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.IOException;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;

public class Main {

    public static void main(String[] args){

        FastReader fastReader = new FastReader();

        long n = fastReader.nextLong();

        long[] array = new long[(int) n];

        long even = 0 , odd = 0;

        for(long i=0 ; i< array.length ; i++){

            array[(int) i] =  fastReader.nextLong();

            long element = array[(int) i];

            if(element%2 ==0){

                even++ ;

            }

            else {

                odd++ ;

            }

        }

        Arrays.sort(array);

        if(even==0 || odd==0){

            long sum=0;

            for(long i=0 ; i< array.length-1 ; i++){

                sum += array[(int) i];

            }

            System.out.println(sum);

        }


        else {

            boolean ansZero = false;

            if (n % 2 == 0) {

                if (even == (n / 2) && odd == (n / 2) ) {

                    ansZero = true;

                    System.out.println(0);

                }

            } else {

                if ( (even == n / 2 && odd == ((n / 2) + 1 )) || (odd == n/2 && even == ((n/2)+1)) ){

                    ansZero = true;

                    System.out.println(0);

                }

            }

            if (!ansZero) {

                ArrayList<Long> oddArrayList = new ArrayList<>();
                ArrayList<Long> evenArrayList = new ArrayList<>();

                for (long i = 0; i < array.length; i++) {

                    long element = array[(int) i];

                    if (element % 2 == 0) {

                        evenArrayList.add(element);

                    } else {

                        oddArrayList.add(element);

                    }

                }

                Collections.reverse(oddArrayList);
                Collections.reverse(evenArrayList);

                while (!oddArrayList.isEmpty() && !evenArrayList.isEmpty()) {

                    evenArrayList.remove(0);
                    oddArrayList.remove(0);

                }
                
                if(!oddArrayList.isEmpty()){
                    
                    oddArrayList.remove(0);
                    
                }
                
                if(!evenArrayList.isEmpty()){
                    
                    evenArrayList.remove(0);
                    
                }

                long sum = 0;

                for (long value : oddArrayList) {

                    sum += value;

                }

                for (long value2 : evenArrayList) {

                    sum += value2;
                }


                System.out.println(sum);


            }

        }








    }

































































































            static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader()
        {
            br = new BufferedReader(
                    new InputStreamReader(System.in));
        }

        String next()
        {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() { return Integer.parseInt(next()); }

        long nextLong() { return Long.parseLong(next()); }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine()
        {
            String str = "";
            try {
                str = br.readLine();
            }
            catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }



    }

