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;
vector<int> js;
vector<int> ous;
void Init() {
  js.clear();
  ous.clear();
}
int n;
bool cmp(const int &a, const int &b) { return a < b; }
int main() {
  while (~scanf("%d", &n)) {
    Init();
    for (int i = 0; i < n; i++) {
      int ans;
      scanf("%d", &ans);
      if (ans % 2) {
        js.push_back(ans);
      } else {
        ous.push_back(ans);
      }
    }
    sort(js.begin(), js.end(), cmp);
    sort(ous.begin(), ous.end(), cmp);
    if (js.size() == ous.size()) {
      printf("0\n");
    } else if (js.size() > ous.size()) {
      int ans = js.size() - ous.size();
      ans = ans - 1;
      int sum = 0;
      for (int i = 0; i < ans; i++) {
        sum += js[i];
      }
      printf("%d\n", sum);
    } else {
      int ans = ous.size() - js.size();
      ans = ans - 1;
      int sum = 0;
      for (int i = 0; i < ans; i++) {
        sum += ous[i];
      }
      printf("%d\n", sum);
    }
  }
  return 0;
}
