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=[0]+list(map(int,input().split()))

dp=[[0]*(N+1) for i in range(3)]

dp[0][1]=-float("inf")
dp[2][1]=A[1]
dp[0][2]=0
dp[1][2]=max(A[1],A[2])
dp[2][2]=-float("inf")

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

print(dp[1][N])