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()))
choice = n // 2

dic1 = {0:0}
dic2 = {0:0, 1:a[0]}

for i in range(1, n):
    mini = choice - (n-i+1)//2
    new = {}
    for j in range(mini, (i+2)//2+1):
        if j == 0:
            new[j] = 0
            continue
        if j in dic2:
            new[j] = max(dic2[j], dic1[j-1]+a[i])
        else:
            new[j] = dic1[j-1]+a[i]
    dic1 = dic2
    dic2 = new

print(dic2[choice])