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

import java.util.*;
import java.lang.*;
import java.io.*;

/* Name of the class has to be "Main" only if the class is public. */
public class Ideone
{
	public static void main (String[] args) throws java.lang.Exception
	{
		// your code goes here
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt(),odd=0,even=0;
		int[] a=new int[n];
		int sum=0;
		for(int i=0;i<n;i++){
			a[i]=sc.nextInt();
			sum+=a[i];
			if(a[i]%2==0){
				even++;
			}
			else{
				odd++;
			}
		}
		int[] o=new int[odd], e=new int[even];
		even=0;odd=0;
		for(int i=0;i<n;i++){
			if(a[i]%2==0)e[even++]=a[i];
			else o[odd++]=a[i];
		}
		Arrays.sort(o);Arrays.sort(e);
		odd=o.length-1;even=e.length-1;
		boolean flag=false;int ans=0;
		while(true){
			if(!flag){if(odd==-1)break;ans+=o[odd--];flag=true;}
			else {if(even==-1)break;ans+=e[even--];flag=false;}
		}
		flag=true;int res=0;
		odd=o.length-1;even=e.length-1;
		while(true){
			if(!flag){if(odd==-1)break;res+=o[odd--];flag=true;}
			else {if(even==-1)break;res+=e[even--];flag=false;}
		}
		System.out.println((sum-Math.max(ans,res)));
	}
}