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 = list(map(int, input().split())) + [0]

dp0, dp1, dp2 = [0] * (N + 1), [0] * (N + 1), [0] * (N + 1)
dp0[0] = A[0]
dp1[1] = A[1]
dp2[2] = A[2]

for i in range(N - 3):
    dp0[i + 2] = 0 if i % 2 else dp0[i] + A[i + 2]
    dp1[i + 3] = max(dp0[i], dp1[i + 1]) + A[i + 3]
    dp2[i + 4] = max(dp0[i], dp1[i + 1], dp2[i + 2]) + A[i + 4]

if N % 2:
    print(max(dp0[N - 3], dp1[N - 2], dp2[N - 1]))
else:
    print(max(dp0[N - 2], dp1[N - 1]))
