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
def main():
    jumlah_int = int(input())
    list_int = []
    numbers_unsplit = input()
    for i in numbers_unsplit.split(" "):
        list_int.append(int(i))
    parity_alternated_deletions(list_int)


def parity_alternated_deletions(list_int):
    list_even = []
    list_odd = []
    for i in list_int:
        if(i % 2 == 0):
            list_even.append(i)
        else:
            list_odd.append(i)
    if(len(list_even) == len(list_odd)):
        print("0")
    elif(len(list_even) > len(list_odd)):
        count = 0
        diff = len(list_even) - len(list_odd)
        for i in range(diff-1):
            min_val = list_even[0]
            index_val = 0
            for j in range(1, len(list_even)):
                if(min_val > list_even[j]):
                    min_val = list_even[j]
                    index_val = j
            count += min_val
            list_even.pop(index_val)
        print(count)
    else:
        count = 0
        diff = len(list_odd) - len(list_even)
        for i in range(diff-1):
            min_val = list_odd[0]
            index_val = 0
            for j in range(1, len(list_odd)):
                if(min_val > list_odd[j]):
                    min_val = list_odd[j]
                    index_val = j
            count += min_val
            list_odd.pop(index_val)
        print(count)
main()