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.*;
public class Main{
    public static void main(String[] args){
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        ArrayList<Integer> a=new ArrayList<Integer>();
        int even=0;
        int odd=0;
        for(int i=0;i<n;i++)
        {
            int x=sc.nextInt();
            if(x%2==0)
            {
                even++;
            }
            else
            {
                odd++;
            }
            a.add(x);
        }
        Collections.sort(a);
        if(even>odd)
        {
            for(int i=0;i<n;i++)
            {
                boolean r=false;
                if(i%2==0)
                {
                for(int k=a.size()-1;k>=0;k--)
                {
                 if(a.get(k)%2==0)
                 {
                     a.remove(k);
                     r=true;
                     break;
                 }
                }
                }
                else
                {
                    for(int k=a.size()-1;k>=0;k--)
                    {
                        if(a.get(k)%2!=0)
                        {
                        r=true;
                        a.remove(k);
                        break;
                        }
                    }
                    
                }
                if(r==false)
                {
                    break;
                }
            }
        }
        else
        {
              for(int i=0;i<n;i++)
            {
                  boolean r=false;
                if(i%2==0)
                {
                for(int k=a.size()-1;k>=0;k--)
                {
                 if(a.get(k)%2!=0)
                 {
                     r=true;
                     a.remove(k);
                     break;
                 }
                }
                }
                else
                {
                    for(int k=a.size()-1;k>=0;k--)
                    {
                        if(a.get(k)%2==0)
                        {
                        r=true;
                        a.remove(k);
                        break;
                    }
                    }
                    
                }
                if(r==false)
                {
                    break;
                }
            }
        }
        long sum=0;
        for(int i=0;i<a.size();i++)
        {

            sum+=a.get(i);
        }
            System.out.println(sum);
    }
            
            
        }
 			 							 			 	 	 	 	  				