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 = [
  [2,0,as[0]],
  [1,1,as[1]],
  [2,2,as[0]+as[2]],
  # [0,2,as[2]]
]
cap0even = as[2]
cap0odd = -10**9
max = [as[0],as[1],as[2],as[0]+as[2]].max

as[3..-1].each.with_index(3) do |a,i|
  arr_ = []
  arr.each {|cap,pos,sum|
    if i-pos != 1
      if i-pos-2 == cap
        if i.even?
          cap0even = (cap0even < sum) ? sum : cap0even
        else
          cap0odd = (cap0odd < sum) ? sum : cap0odd
        end
      elsif i-pos-2 < cap
        arr_ << [cap-(i-pos-2),i,sum+a]
      end
    end
    if i-pos-2 <= cap
      arr_ << [cap,pos,sum]
    end
  }
  if i.even?
    cap0even += a
  else
    cap0odd += a
  end
  arr = arr_
end

max = [max,cap0even,cap0odd].max
puts max