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.lang.reflect.Array;
import java.util.*;

public class Main {
    static  OutputWriter out;
    public static void main(String[] args) throws Exception
    {
        Scanner in = new Scanner(System.in);
        out = new OutputWriter(System.out);
        int n = in.nextInt();
        PriorityQueue<Integer>odd =new PriorityQueue<>();
        PriorityQueue<Integer>even = new PriorityQueue<>();
        for (int i =0;i<n;i++)
        {
            int item = in.nextInt();
            if (item%2==0)
                even.add(-item);
            else
                odd.add(-item);
        }
        while (!odd.isEmpty()&&!even.isEmpty())
        {
            odd.poll();
            even.poll();
        }
        if (!odd.isEmpty())
            odd.poll();
        if (!even.isEmpty())
            even.poll();
        long ans = 0;
        while (!odd.isEmpty())
        {
            ans+=(long)(-odd.poll());
        }
        while (!even.isEmpty())
        {
            ans+=(long)(-even.poll());
        }
        out.printLine(ans);
         out.flush();
    }

    static void MergeSort(int[] a, int[] b,  int p, int r)
    {
        if (p < r)
        {
            int q = (r + p) / 2;
            MergeSort(a, b,  p, q);
            MergeSort(a, b,  q + 1, r);
            Merge(a, b, p, q, r);
        }
    }
    static void Merge(int[] a, int[] b,int p, int q, int r)
    {
        int n1 = q - p + 1;
        int n2 = r - q;
        int[] R = new int[n1 + 1];
        int[] L = new int[n2 + 1];
        int[] R1 = new int[n1];
        int[] L1 = new int[n2];

        for (int i = 0; i < n1; i++)
        {
            R[i] = a[p + i];
            R1[i] = b[p + i];

        }
        R[n1] = Integer.MAX_VALUE;
        for (int i = 0; i < n2; i++)
        {
            L[i] = a[q + i + 1];
            L1[i] = b[q + i + 1];

        }
        L[n2] =Integer.MAX_VALUE;
        int n = a.length;
        int j = 0;
        int k = 0;
        for (int i = p; i <= r; i++)
        {
            if (L[j] < R[k])
            {
                a[i] = L[j];
                b[i] = L1[j];

                j++;
            }
            else if (L[j]>R[k])
            {
                a[i] = R[k];
                b[i] = R1[k];

                k++;
            }
            else
            {
                if (L1[j] < R1[k])
                {
                    a[i] = L[j];
                    b[i] = L1[j];

                    j++;
                }
                else
                {
                    a[i] = R[k];
                    b[i] = R1[k];

                    k++;
                }
            }

        }
    }
}
class Graph {


    int n;
    ArrayList<Integer>[] adjList;

    public Graph(int n) {
        this.n = n;
        adjList = new ArrayList[n];
        for (int i = 0; i < n; i++)
            adjList[i] = new ArrayList<>();
    }

}
class pair  implements Comparable
{

    int key;
    int value;

    public pair(Object key, Object value) {

        this.key = (int)key;
        this.value=(int)value;

    }

    @Override
    public int compareTo(Object o) {
        pair temp =(pair)o;
        return  key-temp.key;
    }
}
class Scanner {

    StringTokenizer st;
    BufferedReader br;

    public Scanner(InputStream s) {
        br = new BufferedReader(new InputStreamReader(s));
    }

    public Scanner (FileReader f) {
        br = new BufferedReader(f);
    }

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

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

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

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

    public double nextDouble() throws IOException {
        String x = next();
        StringBuilder sb = new StringBuilder("0");
        double res = 0, f = 1;
        boolean dec = false, neg = false;
        int start = 0;
        if (x.charAt(0) == '-') {
            neg = true;
            start++;
        }
        for (int i = start; i < x.length(); i++)
            if (x.charAt(i) == '.') {
                res = Long.parseLong(sb.toString());
                sb = new StringBuilder("0");
                dec = true;
            } else {
                sb.append(x.charAt(i));
                if (dec)
                    f *= 10;
            }
        res += Long.parseLong(sb.toString()) / f;
        return res * (neg ? -1 : 1);
    }

    public boolean ready() throws IOException {
        return br.ready();
    }

    public boolean nextEmpty() throws IOException {
        String s = nextLine();
        st = new StringTokenizer(s);
        return s.isEmpty();
    }
}
class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }


    public void printLine(Object... objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

    public void flush() {
        writer.flush();
    }

}