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,*as=$<.read.split.map &:to_i
if n.odd?
  t=0
  s=[]
  (n/2).downto(0){|i|
     s[i]=t+=as[i*2]
  }
  y=[as[n-2],as[n-1]].max
  x=[as[n-3],y].max
  b=n-3
  while 0<=b-=2 
    y=[as[b+1]+y,s[b/2+1]].max
    x=[as[b]+x,y].max
  end
  puts x
else
  t=0
  s=[]
  (n/2-1).downto(0){|i|
     s[i]=t+=as[i*2+1]
  }
  x=[as[n-2],as[n-1]].max
  b=n-2
  while 0<=b-=2 
    x=[as[b]+x,s[b/2]].max
  end
  puts x
end