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()))
if n%2 == 0:
    dmax = 0
    ans = sum(A[::2])
    d = [0]*(n//2 + 1)
    for i in range(n//2):
        d[i+1] = d[i] + A[-2*i-1] - A[-2*i-2]
        dmax = max(dmax, d[i+1])
    print(ans + dmax)
else:
    d1 = [0]*(n//2 + 1)
    d1max = [0]*(n//2 + 1)
    d2 = [0]*(n//2 + 1)
    d2max = 0
    ans = sum(A[:-2:2])
    for i in range(n//2):
      d1[i+1] = d1[i] + A[-2*i-1] - A[-2*i-2]
      d1max[i+1] = max(d1max[i], d1[i+1])
      d2[i+1] = d2[i] + A[-2*i-2] - A[-2*i-3]
      d2max = max(d2max, d2[i+1] + d1max[i+1])
    print(ans + d2max)
