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.Arrays;
import java.util.Scanner;

public class Parity_Alternated_Deletions {
    public static void main(String[] args){
        int odd_cnt=0;
        int even_cnt=0;
        int n;
        Scanner scanner=new Scanner(System.in);
        n=scanner.nextInt();
        int[] a=new int[n];
        for(int i=0;i<n;i++){
            a[i]=scanner.nextInt();
            if(a[i]%2==0){
                even_cnt++;
            }else {
                odd_cnt++;
            }
        }
        if(even_cnt==odd_cnt||Math.abs(even_cnt-odd_cnt)==1){
            System.out.println(0);
        }else {
            int[] b;
            int res=0;
            if(even_cnt>odd_cnt){
                b=new int[even_cnt];
                int k=0;
                for(int i=0;i<n;i++){
                    if(a[i]%2==0){
                        b[k++]=a[i];
                    }
                }
                Arrays.sort(b);
                for(int j=0;j<even_cnt-odd_cnt-1;j++){
                    res+=b[j];
                }
                System.out.println(res);
            }
            if(even_cnt<odd_cnt){
                b=new int[odd_cnt];
                int k=0;
                for(int i=0;i<n;i++){
                    if(a[i]%2==1){
                        b[k++]=a[i];
                    }
                }
                Arrays.sort(b);
                for(int j=0;j<odd_cnt-even_cnt-1;j++){
                    res+=b[j];
                }
                System.out.println(res);
            }




        }








    }




}
