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 R550b
{
	static boolean getParity(int n) 
	{ 
		if(n%2==0)
			return false;
		else
			return true;
		
	} 
	public static void main(String args[])
	{
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),i,j=0,k=0;
		int ar[]=new int[n];
		long sum=0;
		for(i=0;i<n;i++)
		{
			ar[i]=sc.nextInt();
		}
		int a[]=new int[n];
		int b[]=new int[n];
		for(i=0;i<n;i++)
		{
			if(getParity(ar[i])==true)
				a[j++]=ar[i];
			else
				b[k++]=ar[i];
		}
		Arrays.sort(a);
		Arrays.sort(b);
		if(j!=k)
		{
			if(j>k)
			{
				j=k+1;
			}
			else
			{
				k=j+1;
			}
		}
		for(i=0;i<n-j;i++)
			sum+=a[i];
		for(i=0;i<n-k;i++)
			sum+=b[i];
		System.out.println(sum);
	}
}