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)

def calc(a, memo, i, c, n)
    if i + c >= n
        0
    elsif memo[c][i].nil?
        memo[c][i] = calc(a, memo, i + 2, c, n) + a[i]
        if c != 0 
            x = calc(a, memo, i + 1, c - 1, n)
            memo[c][i] = x if memo[c][i] < x
        end
        memo[c][i]
    else
        memo[c][i]
    end
end

n = gets.to_i
a = gets.split.map(&:to_i)
memo = Array.new(3) {Array.new(n)}

puts n.even? ? calc(a, memo, 0, 1, n) : calc(a, memo, 0, 2, n)