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


input = sys.stdin.readline


n = input().rstrip()
poly = list(map(int, input().split()))
removed = ''
odds = list()
evens = list()
for i in poly:
    if i%2 == 0:
        evens.append(i)
    else:
        odds.append(i)

l_o = len(odds)
l_e = len(evens)

if abs(len(odds) - len(evens)) <= 1:
    print(0)
elif l_o == 0 or l_e == 0:
    if l_o == 0:
        print(sum(evens)-max(evens))
    elif l_e == 0:
        print(sum(odds)-max(odds))
else:
    if len(odds) < len(evens):
        evens.remove(max(evens))
        removed = 'e'

    if len(odds) > len(evens):
        odds.remove(max(odds))
        removed = 'o'

    if len(odds) == len(evens):
        if max(odds) > max(evens):
            odds.remove(max(odds))
            removed = 'o'
        else:
            evens.remove(max(evens))
            removed = 'e'

    while len(odds) != 0 and len(evens) != 0:
        if removed == 'o':
            evens.remove(max(evens))
            removed = 'e'
        else:
            odds.remove(max(odds))
            removed = 'o'
    
    if removed == 'o' and evens != []:
        evens.remove(max(evens))
    if removed == 'e' and odds != []:
        odds.remove(max(odds))


    print(sum(odds) + sum(evens))
