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
times = int(input())
even = 0
final = 0
evenArray = [10000001]*times
oddArray = [10000001]*times
even = 0
odd = 0
numbers = input().split()
for counter in range(times):
    numbers[counter] = int(numbers[counter])
for count in range(times):
    if numbers[count]%2==0:
        evenArray[even] = numbers[count]
        even +=1
    if numbers[count]%2==1:
        oddArray[odd] = numbers[count]
        odd +=1
'''print(oddArray)
print(evenArray)'''
if even+1<odd:
    if times ==2:
        final = oddArray[0]
    else:
        oddArray.sort()
        for count in range(odd-even-1):
            final = final+oddArray[count]
if odd+1<even:
    if times ==2:
        final = evenArray[0]
    else:
        evenArray.sort()
        for count in range(even-odd-1):
            final = final+evenArray[count]
if even==odd or even==odd+1 or odd==even+1:
    final = 0
print(final)