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: Wrong Answer)

k=int(input())
l=list(map(int,input().split()))
odd=0
even=0
ct=0
c=0
le=[]
lo=[]
odd_mn=-1000000001
odd_mn1=-1000000001
even_mn=-1000000001
even_mn=-1000000001
for i in range(k):
  if i%2==0:
    if l[i]>=0:
      c+=1
      even+=l[i]
    if l[i]>even_mn and l[i]<0:
      even_mn=l[i]
      ind=i
    le.append(l[i])
  else:
    if l[i]>=0:
      odd+=l[i]
      ct+=1
    if l[i]>odd_mn and l[i]<0:
      odd_mn=l[i]
      ino=i
    lo.append(l[i])
if c==1:
  even+=even_mn
if ct==1:
  odd+=odd_mn
if c==0:
  even+=even_mn
  even_mn=-1000000001
  for i in range(len(le)):
    if l[i]>even_mn and ind!=i//2:
      even_mn=l[i]
  even+=even_mn
if ct==0:
  odd+=odd_mn
  odd_mn=-1000000001
  for i in range(len(lo)):
    if l[i]>odd_mn and ino!=(i//2+1):
      odd_mn=l[i]
  odd+=odd_mn

if odd>even:
  print(odd)
else:
  print(even)