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.*;

import javafx.util.Pair;




public class tt
{



	
	public static void main(String args[])
	{


	Scanner s=new Scanner(System.in);

	int n=s.nextInt();


	int a[]=new int[n];


	ArrayList<Integer>even=new ArrayList<Integer>();


	ArrayList<Integer>odd=new ArrayList<Integer>();

	int evensum=0;

	int oddsum=0;

	
	for(int i=0;i<n;i++)
	{

		a[i]=s.nextInt();

		if(a[i]%2==0)
		{
			even.add(a[i]);

			evensum=evensum+a[i];
		}

		else
		{
			odd.add(a[i]);

			oddsum=oddsum+a[i];
		}

	}


	if(even.isEmpty())
	{

		Collections.sort(odd,Collections.reverseOrder());

		odd.remove(0);

		int ans=0;


		for( int e : odd)
		{
			ans=ans+e;
		}


		System.out.println(ans);
	}

	else if(odd.isEmpty())
	{

		Collections.sort(even,Collections.reverseOrder());

		even.remove(0);

		int ans=0;


		for( int e : even)
		{
			ans=ans+e;
		}


		System.out.println(ans);



	}


	


	else
	{

		Collections.sort(odd,Collections.reverseOrder());

		Collections.sort(even,Collections.reverseOrder());

		int k=0;


		if(even.size()>odd.size())
		{

		while((!even.isEmpty())&&(!odd.isEmpty()))
		{
			even.remove(k);

			odd.remove(k);

			


		}

		even.remove(0);


		int sum=0;

			for(int x : even)
			{
				sum=sum+x;
			}

			System.out.println(sum);




	}




	else if(even.size()<odd.size())
		{

		while((!even.isEmpty())&&(!odd.isEmpty()))
		{

			odd.remove(k);
			even.remove(k);

			

			


		}

		odd.remove(0);


		int sum=0;

			for(int x : odd)
			{
				sum=sum+x;
			}

			System.out.println(sum);




	}


	else

	{

		System.out.println(0);
	}







		




	}
	
	}


}


