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.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.Scanner;

public class ParityAlternatedDecisionsB implements Comparator<Integer>
{
    public static void main(String args[])
    {
        Scanner sc=new Scanner(System.in);
        int n=sc.nextInt();
        int i,ans=0;
        ArrayList<Integer> eve=new ArrayList<>();
        ArrayList<Integer> odd=new ArrayList<>();
        for(i=0;i<n;i++)
        {
            int a=sc.nextInt();
            if(a%2==1)
            {
                //System.out.println("Adding in Even parity"+a);
                eve.add(a);
            }
            else
            {
               // System.out.println("Adding in Odd parity "+a);
                odd.add(a);
            }
        }
        if(eve.size()==odd.size() || (Math.abs(eve.size()-odd.size())==1))
        {
            System.out.println("0");
        }
        else if(eve.size()>odd.size())
        {
            Collections.sort(eve,new ParityAlternatedDecisionsB());
            for(i=odd.size()+1;i<eve.size();i++)
            {
                ans+=eve.get(i);
            }
           // if(odd.size()!=0)
            {
                System.out.println(ans);
            }
            //else
            {
              //  System.out.println(ans-eve.get(odd.size()));
            }
        }
        else
        {
            Collections.sort(odd,new ParityAlternatedDecisionsB());
            for(i=eve.size()+1;i<odd.size();i++)
            {
                //System.out.println(odd.get(i)+" ");
                ans+=odd.get(i);
            }
            //if(eve.size()!=0)
            {
                System.out.println(ans);
            }
            //else
            {
              //  System.out.println(ans-odd.get(eve.size()));
            }
        }
    }
    public static int setbits(int n)
    {
        int cnt =0;
        while(n>0)
        {
            n&=n-1;
            cnt++;
        }
        return n%2==0?1:0;
    }

    @Override
    public int compare(Integer o1, Integer o2) {
        return o1<o2?1:-1;
    }
}
