[i++] = tem;
            else a2[j++] = tem;
        }
        Arrays.sort(a1);
        Arrays.sort(a2);
        long ans = 0;
        if (i > j) {
            j++;
            for (int l = n-1-j; l >= 0; l--) ans += a1[l];
        } else {
            i++;
            for (int l = n-1-i; l >= 0; l--) ans+= a2[l];
        }
        System.out.println(ans);
    }
}