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>
using namespace std;
int main() {
  int n;
  cin >> n;
  vector<int> all(n);
  int odd, even;
  odd = 0;
  even = 0;
  for (int i = 0; i < n; i++) {
    cin >> all[i];
    if (all[i] % 2 == 0)
      even++;
    else
      odd++;
  }
  if (abs(odd - even) == 1)
    cout << 0;
  else {
    int k = odd - even;
    unsigned long long out = 0;
    if (k > 0) {
      sort(all.begin(), all.end());
      for (int i = 0; i < n; i++) {
        if (all[i] % 2 == 1) {
          out += all[i];
          k--;
          if (k == 1) break;
        }
      }
    } else if (k < 0) {
      k *= -1;
      sort(all.begin(), all.end());
      for (int i = 0; i < n; i++) {
        if (all[i] % 2 == 0) {
          out += all[i];
          k--;
          if (k == 1) break;
        }
      }
    }
    cout << out;
  }
}
