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.*;
import java.io.*;
public class Solution1{
	public static long deletion(int arr[]){
		ArrayList<Integer> even=new ArrayList<>(),
						   odd=new ArrayList<>();

		for(int i=0;i<arr.length;i++)
			if((arr[i]&1)==1)
				odd.add(arr[i]);
			else
				even.add(arr[i]);


		if(Math.abs(even.size()-odd.size())<=1)
			return 0L;

		long sum=0;
		if(even.size()>odd.size()){
			Collections.sort(even,Collections.reverseOrder());
			for(int i=odd.size()+1;i<even.size();i++)
				sum+=even.get(i);
		}
		else{
			Collections.sort(odd,Collections.reverseOrder());
			for(int i=even.size()+1;i<odd.size();i++)
				sum+=odd.get(i);
		}
		return sum;
	}
	public static void main(String args[]){
		Scanner in=new Scanner(System.in);
			int n=in.nextInt();
			int arr[]=new int[n];
			for(int i=0;i<n;i++)
				arr[i]=in.nextInt();

			System.out.println(deletion(arr));
	}
}