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.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;

public class codeforces{
    public static void main(String[] args) throws Exception{
        InputStreamReader r=new InputStreamReader(System.in);
        BufferedReader br=new BufferedReader(r);
        StringBuilder str=new StringBuilder();
        int t=Integer.valueOf(br.readLine());
        String[] lol=br.readLine().split(" ");
        int odd=0,even=0;
        ArrayList<Integer> odd1=new ArrayList<>();
        ArrayList<Integer> even1=new ArrayList<>();
        int sum=0;
        for(int i=0;i<lol.length;i++)
        {
            sum+=Integer.valueOf(lol[i]);
            if(Integer.valueOf(lol[i])%2==0)
            {
                even++;
                even1.add(Integer.valueOf(lol[i]));
            }
            else
            {
                odd++;
                odd1.add(Integer.valueOf(lol[i]));
            }
        }
        if(Math.abs(odd-even)<=1)
        str.append("0\n");
        else
        {
            Collections.sort(odd1);
            Collections.sort(even1);
            if(even>odd)
            {
                int diff=even-odd;
                sum-=even1.get(even1.size()-1);
                even1.remove(even1.size()-1);
                while(odd1.size()!=0)
                {
                    sum-=odd1.get(odd1.size()-1);
                    odd1.remove(odd1.size()-1);
                    sum-=even1.get(even1.size()-1);
                    even1.remove(even1.size()-1);                    
                }                
            } 
            else
            {
                int diff=odd-even;
                sum-=odd1.get(odd1.size()-1);
                odd1.remove(odd1.size()-1);
                while(even1.size()!=0)
                {                    
                    sum-=even1.get(even1.size()-1);
                    even1.remove(even1.size()-1);
                    sum-=odd1.get(odd1.size()-1);
                    odd1.remove(odd1.size()-1);
                }     
            }        
            str.append(sum+"\n");  
        }
        System.out.print(str);
    }
}