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: Wrong Answer)

n = gets.to_i
a = gets.chomp.split.map(&:to_i)

if n % 2 == 0
  ev = a.map.with_index {|x, i| if i % 2 != 0 then x else 0 end }.inject(:+)
  puts [ev, a.inject(:+) - ev].max
else
  sq = a[0..1].inject(:+)
  sqi = 0
  1.step(a.size - 2) do |i|
    if sq < a[i..(i + 1)].inject(:+)
      sq = a[i..(i + 1)].inject(:+)
      sqi = i
    end
  end
  res = a.map.with_index{|x, j|
    if j < sqi && (sqi - j).abs % 2 != 0
      x
    elsif j > sqi + 1 && j - sqi % 2 == 0
      x
    else
      0
    end
  }.inject(:+)
  puts res
end