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()))

pick_DP = [-float('INF')] * (n//2 + 2)
unpick_DP = [-float('INF')] * (n//2 + 2)
pick_DP[0] = 0
unpick_DP[0] = 0

for i, a in enumerate(A, 1):
    mini = (i-1)//2 - 1
    if mini <= 0:
        mini = 1
    maxi = (i+1)//2

    for num in range(maxi, mini-1, -1):
        if unpick_DP[num] < pick_DP[num]:
            unpick_DP[num] = pick_DP[num]
        pick_DP[num] = max(unpick_DP[num-1] + a, pick_DP[num])

print(max(pick_DP[n//2], unpick_DP[n//2]))