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())
arr=list(map(int,input().split()))
if n<=3:
  print(max(arr))
  exit()
lim=n%2+2
dp=[[0]*lim for _ in range(n+1)]
for i in range(n):
  dp[i+1][0]=dp[i-1][0]+arr[i]
  dp[i+1][1]=max(dp[i-1][1]+arr[i],dp[i-2][0]+arr[i])
  if lim==3:
    dp[i+1][2]=max(dp[i-1][2]+arr[i],dp[i-2][1]+arr[i],dp[i-3][0]+arr[i])
print(max(dp[-1][:lim]))