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.*;
import java.io.*;

public class ParityAlteredDeletions {
    public static void main(String[] args) {
        FastScanner scanner = new FastScanner();
        PrintWriter out = new PrintWriter(System.out);
        int N = scanner.nextInt();
        int[] arr = new int[N];
        int[] arrParity = new int[2];
        int[] copyParity = new int[2];
        long sum = 0;
        for(int i = 0; i < N; i++) {
            arr[i] = scanner.nextInt();
            sum += arr[i];
            arrParity[arr[i]%2]++;
            copyParity[arr[i]%2]++;
        }
        //start with an odd
        long arrSum = sum;
        int cur = 0;
        boolean[] rem = new boolean[N];
        while(true) {
            if (arrParity[cur] == 0) break;
            int ind = -1;
            int bestVal = -1;
            for(int i = 0; i < N; i++) {
                if (!rem[i] && arr[i] % 2 == cur && arr[i] > bestVal) {
                    bestVal = arr[i];
                    ind = i;
                }
            }
            rem[ind] = true;
            arrSum -= arr[ind];
            arrParity[cur]--;
            cur = 1-cur;
        }
        rem = new boolean[N];
        cur = 1;
        while(true) {
            if (copyParity[cur] == 0) break;
            int ind = -1;
            int bestVal = -1;
            for(int i = 0; i < N; i++) {
                if (!rem[i] && arr[i] % 2 == cur && arr[i] > bestVal) {
                    bestVal = arr[i];
                    ind = i;
                }
            }
            rem[ind] = true;
            sum -= arr[ind];
            copyParity[cur]--;
            cur = 1-cur;
        }
        out.println(Math.min(sum, arrSum));
        out.flush();
    }
    
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(Reader in) {
            br = new BufferedReader(in);
        }
        
        public FastScanner() {
            this(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 readNextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
        
        int[] readIntArray(int n) {
            int[] a = new int[n];
            for (int idx = 0; idx < n; idx++) {
                a[idx] = nextInt();
            }
            return a;
        }
    }
}
