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 n;
int a[2005];
priority_queue<int> q1;
priority_queue<int> q2;
int main() {
  int sum = 0, cnt1 = 0, cnt2 = 0, tmp = -1;
  scanf("%d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    tmp = max(tmp, a[i]);
    if (a[i] & 1)
      cnt1++;
    else
      cnt2++;
    sum += a[i];
    if (a[i] & 1)
      q1.push(a[i]);
    else
      q2.push(a[i]);
  }
  if (cnt1 == 0 || cnt2 == 0) {
    printf("%d\n", sum - tmp);
    return 0;
  }
  int flag1 = 0, flag2 = 0;
  int x = q1.top(), y = q2.top();
  if (cnt1 > cnt2) {
    q1.pop();
    sum -= x;
    flag1 = 1;
  }
  if (cnt1 < cnt2) {
    q2.pop();
    sum -= y;
    flag2 = 1;
  }
  if (cnt1 == cnt2) {
    printf("0\n");
    return 0;
  }
  while (1) {
    if (flag1) {
      flag1 = 0;
      flag2 = 1;
      if (q2.empty()) break;
      int x = q2.top();
      q2.pop();
      sum -= x;
    } else {
      flag2 = 0;
      flag1 = 1;
      if (q1.empty()) break;
      int x = q1.top();
      q1.pop();
      sum -= x;
    }
  }
  printf("%d\n", sum);
}
