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
# I believe the following algorithm should work.
# I will basically run two greedy algorithms and pick the one that does
# best.
# In each greedy algorithm, I will delete the largest element available.
# In the first, I will start with an odd element, in the other I will
# start with an even element.

def minimum_remaining_sum(lst):
  def greedy(lst, op_idx):
    while True:
      try:
        lst = ops[op_idx](lst)
        op_idx = (op_idx + 1) % 2
      except NoMatchingElementException:
        return lst

  rem_odd_start = sum(greedy(lst.copy(), 0))
  rem_even_start = sum(greedy(lst.copy(), 1))
  return min(rem_odd_start, rem_even_start)

def delete_odd(lst):
  for i in range(len(lst)):
    if lst[i] % 2 == 1:
      lst.pop(i)
      return lst
  raise NoMatchingElementException

def delete_even(lst):
  for i in range(len(lst)):
    if lst[i] % 2 == 0:
      lst.pop(i)
      return lst
  raise NoMatchingElementException

ops = [delete_odd, delete_even]

class NoMatchingElementException(Exception):
  pass

if __name__ == '__main__':
  _ = int(input())
  lst = sorted(map(int, input().split()), reverse=True)
  print(minimum_remaining_sum(lst))