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
import sys


def input():
    return sys.stdin.readline().strip()


def print(*x, sep=' ', end='\n'):
    return sys.stdout.write(sep.join(map(str, x)) + end)


def read():
    return sys.stdin.read()


def get():
    return int(input()), [int(i) for i in input().split()]


def out(*arg):
    if type(arg[0]) == list:
        for i in arg[0]:
            print(i)
    else:
        print(arg)


def main():
    n, a = get()
    odd = []
    even = []
    for i in range(n):
        if a[i] % 2 == 0:
            odd.append(a[i])
        else:
            even.append(a[i])
    x, y = len(odd), len(even)
    if abs(x - y) <= 1:
        print(0)
    else:
        odd = sorted(odd, reverse=True)
        even = sorted(even, reverse=True)
        if x > y:
            print(sum(odd) - sum(odd[:y + 1]))
        else:
            print(sum(even) - sum(even[:x + 1]))


if __name__ == "__main__":
    main()
