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()))
dp = [{} for _ in range(N+1)]
INF = -float('inf')
for i in range(1,N+1):
    mid = i//2
    dp[i][mid-2],dp[i][mid-1],dp[i][mid],dp[i][mid+1],dp[i][mid+2]=INF,INF,INF,INF,INF
dp[1][1] = A[0]
dp[2][1] = max(A[1],dp[1][1])
dp[1][0],dp[2][0]=0,0

for i in range(2,N):
  a = A[i]
  ma = (i+2)//2
  mi = i//2
  dp[i+1][ma] = max(dp[i][ma],dp[i-1][ma-1]+a)
  dp[i+1][mi] = max(dp[i][mi],dp[i-1][mi-1]+a)

print(dp[-1][N//2])