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
/* package codechef; // don't place package name! */

import java.util.*;
import java.lang.*;
import java.io.*;
import java.util.Arrays;
import java.math.BigInteger;
 
/* Name of the class has to be "Main" only if the class is public. */
public class Main
{
     public static void main (String[] args) throws java.lang.Exception
     {
     	Scanner in =new Scanner(System.in);
		int t,i,j=0,n,m,k=0,l,p=0,h;
		String s,st;
		long sum=0;
		n=in.nextInt();
		int a[]=new int[n];
		for(i=0;i<n;i++)
		{
		     a[i]=in.nextInt();
		     if(a[i]%2==0)
		     k++;
		     else p++;
		}
		Arrays.sort(a);
		     if(k<p)
		     {
		          for(i=n-1;i>=0;i--)
		          {
     		          if(a[i]%2==0)
     		               a[i]=0;
     		          else if(a[i]%2!=0 && k+1>0)
     		          {     a[i]=0;k--;}
     		          sum+=a[i];
		          }
		     }
		     else if(p<k)
		     {
		          for(i=n-1;i>=0;i--)
		          {
     		          if(a[i]%2!=0)
     		               a[i]=0;
     		          else if(a[i]%2==0 && p+1>0)
     		          {    a[i]=0;p--;}
     		          sum+=a[i];
		          }
		     }
		     else
		          sum=0;
		     System.out.println(sum);
	}
}