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() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n;
  cin >> n;
  long long a[n];
  multiset<long long, greater<long long>> even, even1, odd, odd1;
  for (long long i = 0; i < n; i++) {
    cin >> a[i];
    if (a[i] & 1) {
      odd.insert(a[i]);
      odd1.insert(a[i]);
    } else {
      even.insert(a[i]);
      even1.insert(a[i]);
    }
  }
  if (odd.size() == even.size()) {
    cout << 0 << "\n";
    return 0;
  }
  long long chance = 0;
  long long minvalue = LONG_LONG_MAX;
  while (true) {
    if (chance == 0) {
      if (even.empty()) {
        if (!odd.empty()) {
          long long sum = 0;
          for (auto x : odd) sum += x;
          minvalue = min(minvalue, sum);
        } else
          minvalue = 0;
        break;
      } else {
        even.erase(even.begin());
      }
    } else {
      if (odd.empty()) {
        if (!even.empty()) {
          long long sum = 0;
          for (auto x : even) sum += x;
          minvalue = min(minvalue, sum);
        } else
          minvalue = 0;
        break;
      } else {
        odd.erase(odd.begin());
      }
    }
    chance++;
    chance %= 2;
  }
  if (minvalue == 0) {
    cout << minvalue << "\n";
    return 0;
  }
  chance = 1;
  while (true) {
    if (chance == 0) {
      if (even1.empty()) {
        if (!odd1.empty()) {
          long long sum = 0;
          for (auto x : odd1) sum += x;
          minvalue = min(minvalue, sum);
        } else
          minvalue = 0;
        break;
      } else {
        even1.erase(even1.begin());
      }
    } else {
      if (odd1.empty()) {
        if (!even1.empty()) {
          long long sum = 0;
          for (auto x : even1) sum += x;
          minvalue = min(minvalue, sum);
        } else {
          minvalue = 0;
        }
        break;
      } else {
        odd1.erase(odd1.begin());
      }
    }
    chance++;
    chance %= 2;
  }
  cout << minvalue << "\n";
  return 0;
}
