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.io.*;
import java.util.*;
public class Main
	{
		public static void main(String args[])
			{
				Scanner sc=new Scanner(System.in);
				int n=sc.nextInt();
				int a[]=new int[n];
				for(int i=0;i<n;i++)
					a[i]=sc.nextInt();
				ArrayList<Integer> e=new ArrayList<>();
				ArrayList<Integer> o=new ArrayList<>();
				for(int i=0;i<n;i++)
					if(a[i]%2==0)
						e.add(a[i]);
					else
						o.add(a[i]);
				int ee=e.size();
				int oo=o.size();
				if(ee==oo|| oo-ee==-1 || oo-ee==1)
					System.out.println(0);
				else
					{
						Collections.sort(e,Collections.reverseOrder());
						Collections.sort(o,Collections.reverseOrder());
						int s=0;
						if(ee>oo)
							{
								for(int i=oo+1;i<ee;i++)
									s=s+e.get(i);
							}
						else
							{
								for(int i=ee+1;i<oo;i++)
									s=s+o.get(i);
							}
						System.out.println(s);
					}				
			}
	}	
