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.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;
import java.util.TreeSet;
 
public class myFile
{
	public static void main(String args[])
	{
	   Scanner sc = new Scanner(System.in);
	   List<Integer> list = new ArrayList<Integer>();
	   Queue<Integer> odd = new LinkedList<Integer>();
	   Queue<Integer> even = new LinkedList<Integer>();
	   while(sc.hasNextInt())
	   {
		   Integer n = sc.nextInt();
		   list.clear();
		   odd.clear();
		   even.clear();
		   for(int i=0;i<n;i++)
		   {
			   Integer x = sc.nextInt();
			   list.add(x);
		   }
		   Collections.sort(list);
		   for(int i=list.size()-1;i>=0;i--)
		   {
			   Integer number = list.get(i);
			   if((number%2)==0)
				   even.add(number);
			   else
				   odd.add(number);
		   }
		   
		   int min = Math.min(even.size(), odd.size());
		   if(even.size()>odd.size())
		   {
			  even.poll(); 
		   }
		   if(odd.size()>even.size())
		   {
			   odd.poll();
		   }
		   for(int i=1;i<=min;i++)
		   {
			   even.poll();
			   odd.poll();
		   }
		   Long ans =0l;
		   while(even.isEmpty()==false)
		   {
			   Integer x = even.poll();
			   ans=ans+x;
		   }
		   while(odd.isEmpty()==false)
		   {
			   Integer x = odd.poll();
			   ans=ans+x;
		   }
		   System.out.println(ans);
	   }
	}
 
}

