Problem:
Score : 600 points

Problem Statement

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.

Sample Input 1

6
1 2 3 4 5 6

Sample Output 1

12

Choosing 2, 4, and 6 makes the sum 12, which is the maximum possible value.

Sample Input 2

5
-1000 -100 -10 0 10

Sample Output 2

0

Choosing -10 and 10 makes the sum 0, which is the maximum possible value.

Sample Input 3

10
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

5000000000

Watch out for overflow.

Sample Input 4

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

Sample Output 4

295

Solution in Python (3.8.2) (judge verdict: Accepted)

N = int(input())
A = list(map(int, input().split()))

ans = sum(A[1::2])
dA = []
for a1, a2 in zip(A, A[1:]):
    dA.append(a1 - a2)

max_cum_l = 0
cum_l = 0
L = [0]
for idx_l in range(0, N - 1, 2):
    cum_l += dA[idx_l]
    max_cum_l = max(max_cum_l, cum_l)
    L.append(max_cum_l)
max_cum_r = 0
cum_r = 0
R = [0]
for idx_r in range(N - 2, -1, -2):
    cum_r -= dA[idx_r]
    max_cum_r = max(max_cum_r, cum_r)
    R.append(max_cum_r)
R.reverse()
if N%2:
    ma = -(1<<60)
    for l, r in zip(L, R):
        if ma < l+r:
            ma = l+r
    print(ans + ma)
else:
    print(max(L) + ans)