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.Collections;
import java.util.LinkedList;
import java.util.List;
import java.util.Queue;
import java.util.Scanner;

public class Main {
	private static int n;
	private static int sum;

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		Queue<Integer> q1 = new LinkedList<>();//odd
		Queue<Integer> q2 = new LinkedList<>();//even
		n = sc.nextInt();
		for (int i = 0; i < n; i++) {
			int a = sc.nextInt();
			if((a&1)==1) {
				q1.add(a);
			}else {
				q2.add(a);
			}
		}
		int length = Math.abs(q1.size()-q2.size());
//		System.out.println(length);
//		System.out.println(q1.size());
//		System.out.println(q2.size());
		if(length==1) {
			System.out.println("0");
		}else if(q1.size()>q2.size()) {//odd大
			Collections.sort((List<Integer>) q1,(a,b)->((a>b)?1:(a==b?0:-1)));
			for(int i = 0;i<length-1;i++) {
				sum+=q1.poll();
			}
			System.out.println(sum);
		}else {
			Collections.sort((List<Integer>) q2,(a,b)->((a>b)?1:(a==b?0:-1)));
			for(int i = 0;i<length-1;i++) {
				sum+=q2.poll();
			}
			System.out.println(sum);
		}
	}
}
