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 long long N = 1e6;
long long n, m, x, i, z, cnt, sum, rem, tre, ert, ans, used[N];
vector<long long> v, v1, v2, v3;
vector<pair<string, string> > p;
set<char> second;
string s, s1, s2, s3, s4;
map<string, long long> mp;
char g;
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n;
  for (long long i = 1; i <= n; i++) {
    cin >> x;
    v.push_back(x);
    if (x % 2 == 0)
      cnt++;
    else
      ans++;
  }
  x = 0;
  sort(v.begin(), v.end());
  reverse(v.begin(), v.end());
  if (cnt >= ans) {
    for (long long i = 0; i < v.size(); i++) {
      for (long long j = 0; j < v.size(); j++) {
        if (v[j] % 2 == 0 and x == 0 and v[j] != 0) {
          v[j] = 0;
          x = 1;
          break;
        }
        if (v[j] % 2 != 0 and x == 1) {
          v[j] = 0;
          x = 0;
          break;
        }
      }
    }
    for (long long i = 0; i < v.size(); i++) {
      sum += v[i];
    }
    cout << sum;
  }
  if (cnt < ans) {
    for (long long i = 0; i < v.size(); i++) {
      for (long long j = 0; j < v.size(); j++) {
        if (v[j] % 2 == 0 and x == 1 and v[j] != 0) {
          v[j] = 0;
          x = 0;
          break;
        }
        if (v[j] % 2 != 0 and x == 0) {
          v[j] = 0;
          x = 1;
          break;
        }
      }
    }
    for (long long i = 0; i < v.size(); i++) {
      sum += v[i];
    }
    cout << sum;
  }
}
