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.Arrays;
import java.util.Scanner;
public class Main{
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int a[] = new int[n];
		int x = 0, y = 0, min = 0;
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			if (a[i] % 2 == 0)
				x++;
			else
				y++;
		}
		int b[] = new int[x];
		int c[] = new int[y];
		for (int i = 0, j = 0, k = 0; i < n; i++) {
			if (a[i] % 2 == 0) {
				b[j] = a[i];
				j++;
			} else {
				c[k] = a[i];
				k++;
			}
		}
		Arrays.sort(b);
		Arrays.sort(c);

		if (Math.abs(x - y) <= 1)
			System.out.println(min);
		else {
			if (x > y) {
				for (int i = 0; i < (x - y - 1); i++)
					min += b[i];
				System.out.println(min);
			} else {
				for (int i = 0; i < (y - x - 1); i++)
					min += c[i];
				System.out.println(min);
			}
		}
	}
}
			   		  			 	 	   		  			 		