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,*as=$<.read.split.map(&:to_i)

n = 0
m = 0
as.each.with_index do |a,i|
  if i.even?
    n += a
  else
    m += a
  end
end

if N.even?
  ret = (n<m) ? m : n
  puts ret
  exit 0
end

arr = [
  [2,2,as[0]],
  [1,1,as[1]],
  [2,0,as[0]+as[2]],
]

sums = [0]*(N+2)
i = N-1
while 0 <= i
  sums[i] = as[i] + sums[i+2]
  i -= 1
end
max = sums[2]

as[3..-1].each.with_index(3) do |a,i|
  arr_ = []
  arr.each do |cap,d,sum|
    if d == 0
      arr_ << [cap,d+1,sum]
    elsif d == 1
      arr_ << [cap,d+1,sum]
      arr_ << [cap,0,sum+a]
    elsif d == 2
      arr_ << [cap,d+1,sum]
      if cap == 1
        s = sum + sums[i]
        max = s if max < s
      else
        arr_ << [cap-1,0,sum+a]
      end
    elsif d == 3
      if cap == 2
        s = sum + sums[i]
        max = s if max < s
      end
    end
  end
  arr = arr_
  # p [max,arr]
end

puts max