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
def main():
    n = int(input())
    s = [int(x) for x in input().split()]
    sum = 0
    sum1 = 0
    sum2 = 0
    for i in range(n):
        sum += s[i]
    arr1 = []
    arr2 = []
    for i in range(n):
        if s[i] % 2 == 0:
            arr2.append(s[i])
        else:
            arr1.append(s[i])
    arr1.sort()
    arr2.sort()
    arr1 = arr1[::-1]
    arr2 = arr2[::-1]
    if abs(len(arr1) - len(arr2)) <= 1:
        ans = 0
    elif len(arr1) == 0 or len(arr2) == 0:
        ans = sum - max(s)
    elif len(arr1) > len(arr2):
        for i in range(len(arr2)):
            sum1 += arr1[i]
            sum2 += arr2[i]
        ans = sum - sum1 - sum2
        ans -= arr1[len(arr2)]
    else:
        for i in range(len(arr1)):
            sum1 += arr1[i]
            sum2 += arr2[i]
        ans = sum - sum1 - sum2
        ans -= arr2[len(arr1)]
    print(ans)





main()
