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.ArrayList;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class ParityAlternateDeletions {

	public static void main(String[] args) {
		
		Scanner s = new Scanner(System.in);
		
		int size = s.nextInt();
		List<Integer> odd = new ArrayList<Integer>();
		List<Integer> even = new ArrayList<Integer>();
		int num = 0, sum = 0, temp = 0;
		
		for(int i=0; i<size; i++) {
			num = s.nextInt();
			if(num%2==0) {
				even.add(num);
			}else {
				odd.add(num);
			}
		}
		
		Collections.sort(even);
		Collections.sort(odd);
		
		if(even.size()<odd.size()) {
			odd.remove(odd.size() - 1);
			temp = even.size();
			for(int i =0; i<temp; i++) {
				even.remove(even.size() - 1);
				odd.remove(odd.size() - 1);
			}
			
			for(int d : odd) {
			    sum += d;
			}
			System.out.println(sum);
			
		}else if(even.size()>odd.size()) {
			even.remove(even.size() - 1);
			temp = odd.size();
			for(int i =0; i<temp; i++) {
				even.remove(even.size() - 1);
				odd.remove(odd.size() - 1);
			}
			
			for(int d : even) {
			    sum += d;
			}
			System.out.println(sum);
		}else {
			temp = odd.size();
			for(int i =0; i<temp; i++) {
				even.remove(even.size() - 1);
				odd.remove(odd.size() - 1);
			}
			for(int d : even) {
			    sum += d;
			}
			System.out.println(sum);
	
		}

	}

}
