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.security.cert.CollectionCertStoreParameters;
import java.util.ArrayList;
import java.util.Collection;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		int sum = 0;
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		List<Integer> list = new ArrayList<>();
		List<Integer> list1 = new ArrayList<>();
		List<Integer> list2 = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			list.add(scan.nextInt());
		}
		for (int i = 0; i < list.size(); i++) {
			if (list.get(i) % 2 == 0) {
				list1.add(list.get(i));
			} else {
				list2.add(list.get(i));
			}
		}
		Collections.sort(list1);
		Collections.sort(list2);
		// for (int i = 0; i < list1.size(); i++) {
		// System.out.println(list1.get(i));
		// }
		if (Math.abs(list1.size() - list2.size()) <= 1) {
			System.out.println("0");
		}
		if (list1.size() - list2.size() >= 2) {
			for (int i = 0; i < list1.size() - list2.size() - 1; i++) {
				sum = sum + list1.get(i);
			}
			System.out.println(sum);
		}
		if (list2.size() - list1.size() >= 2) {
			for (int i = 0; i < list2.size() - list1.size() - 1; i++) {
				sum = sum + list2.get(i);
			}
			System.out.println(sum);
		}
	}

}