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())

v1 = 0
v2 = 0
v3 = 0
m = N // 2 *2 
if N % 2 == 0:
  for i in range(0, m, 2):
    v1 += A[i]
    v2 += A[i+1]
    v2 = max(v1,v2)
  print(v2)  
#
else:
  for i in range(0, m, 2):
    v1 += A[i]
    v2 += A[i+1]
    v3 += A[i+2]
    v2 = max(v1,v2)
    v3 = max(v2,v3)
  print(v3)
#
  
