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.*;
public class _1144B
{
	public static void main(String args[])
	{
		int n;
		Scanner scan = new Scanner(System.in);
		n = scan.nextInt();
		int[] a = new int[n];
		ArrayList<Integer> e = new ArrayList<Integer>();
		ArrayList<Integer> o = new ArrayList<Integer>();
		int i,j,sum=0;
		for(i=0;i<n;i++)
		{
			a[i] = scan.nextInt();
			if(a[i]%2==0)
				e.add(a[i]);
			else
				o.add(a[i]);
		}
		Collections.sort(e);
		Collections.sort(o);
		if(e.size()-o.size()-1>0)
		{
			for(i=0;i<e.size()-o.size()-1;i++)
			{
				sum+=e.get(i);
			}
			System.out.println(sum);
		}
		else if(o.size()-e.size()-1>0)
		{
			for(i=0;i<o.size()-e.size()-1;i++)
			{
				sum+=o.get(i);
			}
			System.out.println(sum);
		}
		else
			System.out.println(0);
	}
}