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.*;
public class shashwat{
    static Scanner in=new Scanner(System.in);
public static void main(String args[]){
    int n=in.nextInt();
    int arr[]=new int[n];
    
    PriorityQueue<Integer> o=new PriorityQueue<Integer>(Collections.reverseOrder());
    PriorityQueue<Integer> e=new PriorityQueue<Integer>(Collections.reverseOrder());
    
    for(int i=0;i<n;i++) {
        arr[i]=in.nextInt();
        if(arr[i]%2==0)
            e.add(arr[i]);
        else
            o.add(arr[i]);
    }
   // System.out.println(o.peek());
    PriorityQueue<Integer> temp=new PriorityQueue<Integer>(Collections.reverseOrder());
   // System.out.println(o.size()+" "+e.size());
    if(o.size()<e.size()){
        
   // System.out.println(o.size()+" "+e.size());
        temp=e;
        e=o;
        o=temp;
    }
    
   // System.out.println(o.size()+" "+e.size());
    while(e.size()!=0){
        e.poll();
        o.poll();
    }
    if(o.size()!=0){
        o.poll();
    }
    long sum=0;
    while(o.size()!=0){
        sum+=o.poll();
    }
    System.out.println(sum);
}
}