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
from __future__ import absolute_import, division, print_function, unicode_literals
from typing import List
import sys
# **Note: To enable DEBUG, just add argument "-d" to the binary**. I.e.:
# `python solution.py -d`
DEBUG = len(sys.argv) > 1 and sys.argv[1] == '-d'


# Sample usage: `LOG("a =", 1,"b =", 2)`.
def LOG(*argv):
  if (DEBUG):
    print(*argv, file=sys.stderr)


def CHECK(cond, err_msg=''):
  if (DEBUG):
    assert cond, err_msg


def CHECK_EQ(a, b, err_msg=''):
  CHECK(a == b, err_msg='{} v.s. {} {}'.format(a, b, err_msg))


def readval(typ=int):
  return typ(input())


def readvals(typ=int):
  return map(typ, input().split())


###############################################################################/
############################* Above are tmpl code #############################/
###############################################################################/


def solve(arr: List[int]) -> int:
  pile1, pile2 = [], []
  for a in arr:
    if a % 2 == 0:
      pile1.append(a)
    else:
      pile2.append(a)
  if len(pile1) < len(pile2):
    pile1, pile2 = pile2, pile1
  LOG(pile1)
  LOG(pile2)
  # pile1 is always longer than pile2.
  if len(pile1) - len(pile2) <= 1:
    return 0
  pile1.sort(reverse=True)
  return sum(pile1[len(pile2)+1:])


if __name__ == '__main__':
  CHECK_EQ(solve([1, 2, 3]), 0)
  CHECK_EQ(solve([2, 3, 4, 4]), 2)
  CHECK_EQ(solve([4, 4, 4]), 8)
  CHECK_EQ(solve([4, 5]), 0)
  CHECK_EQ(solve([1, 5, 8, 7, 2]), 0)
  _ = readval()
  arr = readvals()
  print(solve(arr))