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 cp{

	public static void main(String[] args) {
		Scanner sc = new Scanner();

		int n = sc.nextInt();


		ArrayList<Integer> ev = new ArrayList<>();
		ArrayList<Integer> od = new ArrayList<>();

		for(int i=0;i<n;i++)
		{
			int x = sc.nextInt();

			if(x%2==0)
				ev.add(x);
			else od.add(x);
		}

		if(Math.abs(ev.size()-od.size())<=1)
		{
			out.println("0");
		}else{

			Collections.sort(ev);
			Collections.sort(od);

			int evs = ev.size();
			int ods = od.size();

			if(evs<ods)
			{
				ods = ods-(evs+1);
				long sum=0;
				for(int i=0;i<ods;i++)
					sum+=od.get(i);
				out.println(sum);
			}else{


				evs = evs-(ods+1);
				long sum=0;
				for(int i=0;i<evs;i++)
					sum+=ev.get(i);
				out.println(sum);

			}


		}

			
		
out.close();

	}

	static	PrintWriter out=new PrintWriter(System.out);
	static class Scanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String nextLine() {
			while (!st.hasMoreTokens())
				try { 
                                        st=new StringTokenizer(br.readLine());				               
                                } catch (IOException e) {}
			return st.nextToken();
		}
		char nextChar() {
			char c = '$';
				try { 
                                        c = (char)br.read();			               
                                } catch (IOException e) {}
			return c;
		}		
		int nextInt() {
			return Integer.parseInt(nextLine());
		}
		Double nextDouble() {
			return Double.parseDouble(nextLine());
		}
		long nextLong() {
			return Long.parseLong(nextLine());
		}
	}
}