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.Arrays;
public class B550 {
	public static void main(String args[])
	throws java.io.IOException{
		int n;
		long sum=0;
		long res=0;
		int sizee=0, sizen=0;
		int even=0, noteven=0;
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		n = Integer.parseInt(reader.readLine());
		int a[] = new int[n];
		String str[] = new String[n];
		str = reader.readLine().split(" ");
		for(int i=0; i<n; i++) {
			a[i]=Integer.parseInt(str[i]);
			sum+=a[i];
			if(a[i]%2==0) even++;
			else noteven++;
			}
		int e[] = new int[even];
		int not[] = new int[noteven];
		for(int i=0; i<n;i++) {
			if(a[i]%2==0) {
				e[sizee]=a[i];
				sizee++;
			}
			else {
				not[sizen]=a[i];
				sizen++;
			}
		}
		Arrays.sort(e);
		Arrays.sort(not);
		if(even==noteven) {
			System.out.println(0);
		}
		else if (even>noteven) {
			even=even-noteven-1;
			for(int i=0; i<even;i++) {
				res+=e[i];
			}
			System.out.println(res);
		}
		else {
			noteven=noteven-even-1;
			for(int i=0; i<noteven;i++) {
				res+=not[i];
			}
			System.out.println(res);
		}
}}
