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.*;
public class MyClass {
    public static void main(String args[]) {
        Scanner scan = new Scanner(System.in);
        ArrayList<Long> even = new ArrayList<>(), odd = new ArrayList<>();
        int n = scan.nextInt();
        long res = Long.MAX_VALUE;
        for(int i = 0; i < n; i++) {
            long l = scan.nextLong();
            if(l % 2 == 0) even.add(l);
            else odd.add(l);
        }
        Collections.sort(even);
        Collections.sort(odd);
        ArrayList<Long> a = new ArrayList<>(even), b = new ArrayList<>(odd);
        int turn = 0;
        while(true) {
            if(turn == 0) {
                if(a.isEmpty()) break;
                a.remove(a.size()-1);
            }
            else {
                if(b.isEmpty()) break;
                b.remove(b.size()-1);
            }
            turn ^= 1;
        }
        res = sum(a, b);
        a = new ArrayList<>(even);
        b = new ArrayList<>(odd);
        turn = 1;
        while(true) {
            if(turn == 0) {
                if(a.isEmpty()) break;
                a.remove(a.size()-1);
            }
            else {
                if(b.isEmpty()) break;
                b.remove(b.size()-1);
            }
            turn ^= 1;
        }
        res = Math.min(res, sum(a, b));
        System.out.println(res);
    }
    
    static long sum(ArrayList<Long> a, ArrayList<Long> b) {
        long res = 0;
        for(Long i : a) res += i;
        for(Long i : b) res += i;
        return res;
    }
}