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
#include <bits/stdc++.h>
using namespace std;
int make_positive(int a) { return a > 0 ? a : a * -1; }
int main(void) {
  int number;
  int temp;
  scanf("%d", &number);
  vector<int> even;
  vector<int> odd;
  for (int i = 0; i < number; i++) {
    scanf("%d", &temp);
    if (!(temp % 2)) {
      even.push_back(temp);
    } else {
      odd.push_back(temp);
    }
  }
  if (even.size() == odd.size() ||
      (even.size() - 1 == odd.size() || odd.size() - 1 == even.size())) {
    printf("0\n");
    return 0;
  }
  sort(even.begin(), even.end());
  sort(odd.begin(), odd.end());
  int limit = make_positive(even.size() - odd.size()) - 1;
  long long sum = 0;
  for (int i = 0; i < limit; i++) {
    if (even.size() > odd.size()) {
      sum += even[i];
    } else {
      sum += odd[i];
    }
  }
  printf("%d\n", sum);
  return 0;
}
