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.text.DecimalFormat;
import java.util.*;
public class BCF1055A {
    public static void main(String[]args)throws Exception
    {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n=Integer.parseInt(br.readLine());
        int e_count = 0;
        int o_count = 0;
        StringTokenizer st = new StringTokenizer(br.readLine());
        int arr[] = new int[n];
        for(int i=0;i<n;i++)
        {
            int no=Integer.parseInt(st.nextToken());
            arr[i]=no;
        }
        Arrays.sort(arr);
        for(int i=0;i<n;i++)
        {
            int no = arr[i];
            if(no%2==0)
                e_count++;
            else
             o_count++;
        }
//        System.out.println(e_count+" "+o_count);
        if(Math.abs(e_count-o_count)<2)
        {
            System.out.println(0);
        }
        else{
            int res=0;
            if(e_count>o_count)
            {
                int c=0;
                for(int i=0;i<n;i++)
                    if(arr[i]%2==0){
                        {
                            res+=arr[i];
                            c+=1;
                            if(c==(e_count-o_count-1))
                                break;
                        }
                    }
            }
            else
            {
                int c=0;
                for(int i=0;i<n;i++)
                    if(arr[i]%2==1){
                        res+=arr[i];
                        c+=1;
                        if(c==(o_count-e_count-1))
                            break;
                    }
            }
            System.out.println(res);
        }
    }
}
