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 PyPy3 (7.3.0) (judge verdict: Accepted)

# F - Select Half

n = int(input())
a = list(map(int, input().split()))
assert len(a) == n

l = [0] * n # a[0]〜a[i]からfloor((i+1)/2)個選ぶときの最大値
u = [0] * n # a[0]〜a[i]からceil((i+1)/2)個選ぶときの最大値

l[0] = 0
u[0] = a[0]
u[1] = max(a[:2])
l[1] = u[1]

# 0 1 2 3 4 5 6 7 8 9 10 i
# . . . . . . . . . . .
# 1 1 2 2 3 3 4 4 5 5 6  u[i]
# 0   1   2   3   4   5  l[i]

for i in range(2, n):
    l[i] = max(u[i - 1], l[i - 2] + a[i])
    u[i] = u[i - 2] + a[i]
    if i % 2 != 0:
        u[i] = max(u[i - 1], u[i])

print(l[-1])