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 B {

    public static long sum(List<Long> aIn, List<Long> bIn) {
        List<Long> a = new LinkedList<>(aIn);
        List<Long> b = new LinkedList<>(bIn);

        Iterator<Long> aIterator = a.iterator();
        Iterator<Long> bIterator = b.iterator();

        Iterator<Long> iterator = aIterator;
        while (iterator.hasNext()) {
            iterator.next();
            iterator.remove();
            iterator = aIterator == iterator ? bIterator : aIterator;
        }

        long summ = 0;
        while (aIterator.hasNext()) {
            summ += aIterator.next();
        }

        while (bIterator.hasNext()) {
            summ += bIterator.next();
        }

        return summ;
    }

    public static void main(String[] args) {
        Comparator<Long> desc = new Comparator<Long>() {
            @Override
            public int compare(Long a, Long b) {
                return (int) (b - a);
            }
        };

        Scanner scanner = new Scanner(System.in);
        int n = scanner.nextInt();

        if (n > 1) {
            List<Long> odd = new LinkedList<>();
            List<Long> even = new LinkedList<>();

            while (n-- > 0) {
                long next = scanner.nextLong();

                if (next % 2 == 0) {
                    odd.add(next);
                } else {
                    even.add(next);
                }
            }

            Collections.sort(odd, desc);
            Collections.sort(even, desc);

            long aSumm = sum(odd, even);
            long bSumm = sum(even, odd);

            System.out.println(Math.min(aSumm, bSumm));
        } else {
            System.out.println(0);
        }
        scanner.close();
    }
    
}

