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)

# Your code here!
n=gets.to_i
array=gets.split.map(&:to_i)
sum=0
plus1array=Array.new(n/2,0)
plus2array=Array.new(n/2,0)

(n/2).times{|i|
    sum+=array[i*2]
}

(n/2).times{|i|
    plus1array[i]=array[i*2+1]-array[i*2]
}

if n%2==0
    
    
   plus1array=plus1array.reverse
   ruiseki=0
   max=0
    (n/2).times{|i|
        ruiseki+=plus1array[i]
        if ruiseki>max
            max=ruiseki
        end
    }
    
    puts sum+max
    
else
    
    (n/2).times{|i|
        plus2array[i]=array[i*2+2]-array[i*2]
    }
    
    kokomaxarray=Array.new(n/2,0)
    kokomax=0
    kokonow=0
    (n/2).times{|i|
        kokonow+=plus1array[i]
        if kokonow>kokomax
            kokomax=kokonow
        end
        kokomaxarray[i]=kokomax
    }
    
    
    max=plus2array.inject(:+)
    now=plus2array.inject(:+)
    sitawa=plus2array.inject(:+)
    (n/2).times{|i|
        sitawa-=plus2array[i]
        now=sitawa+kokomaxarray[i]
        
        if now>max
            max=now
        end
    }
    
    puts sum+max
    
end