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
#基本1つ飛ばしだが、パスも使える。
#奇数ならパス2回、偶数ならパス1回。
N = int(input())
A = [int(hoge) for hoge in input().split()]
DP = [[0]*3 for n in range(N)] #DP[n][y] = n桁目までみて、パスをy回使ったときの最大値

DP[0][0] = A[0]

for n in range(1,N):#n桁目までみる。
    #「選ぶ」か「パスを使う」かの2択。
    DP[n][0] = DP[n-2][0] + A[n]
    DP[n][1] = max((DP[n-2][1]+A[n],DP[n-1][0]))
    DP[n][2] = max((DP[n-2][2]+A[n],DP[n-1][1]))
if N%2:
    print(DP[n][2])
else:
    print(DP[n][1])