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()))
s = [0]*N
for i in range(N):
    s[i] = s[i-2]+A[i]

dp = [0]*N
dp[1] = max(A[0],A[1])
if N>=3:
    dp[2] = max(A[0],A[1],A[2])
for n in range(3,N):
    if n%2==1:
        dp[n] = max(A[n]+dp[n-2],s[n-1])
    else:
        dp[n] = max(A[n]+dp[n-2],A[n-1]+dp[n-3],s[n-2])

print(dp[-1])