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
INF = 10 ** 15

N = int(input())
As = list(map(int, input().split()))
As.append(-INF)

INF = 10 ** 15
dp = [[-INF] * (N//2) for _ in range(3)]
dp[0][0] = As[0]
dp[1][0] = As[1]
dp[2][0] = As[2]

for i in range(1, N//2):
    dp[0][i] = dp[0][i-1] + As[2*i]
    dp[1][i] = max(dp[0][i-1], dp[1][i-1]) + As[2*i+1]
    dp[2][i] = max(dp[0][i-1], dp[1][i-1], dp[2][i-1]) + As[2*i+2]

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

