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;
  long long a[n];
  long long int sum = 0;
  int ev = 0, od = 0;
  for (int i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] % 2 == 0)
      ev++;
    else
      od++;
  }
  if (od == 0 || ev == 0) {
    std::sort(a, a + n);
    for (int i = 0; i < n - 1; i++) {
      sum += a[i];
    }
    cout << sum;
    return 0;
  }
  if (n % 2 == 0 && ev == n / 2) {
    cout << "0";
    return 0;
  } else if (n % 2 != 0 &&
             (ev > od && ev - od == 1 || od > ev && od - ev == 1)) {
    cout << "0";
    return 0;
  } else {
    std::sort(a, a + n);
    int dif = 0;
    if (ev > od) {
      int dif = ev - od;
      int cnt = 0;
      for (int i = 0; i < n; i++) {
        if (a[i] % 2 == 0 && cnt < dif - 1) {
          sum += a[i];
          cnt++;
        }
      }
    } else {
      int dif = od - ev;
      int cnt = 0;
      for (int i = 0; i < n; i++) {
        if (a[i] % 2 != 0 && cnt < dif - 1) {
          sum += a[i];
          cnt++;
        }
      }
    }
    cout << sum << endl;
    return 0;
  }
}
