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)

s = [0]*(N+2)
(N-1).downto(0) do |i|
  s[i] = as[i] + s[i+2]
end

if N.even?
  puts (s[0]<s[1]) ? s[1] : s[0]
  exit 0
end

AS = as
S = s
def f(cap,sum,i)
  if cap == 0 && i < N
    return sum + S[i]
  elsif N <= i
    return -10**9-1
  end

  sum += AS[i]
  [
    f(cap,sum,i+2),
    f(cap-1,sum,i+3),
    f(cap-2,sum,i+4),
  ].max
end

ret = [
  f(2,0,0),
  f(1,0,1),
  f(0,0,2)
].max

puts ret