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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {
	private static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
	public static void main(String[] args) throws NumberFormatException, IOException {
		int n = Integer.parseInt(br.readLine().trim());
		int odd = 0, even = 0;
		int a[] = new int[n];
		String s[] = br.readLine().trim().split(" ");
		for(int i = 0; i < n; i++) {
			a[i] = Integer.parseInt(s[i]);
			if(a[i]%2 == 0) {
				even++;
			}
			else odd++;
		}
		int ans = 0;
		Arrays.sort(a);
		if(even > odd + 1) {
			int c = even-odd-1;
			int i = 0;
			while(c > 0 && i < n) {
				if(a[i]%2 == 0) {
					ans += a[i];
					c--;
				}
				i++;
			}
		}
		else if(odd > even + 1) {
			int c = odd-even-1;
			int i = 0;
			while(c > 0 && i < n) {
				if(a[i]%2 == 1) {
					ans += a[i];
					c--;
				}
				i++;
			}
		}
		System.out.println(ans);
	}
}
