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
t = int(input())
cnt = 0
su =0
def init(a):
    for p in range(len(a)):
        a[p] = int(a[p])
    return(a)
'''def swap(a):
    for i in range(len(a)-1):
        temp = a[i] 
        a[i] = a[i+1]
        a[i+1] = temp
    return(a)'''
d = input().split()
d =  init(d)
e =[]
o = []
for i in range(len(d)):
    if d[i]%2 == 0:
        e.append(d[i])
    else:
        o.append(d[i])
e = sorted(e)
o = sorted(o)
h = len(e)-len(o)
if abs(h) < 2:
    su = 0
elif h > 0:
    su =  sum(e[:abs(h)-1])
elif h < 0:
    su = sum(o[:abs(h)-1])
print(su)



    

