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
/* package whatever; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) 
	{
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		ArrayList<Integer> even = new ArrayList<Integer>();
		ArrayList<Integer> odd = new ArrayList<Integer>();
		int sum = 0;
		for (int i = 0; i < n; ++i){
			int tmp;
			tmp = in.nextInt();
			if (tmp % 2 == 0){
				even.add(tmp);
			}
			else{
				odd.add(tmp);
			}
			sum += tmp;
		}
		Collections.sort(even);
		Collections.sort(odd);
		if (even.size() == 0){
			System.out.println(sum - odd.get(odd.size() - 1));
			System.exit(0);
		}
		else if (odd.size() == 0){
			System.out.println(sum - even.get(even.size() - 1));
			System.exit(0);
		}
		boolean start = false;
		if (even.size() < odd.size()) start = true;
		while (true){
			//System.out.print(cte);
			//System.out.println(cto);
			if (start){
				if (odd.size() == 0) break;
				odd.remove(odd.size() - 1);
				start = false;
			}
			else {
				if (even.size() == 0) break;
				even.remove(even.size() - 1);
				start = true;
			}
		}
		int ans = 0;
		for (int i = 0; i < even.size(); ++i){
			ans += even.get(i);
		}
		for (int i = 0; i < odd.size(); ++i){
			ans += odd.get(i);
		}
		System.out.println(ans);
	}
}