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;
const int INF = 0x7fffffff;
const int maxn = 2e6 + 7;
int judge(vector<int> v1, vector<int> v2) {
  int i = 0, j = 0;
  for (int k = 0;; k++) {
    if (k % 2 == 0) {
      if (i >= v1.size()) break;
      i++;
    } else {
      if (j >= v2.size()) break;
      j++;
    }
  }
  int ans = 0;
  for (; i < v1.size(); i++) {
    ans += v1[i];
  }
  for (; j < v2.size(); j++) {
    ans += v2[j];
  }
  return ans;
}
bool cmp(int a, int b) { return a > b; }
int main() {
  int n;
  while (cin >> n) {
    vector<int> odd, even;
    for (int i = 0; i < n; i++) {
      int a;
      cin >> a;
      if (a % 2)
        odd.push_back(a);
      else
        even.push_back(a);
    }
    sort(odd.begin(), odd.end(), cmp);
    sort(even.begin(), even.end(), cmp);
    int ans = INF;
    ans = min(judge(odd, even), judge(even, odd));
    cout << ans << endl;
  }
  return 0;
}
