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 abc {
    public static void main(String[] args){
        Scanner scan = new Scanner(System.in);
        int n=scan.nextInt();
        int[]a=new int[n];
        int[]ch=new int[n];int[] nch=new int[n];
        for(int i=0;i<n;i++){
            a[i]=scan.nextInt();
        }
        int countOfch=0;
        int countOfNch=0;
        for (int i=0;i<n;i++){
            if(a[i] % 2==0){
                ch[i]=a[i];
                countOfch++;
            }else {
                nch[i]=a[i];
                countOfNch++;
            }
        }
        Arrays.sort(ch);
        Arrays.sort(nch);
        if(countOfch>countOfNch){
            for(int i=n-1;i>0;i--) {
                if(ch[i]!=0){
                    ch[i]=0;
                    if(nch[i]!=0){
                        nch[i]=0;
                    }else break;;
                }else break;
            }
        }else {
            for(int i=n-1;i>0;i--) {
                if(nch[i]!=0){
                    nch[i]=0;
                    if(ch[i]!=0){
                        ch[i]=0;
                    }else break;
                }else break;
            }
        }int summ=0;
        for (int i=0;i<n;i++){
            summ+=ch[i]+nch[i];
        }
        System.out.println(summ );
    }
}