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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class PAD {
    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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;
        }
    }

    private static int helper(int[] arr, int n, MyScanner ms) {
        int evens = 0, odds = 0;
        for (int i = 0; i < n; i++) {
            arr[i] = ms.nextInt();
            if (arr[i] % 2 == 1) odds++;
            else evens++;
        }

        if (evens == odds) {
            return 0;
        }

        Arrays.sort(arr);

        int leftEvens = 0, leftOdds = 0;
        if (evens  > odds) {
            leftEvens = evens - odds - 1;
            leftOdds = 0;
        }
        else {
            leftOdds = odds - evens - 1;
            leftEvens = 0;
        }


        int sum = 0;
        int evenCnt = 0, oddCnt = 0;
        for (int i = 0; i < n; i++) {
            if (arr[i] % 2 == 0 && evenCnt < leftEvens) {
                sum += arr[i];
                evenCnt++;
            }
            if (arr[i] % 2 == 1 && oddCnt < leftOdds) {
                sum += arr[i];
                oddCnt++;
            }
        }


        return sum;

    }
    public static void main(String[] args) {
        MyScanner ms = new MyScanner();
        int n = ms.nextInt();
        int[] arr = new int[n];

        System.out.println(helper(arr, n, ms));

    }
}
