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.math.*;
import java.text.*;
import java.util.*;
import java.util.regex.*;

public class Solution {

    public static void main(String[] args) throws IOException 
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        int t=1;//Integer.parseInt(br.readLine().trim());
        while(t-->0)
        {
            int n=Integer.parseInt(br.readLine().trim());
            String s[]=br.readLine().trim().split(" ");
            int j=0,k=0;
            for(int i=0;i<n;i++)
                if(Integer.parseInt(s[i])%2==0) j++;
                else    k++;
            int a[]=new int[j];
            int b[]=new int[k];
            for(int i=0,l=0,m=0;i<n;i++)
                if(Integer.parseInt(s[i])%2==0)
                    a[l++]=Integer.parseInt(s[i]);
                else
                    b[m++]=Integer.parseInt(s[i]);
            Arrays.sort(a);
            Arrays.sort(b);
            int max=j;
            if(max<k)
                max=k;
            if(max==j)
            {
                int temp=j-k,sum=0;
                for(int i=0;i<temp-1;i++)
                    sum+=a[i];
                System.out.println(sum);
            }
            else
            {
                int temp=k-j,sum=0;
                for(int i=0;i<temp-1;i++)
                    sum+=b[i];
                System.out.println(sum);
            }
        }
    }
}
