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 Ruby (2.7.1) (judge verdict: Accepted)

N = gets.to_i
As = gets.split.map(&:to_i)

mx = ->(a, b){a > b ? a : b}
es, os = [0], [0]
As.each_with_index do |a, i|
  if i.even?
    es << es.last + a
    os << os.last
  else
    es << es.last
    os << os.last + a
  end
end
esl, osl = es.last, os.last
if N.even?
  puts osl + 0.step(N, 2).map{|i| -os[i] + es[i]}.max
else
  x, ans = 0, es[-2]
  1.step(N, 2) do |i|
    ans = mx[ans, esl - es[i] + os[i] + x]
    x = mx[x, es[i + 1] - os[i +1]] if i < N
  end
  puts ans
end