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())
l = list(map(int,input().split()))

INF = 10 ** 17

start = []
start.append((0, l[0]))
start.append((0,max(l[0],l[1])))

for i in range(2, N):
    if i % 2 == 0:
        left = [start[-1][1], start[-2][0] + l[i]]
        right = [start[-2][1] + l[i]]
    else:
        left = [start[-1][0], start[-2][0] + l[i]]
        right = [start[-1][1], start[-2][1] + l[i]]
    start.append((max(left),max(right)))

if N % 2:
    print(start[-1][0])
else:
    print(start[-1][1])
