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;
bool cmp(long long int a, long long int b) { return a > b; }
int main() {
  vector<long long int> v, v_od, v_ev;
  long long int n, t_sum = 0, sum = 0, input, sz_od, sz_ev;
  cin >> n;
  for (long long int i = 1; i <= n; i++) {
    cin >> input;
    t_sum += input;
    v.push_back(input);
    if (input % 2)
      v_od.push_back(input);
    else
      v_ev.push_back(input);
  }
  sort(v_ev.begin(), v_ev.end(), cmp);
  sort(v_od.begin(), v_od.end(), cmp);
  sz_od = v_od.size();
  sz_ev = v_ev.size();
  if (sz_od == sz_ev)
    sum = t_sum;
  else if (sz_od < sz_ev) {
    for (long long int i = 0; i < sz_od; i++) sum += v_od[i];
    for (long long int i = 0; i < sz_od + 1; i++) sum += v_ev[i];
  } else {
    for (long long int i = 0; i < sz_ev; i++) sum += v_ev[i];
    for (long long int i = 0; i < sz_ev + 1; i++) sum += v_od[i];
  }
  cout << t_sum - sum << endl;
  return 0;
}
