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.util.*;
import java.lang.*;

public class Rextester{
    static void shuffle(int[] array){
        Random rand = new Random();
        for(int i=0;i<array.length;i++){
            int x = rand.nextInt(array.length-i)+i;
            int temp = array[x];
            array[x]=array[i];
            array[i]=temp;
        }
    }
    public static void main(String[] args)throws IOException{
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = new Integer(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        br.close();
        int[] odd = new int[n];
        int[] even = new int[n];
        Arrays.fill(odd,-1);
        Arrays.fill(even,-1);
        int o=0,e=0;
        long sum=0;
        for(int i=0;i<n;i++){
            int x = new Integer(st.nextToken());
            if(x%2==0){
                even[e++]=x;
            }
            else{
                odd[o++]=x;
            }
            sum+=x;
        }
        shuffle(even);
        shuffle(odd);
        Arrays.sort(even);
        Arrays.sort(odd);
        int i=n-1;
        while(odd[i]!=-1&&even[i]!=-1){
            sum-=odd[i];
            sum-=even[i];
            //System.out.println(odd[i]+" "+even[i]);
            i--;
        }
        if(odd[i]!=-1||even[i]!=-1){
            sum-=Math.max(odd[i],even[i]);
        }
        System.out.println(sum);
    }
}
        
        
        
        
        
        
        