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
#-- Parity Alternated Deletions
# https://codeforces.com/problemset/problem/1144/B

import sys
from functools import reduce
from collections import defaultdict

def padOpt(ints):
  sInts = sorted(ints)[::-1]
  odd = []
  even = []

  # Lets start with the highest number
  for i in sInts:
    if i % 2 == 0:
      even.append(i)
    else:
      odd.append(i)

  # i am here.
  total = sum(sInts)
  k = min(len(odd), len(even))
  total -= sum(odd[0: k])
  total -= sum(even[0: k])
  
  # Now subtract the element that has less value.
  n = 0
  if len(odd) > k:
    n = odd[k]

  if len(even) > k:
    if n < even[k]:
      n = even[k]

  total -= n
  print (total) 


def io():
  ''' This function read input from standard input. '''
  totalIns = int(sys.stdin.readline(), 10)
  ints = [] * totalIns

  for i in sys.stdin.readline().strip().split():
    ints.append(int(i, 10))
    
  padOpt(ints)

if __name__ == "__main__":
  io()
