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: Runtime Error)

n = int(input())
ai = [int(i) for i in input().split()]

is_odd = True

if n % 2 == 0:
    is_odd = False

if is_odd == True:
    dp = [[0 for i in range(3)] for j in range(n)]
else:
    dp = [[0 for i in range(2)] for j in range(n)]

if n == 3:
    print(max(ai[0],ai[2],ai[1]))
    print(ai[n+3])
    exit()
elif n == 2:
    print(max(ai[0],ai[1]))
    exit()
    

if is_odd == True:
    for i in range(n):
        dp[i][0] = dp[i-2][0]+ai[i]
        dp[i][1] = max(dp[i-2][1]+ai[i],dp[i-3][0]+ai[i])
        dp[i][2] = max(dp[i-4][0]+ai[i],dp[i-3][1]+ai[i],dp[i-2][2]+ai[i])
    print(max(dp[n-1][0],dp[n-1][1],dp[n-1][2]))
else:
    for i in range(n):
        dp[i][0] = dp[i-2][0]+ai[i]
        dp[i][1] = max(dp[i-2][1]+ai[i],dp[i-3][0]+ai[i])
    print(max(dp[n-1][0],dp[n-1][1]))