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 Parity_Alternated_Deletions
{
	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>();
		long sum=0,s=0;
		for(int i=0;i<n;i++)
		{
			int a=in.nextInt();
			if(a%2==0)
			{
				even.add(a);
			}
			else
			{
				odd.add(a);
			}
			sum=sum+a;
			s=s+a;
		}
		Collections.sort(even);
		Collections.sort(odd);
		int size_even=even.size();
		int size_odd=odd.size();
        int c=0;
        boolean bool=true;
        while(bool==true)
        {
        	if(c%2==0)
        	{
        	   if(size_even!=0)
        	   {
        		   sum=sum-even.get(size_even-1);
        		   size_even--;
        	   }
        	   else
        	   {
        		   bool=false;
        	   }
        	}
        	else if(c%2!=0)
        	{
        	   if(size_odd!=0)
        	   {
        		   sum=sum-odd.get(size_odd-1);
        		   size_odd--;
        	   }
        	   else
        	   {
        		   bool=false;
        	   }
        	}
        	c++;
        }
        size_even=even.size();size_odd=odd.size();c=1;bool=true;
        while(bool==true)
        {
        	if(c%2==0)
        	{
        	   if(size_even!=0)
        	   {
        		   s=s-even.get(size_even-1);
        		   size_even--;
        	   }
        	   else
        	   {
        		   bool=false;
        	   }
        	}
        	else if(c%2!=0)
        	{
        	   if(size_odd!=0)
        	   {
        		   s=s-odd.get(size_odd-1);
        		   size_odd--;
        	   }
        	   else
        	   {
        		   bool=false;
        	   }
        	}
        	c++;
        }
        System.out.println(Math.min(s, sum));
	}
}
        