p02716 AtCoder Beginner Contest 162 - Select Half
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
```python
N=int(input())
A=list(map(int, input().split()))

dp = [[0 for i in range(2)] for j in range(N+1)]

if N in [2, 3]: print(max(A))
else:
  dp[2][0] = A[1]
  dp[2][1] = A[0]
  dp[3][0] = A[2]
  dp[3][1] = max(A[1], A[0])
  
  for i in range(4, N+1):
    if i % 2 == 0:
      dp[i][0] = max(max(dp[i-2][0], dp[i-2][1])+A[i-1], dp[i-1][1]+A[i-1])
      dp[i][1] = dp[i-2][1]+A[i-2]
    else:
      dp[i][0] = max(dp[i-2][0], dp[i-2][1])+A[i-1]
      dp[i][1] = max(dp[i-1][0], dp[i-1][1])

  print(max(dp[-1][0], dp[-1][1]))
```