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=[[-10**16 for i in range(N)]for j in range(3)]

DP[1][0]=0
DP[2][0]=0
DP[2][1]=0
DP[0][0]=A[0]
DP[1][1]=A[1]
if N>=3:
    DP[2][2]=A[2]

for i in range(2,N):
    DP[0][i]=DP[0][i-2]+A[i]
    DP[1][i]=DP[1][i-2]+A[i]
    DP[2][i]=DP[2][i-2]+A[i]
    if i-3>=0:
        DP[1][i]=max(DP[1][i],DP[0][i-3]+A[i])
        DP[2][i]=max(DP[2][i],DP[1][i-3]+A[i])
    if i-4>=0:
        DP[2][i]=max(DP[2][i],DP[0][i-4]+A[i])

if N%2==0:
    print(max(DP[0][-2],DP[1][-1]))
else:
    print(max(DP[0][-3],DP[1][-2],DP[2][-1]))