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 comp(int a, int b) { return a > b; }
int main() {
  int a;
  while (scanf("%d", &a) != EOF) {
    int arr[a];
    int arr2[a];
    int m1 = 0;
    int m2 = 0;
    for (int i = 0; i < a; i++) {
      int temp;
      scanf("%d", &temp);
      if (temp % 2 == 0)
        arr[m1++] = temp;
      else
        arr2[m2++] = temp;
    }
    sort(arr, arr + m1, comp);
    sort(arr2, arr2 + m2, comp);
    if (m1 - m2 > -2 && m1 - m2 < 2)
      printf("0");
    else if (m1 == 0) {
      long long sum = 0;
      for (int i = 1; i < m2; i++) sum += (long long)arr2[i];
      printf("%I64d", sum);
    } else if (m2 == 0) {
      long long sum = 0;
      for (int i = 1; i < m1; i++) sum += (long long)arr[i];
      printf("%I64d", sum);
    } else if (m1 < m2) {
      long long sum = 0;
      int lol = m2 - m1 - 1;
      for (int i = (m2 - lol); i < m2; i++) {
        sum += (long long)arr2[i];
      }
      printf("%I64d", sum);
    } else {
      long long sum = 0;
      int lol = m1 - m2 - 1;
      for (int i = (m1 - lol); i < m1; i++) {
        sum += (long long)arr[i];
      }
      printf("%I64d", sum);
    }
    printf("\n");
  }
  return 0;
}
