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
#wrong
n = int(input())
a = sorted(list(map(int, input().split(" "))), reverse = True)
even = [x for x in a if x%2 == 0]
odd = [y for y in a if y%2 != 0]
if abs(len(even) - len(odd)) == 1:
    print(0)
elif len(even) == len(odd):
    print(0)
else:
    if len(even) > len(odd):
        even = even[::-1]
        l = len(even) - len(odd)
        even = even[:l-1]
        print(sum(even))
    elif len(odd) > len(even):
        odd = odd[::-1]
        l = len(odd) - len(even)
        odd =odd[:l-1]
        print(sum(odd))


# a = a[::-1]
# if n == 1:
#     print(a)
# else:
#     flag = 0
#     i = 0
#     while i < n-1:
#         if a[i]%2 == 0 and flag == 0:
#             a.pop(i)
#             flag = 1
#         elif i%2 != 0 and flag == 1:
#             a.pop(i)
#             flag = 0
#         i += 1
# print(sum(a))    
