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.BufferedReader;
import java.io.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;

public class Main {

	static int N;

	public static void main(String[] args) throws Exception {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));

		N = Integer.parseInt(br.readLine());
		ArrayList<Integer> lista = new ArrayList<>();
		ArrayList<Integer> listb = new ArrayList<>();
		StringTokenizer st = new StringTokenizer(br.readLine());
		for (int i = 0; i < N; i++) {
			int t = Integer.parseInt(st.nextToken());
			lista.add(t);
			listb.add(t);
		}

		Collections.sort(lista);
		Collections.sort(listb);
		Collections.reverse(lista);
		Collections.reverse(listb);
		int aflag = 1;
		while (true) {
			if (aflag == 0) {
				for (int i = 0; i < lista.size(); i++) {
					if (lista.get(i) % 2 == 0) {
						lista.remove(i);
						aflag = 1;
						break;
					}
				}
				if (aflag == 0) {
					break;
				}
			} else {
				for (int i = 0; i < lista.size(); i++) {
					if (lista.get(i) % 2 == 1) {
						lista.remove(i);
						aflag = 0;
						break;
					}
				}
				if (aflag == 1) {
					break;
				}
			}
		}
		int bflag = 0;
		while (true) {
			if (bflag == 0) {
				for (int i = 0; i < lista.size(); i++) {
					if (lista.get(i) % 2 == 0) {
						lista.remove(i);
						bflag = 1;
						break;
					}
				}
				if (bflag == 0) {
					break;
				}
			} else {
				for (int i = 0; i < lista.size(); i++) {
					if (lista.get(i) % 2 == 1) {
						lista.remove(i);
						bflag = 0;
						break;
					}
				}
				if (bflag == 1) {
					break;
				}
			}
		}

		long answerA = 0;
		long answerB = 0;
		for(int a : lista) {
			answerA += a;
		}
		for(int b : listb) {
			answerB += b;
		}
		
		long answer = Math.min(answerA, answerB);
		bw.write(answer + "");
		bw.flush();
		br.close();
		bw.close();
	}

}
