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>
const char endl = '\n';
int32_t main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  std::cout.tie(0);
  long long n, temp, O = 0, E = 0;
  std::vector<long long> odds;
  std::vector<long long> evens;
  std::cin >> n;
  for (long long i = 0; i < n; i++) {
    std::cin >> temp;
    if (temp % 2 == 1) {
      odds.push_back(temp);
      O++;
    } else {
      evens.push_back(temp);
      E++;
    }
  }
  std::sort(odds.begin(), odds.end());
  std::sort(evens.begin(), evens.end());
  long long diff = E - O;
  long long ans = 0;
  if (diff > 1) {
    for (long long i = 0; i < diff - 1; i++) {
      ans += evens[i];
    }
  }
  if (diff < -1) {
    diff *= -1;
    for (long long i = 0; i < diff - 1; i++) {
      ans += odds[i];
    }
  }
  std::cout << ans << endl;
}
