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
amount = int(input())

all_numbers = map(int, input().split())
even = []
odd = []

for element in all_numbers:
    if element % 2:
        odd.append(element)
    else:
        even.append(element)

even.sort()
odd.sort()


def good(even, odd):
    even_cpy = even[:]
    odd_cpy = odd[:]
    alter = True
    flag = True
    #breakpoint()
    while flag:
        if alter:
            if len(odd) > 0:
                odd.pop()
            else:
                flag = False
                if len(odd_cpy) > 0:
                    odd_cpy.pop()
            if len(even_cpy) > 0:
                even_cpy.pop()
            else:
                flag = False
                if len(even) > 0:
                    even.pop()
            alter = not alter
        else:
            if len(even) > 0:
                even.pop()
            else:
                flag = False
                if len(even_cpy) > 0:
                    even_cpy.pop()
            if len(odd_cpy) > 0:
                odd_cpy.pop()
            else:
                flag = False
                if len(odd) > 0:
                    odd.pop()
            alter = not alter
    
    return min(sum(even)+sum(odd), sum(even_cpy)+sum(odd_cpy))


if len(odd) == 0:
    print(sum(even)-max(even))
elif len(even) == 0:
    print(sum(odd)-max(odd))
else:
    print(good(even, odd))
