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
from math import fabs

b = input()
a = raw_input()
s = []
s = a.split(' ')
sum_c = 0
sum_n = 0
result = 0
end = 0
raznica = 0
mas_n = []
mas_c = []
for number in s:
    if (int(number)%2==0):
        sum_c = sum_c + 1
        mas_c.append(int(number))
    else:
        sum_n = sum_n + 1
        mas_n.append(int(number))
if(sum_c == sum_n):
    end = end + 1
elif(fabs(sum_c - sum_n) == 1.0):
    end = end + 1
else:
    raznica = fabs(sum_c - sum_n) - 1
    if (sum_c > sum_n):
        mas_c = sorted(mas_c)
        sw = 0
        for nu in mas_c:
            if(sw < raznica):
                result=result+nu
            else:
                break
            sw = sw + 1
    else:
        mas_n = sorted(mas_n )
        sw = 0
        for nu in mas_n:
            if (sw < raznica):
                result = result + nu
            else:
                break
            sw = sw + 1
print(result)

