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 PyPy3 (7.3.0) (judge verdict: Time Limit Exceeded)

import sys
sys.setrecursionlimit(10 ** 9)

n = int(input())
a = list(map(int,input().split()))

mx = 0
def dfs(i,c,s,p,q):
  global mx
  #print(i,c,s)
  if c == n//2:
    mx = max(s,mx)
    return
  if i > n-1:
    return
  dfs(i+2,c+1,s+a[i],p,q)
  if p < 2:
    dfs(i+3,c+1,s+a[i],p+1,q)
  if q < 1:
    dfs(i+4,c+1,s+a[i],p,q+1)
  
dfs(0,0,0,0,0)
dfs(1,0,0,1,1)
dfs(2,0,0,2,1)

print(mx)