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.Scanner;
import java.util.Arrays;
public class Main {
	public static Scanner scanner = new Scanner(System.in);

	public static void main(String[] args) {
		int a = scanner.nextInt(), ev = 0, od = 0;
		int[] Even = new int[a];
		int[] Odd = new int[a];
		for (int i = 0; i < a; i++) {
			Even[i] = Integer.MAX_VALUE;
			Odd[i] = Integer.MAX_VALUE;
			int b = scanner.nextInt();
			if (b % 2 == 1) {
				Odd[od++] = b;
			} else {
				Even[ev++] = b;
			}
		}
		Arrays.sort(Even);
		Arrays.sort(Odd);
		int sum = 0;
		if (od > ev) {
			for (int i = 0; i < od - ev - 1; i++)
				sum += Odd[i];
		} else {
			for (int i = 0; i < ev - od - 1; i++)
				sum += Even[i];
		}
		System.out.println(sum);
		scanner.close();
	}

}
