Given is an integer sequence A_1, ..., A_N of length N.

We will choose exactly \left\lfloor \frac{N}{2} \right\rfloor elements from this sequence so that no two adjacent elements are chosen.

Find the maximum possible sum of the chosen elements.

Here \lfloor x \rfloor denotes the greatest integer not greater than x.

Constraints

* 2 \leq N \leq 2\times 10^5
* |A_i|\leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 ... A_N


Output

Print the maximum possible sum of the chosen elements.

Examples

Input

6
1 2 3 4 5 6


Output

12


Input

5
-1000 -100 -10 0 10


Output

0


Input

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


Output

5000000000


Input

27
18 -28 18 28 -45 90 -45 23 -53 60 28 -74 -71 35 -26 -62 49 -77 57 24 -70 -93 69 -99 59 57 -49


Output

295
N = int(input())
A = [0]+list(map(int, input().split(" ")))

dp_list = [{0, 0}, {0: 0, 1: A[1]}, {0: 0, 1: A[1] if A[1] > A[2] else A[2]}]

for i in range(3, N+1):
    b = (i-1)//2
    f = (i+1)//2
    dp_list.append({})
    for j in range(b, f+1):
        if j in dp_list[i-1]:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i] if dp_list[i -
                                                              2][j-1]+A[i] > dp_list[i-1][j] else dp_list[i-1][j]
        else:
            dp_list[i][j] = dp_list[i-2][j-1]+A[i]

print(dp_list[-1][N//2])