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 math
import bisect

def egcd(a, b):
    if a == 0:
        return (b, 0, 1)
    else:
        g, x, y = egcd(b % a, a)
        return (g, y - (b // a) * x, x)



def mulinv(b, n):
    g, x, _ = egcd(b, n)
    if g == 1:
        return x % n


primes = []

def isprime(n):
    for d in range(2, int(math.sqrt(n))+1):
        if n%d==0:
            return False
    return True


def argsort(ls):
    return sorted(range(len(ls)), key=ls.__getitem__)

def f(p=0):
    if p==1:
        return map(int, input().split())
    elif p==2:
        return list(map(int, input().split()))
    else:
        return int(input())



n = f()
cl = sorted(f(2))
a = 0
b = 0
cla = []
clb = []
for i in range(n):
    if cl[i]%2==0:
        b+=1
        clb.append(cl[i])
    else:
        a+=1
        cla.append(cl[i])

if a<b:
    nb = b - a
    nb = max(0, nb-1)
    if nb!=0:
        x = sum(clb[:nb])
    else:
        x = 0
elif b<a:
    na = a-b
    na = max(0, na - 1)
    if na != 0:
        x = sum(cla[:na])
    else:
        x = 0
else:
    x = 0

print(x)