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 = [int(x) for x in input().split()]

# dp(直前の値を取っている)(最大個数取っている)
dp00 = -10**9
dp01 = 0
dp10 = -10**9
dp11 = 0

for i in range(n):
    if i % 2 == 0:
        dp10 = dp00 + a[i]
        dp00 = max(dp01, dp11)
        dp11 = dp01 + a[i]
    else:
        dp01 = dp11
        dp11 = dp00 + a[i]
        dp00 = max(dp00, dp10)
        if i == 3:
            dp10 = a[i]

if n % 2 == 0:
    print(max(dp01, dp11))
else:
    print(max(dp00, dp10))
