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() {
  long long n;
  while (cin >> n) {
    vector<long long> v;
    long long c = 0, d = 0;
    for (int i = 0; i < n; i++) {
      long long p;
      cin >> p;
      v.push_back(p);
      if (p % 2 == 0)
        c++;
      else
        d++;
    }
    sort(v.begin(), v.end());
    if (c == d || (c + 1 == d) || (d + 1 == c)) {
      cout << 0 << endl;
    } else {
      long long sum = 0, x = 0, y = 0;
      if (d == 0 || c == 0) {
        for (int i = 0; i < n - 1; i++) {
          sum += v[i];
        }
        cout << sum << endl;
      } else if (c > d && d != 0) {
        for (int i = n - 1; i >= 0; i--) {
          if (v[i] % 2 != 0) {
            v[i] = -1;
          }
        }
        for (int i = n - 1; i >= 0; i--) {
          if (v[i] % 2 == 0) {
            v[i] = -1;
            x++;
          }
          if (x == d + 1) break;
        }
        for (int i = 0; i < n; i++) {
          if (v[i] != -1) sum += v[i];
        }
        cout << sum << endl;
      } else if (d > c && c != 0) {
        for (int i = n - 1; i >= 0; i--) {
          if (v[i] % 2 == 0) {
            v[i] = -1;
          }
        }
        for (int i = n - 1; i >= 0; i--) {
          if (v[i] % 2 != 0 && v[i] != -1) {
            v[i] = -1;
            y++;
          }
          if (c + 1 == y) break;
        }
        for (int i = 0; i < n; i++) {
          if (v[i] != -1) sum += v[i];
        }
        cout << sum << endl;
      }
    }
  }
  return 0;
}
