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 Python (3.8.2) (judge verdict: Accepted)

n=int(input())
if n%2:
  a=list(map(int,input().split()))
  s=[[a[0],0,0],[0,a[1],0],[a[0]+a[2],0,a[2]]]+[[0,0,0]for i in range(3,n)]
  for i in range(3,n):
    if i%2:
      s[i][1]=max(s[i-2][1],s[i-3][0])+a[i]
    else:
      s[i][0]=s[i-2][0]+a[i]
      s[i][2]=max([s[i-2][2],s[i-3][1],s[i-4][0]])+a[i]
  print(max([s[-1][2],s[-2][1],s[-3][0]]))
else:
  a=list(map(int,input().split()))
  s=[a[0],a[1]]+[0 for i in range(2,n)]
  for i in range(2,n):
    if i%2:
      s[i]=max([s[i-2],s[i-3]])+a[i]
    else:
      s[i]=s[i-2]+a[i]
  print(max(s[-2:]))