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.*;
import java.util.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.StringTokenizer;

public class probB {
    public static void main(String[] args) throws IOException{
        MyScanner sc = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);
        List<Integer> odd = new ArrayList<>();
        List<Integer> even = new ArrayList<>();
        int n = sc.nextInt();
        int sum = 0;
        for (int i = 0; i < n; i++) {
            int temp = sc.nextInt();
            sum += temp;
            if((temp %2)==1) odd.add(temp);
            else even.add(temp);
        }
        even.sort(Collections.reverseOrder());
        odd.sort(Collections.reverseOrder());
        //Collections.sort(even, Collections.reverseOrder());
        //Collections.sort(odd, Collections.reverseOrder());
        Integer[] evenArr = new Integer[n];
        Integer[] oddArr = new Integer[n];

        evenArr = even.toArray(evenArr);
        oddArr = odd.toArray(oddArr);

        int k = Math.min(even.size(), odd.size());

        int minusSum = 0;
        int i;
        for (i = 0; i < k; i++) {
            minusSum += (evenArr[i] + oddArr[i]);
        }

        if(even.size() > k) minusSum += evenArr[i];
        if(odd.size() > k) minusSum += oddArr[i];
        out.println(sum - minusSum);
        out.flush();
    }
    static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

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

        MyScanner(String fileName) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(fileName));
        }

        String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        String nextLine() throws IOException {
            return br.readLine();
        }

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

        long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws NumberFormatException, IOException {
            return Double.parseDouble(next());
        }
    }
}
