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.Scanner;
public class Ishu
{
	public static void main(String[] args)
	{
	Scanner scan=new Scanner(System.in);
	int n,i,j,swap,odd=0,even=0,sum=0,sum1=0;
	int[] a=new int[2000];
	n=scan.nextInt();
	for(i=0;i<n;++i)	
		{
		a[i]=scan.nextInt();	
		sum+=a[i];
		if(a[i]%2==1)
			++odd;
		else
			++even;
		}
	for(i=0;i<n;++i)
		for(j=0;j<n-1;++j)
			if(a[j+1]>a[j])
				{
				swap=a[j+1];
				a[j+1]=a[j];
				a[j]=swap;
				}
	if(odd<even)
		even=odd+1;
	else if(odd>even)
		odd=even+1;
	for(i=0;i<n;++i)
		{
		if(odd>0&&a[i]%2==1)
			{
			sum1+=a[i];
			--odd;
			}
		else if(even>0&&a[i]%2==0)
			{
			sum1+=a[i];
			--even;
			}
		}
	sum-=sum1;
	System.out.println(sum);
	}			
}