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.*;
import java.io.*;

public class B {

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO Auto-generated method stub
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter pw = new PrintWriter(System.out);
		int n = Integer.parseInt(br.readLine());
		StringTokenizer st=new StringTokenizer(br.readLine());
		int e=0;
		int o=0;
		ArrayList<Integer> ea=new ArrayList<>();
		ArrayList<Integer> oa=new ArrayList<>();
		for(int j=0;j<n;j++) {
			int x=Integer.parseInt(st.nextToken());
			if(x%2==0)
				ea.add(x);
			else
				oa.add(x);
		}
		Collections.sort(ea);
		Collections.sort(oa);
		e=ea.size();
		o=oa.size();
		long sum=0;
		if(e>o) {
			for(int i=0;i<e-o-1;i++) {
				sum+=ea.get(i);
			}
		}
		else if(o>e) {
			for(int i=0;i<o-e-1;i++) {
				sum+=oa.get(i);
			}
		}
		pw.println(sum);
		
		pw.flush();

	}

}
