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.Scanner;

import java.util.Collections;
import java.util.Comparator;

public class Solution {

    public static void main(String args[]) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        sc.nextLine();
        int a[] = new int[n];
        int odd = 0;
        ArrayList<Integer> od = new ArrayList<Integer>();
        ArrayList<Integer> ev = new ArrayList<Integer>();
        int even = 0;
        int max = 0;
        int maxi = 0;
        long sum = 0;

        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
            if (a[i] % 2 == 0) {
                even++;
                ev.add(a[i]);
            } else {
                odd++;
                od.add(a[i]);
            }

            if (a[i] > max) {
                max = a[i];
                maxi = i;
            }

            sum = sum + a[i];

        }

        int fodd = odd;
        int feven = even;
        Comparator r = Collections.reverseOrder();
        Collections.sort(ev, r);

        Collections.sort(od, r);

      //  System.out.println(ev);
       // System.out.println(od);
        if (odd - even == 1 || odd - even == 0) {
            System.out.println("0");
        } else if (even == 0 || odd == 0) {

            System.out.println(sum - max);
        } else {

            int o = 0;
            int e = 0;
            long deleted = 0;

            int turn = 1;

//            if (od.get(0) > ev.get(0)) {
//                
//                System.out.println(od.get(0) + " deleted  first odd id ");
//                deleted += od.get(0);
//                o++;
//                odd--;
//                turn = 2;
//
//            } else {
//                 System.out.println(ev.get(0) + " deleted firt evenid ");
//                deleted += ev.get(e);
//                e++;
//                even--;
//                turn = 1;
//
//            }
            while (odd > 0 && even > 0) {

                if (turn == 1) {
                    // System.out.println(od.get(0) + " deleted  first odd id ");

                    deleted += od.get(o);
                    o++;
                    odd--;
                    turn = 2;

                } else if (turn == 2) {
                    // System.out.println(ev.get(0) + " deleted firt evenid ");
                    deleted += ev.get(e);
                    e++;
                    even--;
                    turn = 1;

                }

            }

            if (odd == 0) {
                deleted += ev.get(e);
            } else if (even == 0) {

                deleted += od.get(o);
            }

            //-------------------------------------------------------------------------------------------
            turn = 2;
            o = 0;
            e = 0;
            odd = fodd;
            even = feven;
            long deleted2 = 0;
            while (odd > 0 && even > 0) {

                if (turn == 1) {
                    // System.out.println(od.get(0) + " deleted  first odd id ");

                    deleted2 += od.get(o);
                    o++;
                    odd--;
                    turn = 2;

                } else if (turn == 2) {
                    // System.out.println(ev.get(0) + " deleted firt evenid ");
                    deleted2 += ev.get(e);
                    e++;
                    even--;
                    turn = 1;

                }

            }

            if (odd == 0) {
                deleted2 += ev.get(e);
            } else if (even == 0) {

                deleted2 += od.get(o);
            }

            if (deleted2 > deleted) {
                System.out.println(sum - deleted2);
            } else {
                System.out.println(sum - deleted);
            }
        }

    }
}
