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 go(vector<int>& v, int state) {
  int sum = 0;
  priority_queue<int> odd, even;
  for (int i = 0; i < v.size(); i++) {
    if (v[i] % 2 == 1) {
      odd.push(v[i]);
    } else {
      even.push(v[i]);
    }
  }
  bool turn = false;
  if (state) {
    if (!odd.empty()) {
      odd.pop();
      turn = !turn;
    } else {
      return INT_MAX;
    }
    while (!odd.empty() && !even.empty()) {
      if (turn) {
        even.pop();
      } else {
        odd.pop();
      }
      turn = !turn;
    }
    if (turn && !even.empty()) {
      even.pop();
    }
    if (!turn && !odd.empty()) {
      odd.pop();
    }
    while (!even.empty()) {
      sum += even.top();
      even.pop();
    }
    while (!odd.empty()) {
      sum += odd.top();
      odd.pop();
    }
  } else {
    if (!even.empty()) {
      even.pop();
      turn = !turn;
    } else {
      return INT_MAX;
    }
    while (!even.empty() && !odd.empty()) {
      if (turn) {
        odd.pop();
      } else {
        even.pop();
      }
      turn = !turn;
    }
    if (!turn && !even.empty()) {
      even.pop();
    }
    if (turn && !odd.empty()) {
      odd.pop();
    }
    while (!even.empty()) {
      sum += even.top();
      even.pop();
    }
    while (!odd.empty()) {
      sum += odd.top();
      odd.pop();
    }
  }
  return sum;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  vector<int> v(n);
  for (int i = 0; i < n; i++) {
    cin >> v[i];
  }
  int x = go(v, 0);
  int y = go(v, 1);
  cout << min(x, y) << "\n";
  return 0;
}
