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 random
def ii():
    return int(input())


def mi():
    return map(int, input().split())


def li():
    return list(mi())

def main():
    n = input()
    a = li()
    even = []
    odd = []
    for i in a:
        if i % 2 == 0:
            even.append(i)
        else:
            odd.append(i)

    even = sorted(even)
    odd = sorted(odd)
    even2 = [i for i in even]
    odd2 = [i for i in odd]
    sum1, sum2 = (0,0)
    if len(even) == len(odd):
        print(0)
        exit()
    while(len(even)>0 and len(odd)>0):
        even.pop()
        odd.pop()


    if len(odd) > 0:
        odd.pop()
        sum1 = sum(odd)
    else:
        even.pop()
        sum1 = sum(even)

    while (len(even2) > 0 and len(odd2) > 0):
        even2.pop()
        odd2.pop()

    if len(odd2) > 0:
        odd2.pop()
        sum2 = sum(odd2)
    else:
        even2.pop()
        sum2 = sum(even2)

    print (max(sum1,sum2))





main()




