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;
import java.util.Arrays;

public class Hello {

	public static void main(String[] args)
	{
	
		Scanner s = new Scanner(System.in);
		int length = s.nextInt();
		
		int[] a= new int[length];
		
		for(int i=0;i<length;i++)
		{
			a[i]=s.nextInt();
		}
		
		int[] odd1= new int[length];
		int[] even1= new int[length];
		
		int j=0;
		int k=0;
		
		for(int i=0;i<length;i++)
		{
			
	
			if(a[i]%2==0)
			{
				even1[j]=a[i];
				j++;
			}
			else
			{
				odd1[k]=a[i];
				k++;
				
			}
		}	
		
		int[] odd= new int[k];
		int[] even= new int[j];
		
		for(int i=0;i<k;i++)	
			odd[i]=odd1[i];
		
		for(int i=0;i<j;i++)	
			even[i]=even1[i];
		
			
			
		Arrays.sort(even); //j
		Arrays.sort(odd); //k
		
		
			
		if((j-k)<2 && -2<j-k)
			System.out.print(0);
		else
		{
			if(j<k)
			{
				int summ=0;
				
				for(int i=0;i<k-j-1;i++)
				{
					summ+=odd[i];
					
				}
				
				System.out.print(summ);
			}
			else
			{
				int summ=0;
				
				for(int i=0;i<j-k-1;i++)
				{
					summ+=even[i];
				}
				
				System.out.print(summ);
			}
			
			
		}
			
		
	}

}
