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>
int main() {
  int32_t numbers_count;
  std::string input;
  std::vector<int64_t> numbers;
  std::cin >> numbers_count;
  for (int32_t count = 0; count < numbers_count; count++) {
    std::cin >> input;
    numbers.push_back(std::stoi(input));
  }
  std::sort(numbers.rbegin(), numbers.rend());
  std::vector<int64_t> evens;
  std::vector<int64_t> odds;
  for (auto& number : numbers) {
    if (number % 2 == 0) {
      evens.push_back(number);
    } else {
      odds.push_back(number);
    }
  }
  std::vector<int64_t> sum;
  if (std::abs(static_cast<int64_t>(evens.size()) -
               static_cast<int64_t>(odds.size())) > 1) {
    size_t min_size = std::min(evens.size(), odds.size());
    sum.insert(sum.end(), evens.begin() + min_size, evens.end());
    sum.insert(sum.end(), odds.begin() + min_size, odds.end());
    std::sort(sum.rbegin(), sum.rend());
    int64_t result = 0;
    std::for_each(sum.begin() + 1, sum.end(),
                  [&](int64_t item) { result += item; });
    std::cout << result << std::endl;
  } else {
    std::cout << 0 << std::endl;
  }
  return 0;
}
