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, *A = map(int, open(0).read().split())

dp = [[-10 ** 10] * 3 for _ in range(N + 1)]
dp[0] = [0] * 3
dp[1][0] = A[0]
dp[2][1] = A[1]
for i in range(2, N):
    dp[i + 1][0] = dp[i - 1][0] + A[i]
    dp[i + 1][1] = max(dp[i - 1][1], dp[i - 2][0]) + A[i]
    dp[i + 1][2] = max(dp[i - 1][2], dp[i - 2][1], dp[i - 3][0]) + A[i]

if N % 2 == 1:
    print(max(dp[-3][0], dp[-2][1], dp[-1][2]))
else:
    print(max(dp[-2][0], dp[-1][1]))

