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 JavaApplication4 {

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int evenNum = 0;
        int oddNum = 0;
        int counter=0;
        int sum=0;
        int[] arr = new int[n];
        
        if(n==1)
            System.out.println("0");
        else{
            for (int i = 0; i < n; i++) {
                int x = sc.nextInt();
                if(x%2==0)
                    evenNum++;
                else
                    oddNum++;
                arr[i] = x;
            }
            if((evenNum-oddNum)==0 || Math.abs(evenNum-oddNum)==1 )
                System.out.println("0");
            else{
                Arrays.sort(arr);
                if(evenNum > oddNum){
                    counter = evenNum-oddNum-1;
                    for (int i = 0; i < n && counter != 0; i++) {
                        if(arr[i]%2==0){
                            counter--;
                            sum+=arr[i];
                        }    
                    }
                    System.out.println(sum);
                }
                else{
                    counter = oddNum-evenNum-1;
                    for (int i = 0; i < n && counter != 0; i++) {
                        
                        if(arr[i]%2!=0){
                            counter--;
                            sum+=arr[i];
                        }          
                    }
                    System.out.println(sum);
                }
            } 
        }
    }   
}