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: Wrong Answer)

MOD = 10 ** 9 + 7
INF = 10 ** 10
import sys
input = sys.stdin.readline
sys.setrecursionlimit(100000000)
dy = (-1,0,1,0)
dx = (0,1,0,-1)

def main():
    n = int(input())
    a = list(map(int,input().split()))
    if n%2 == 0:
        ans1 = 0
        ans2 = 0
        for i in range(n):
            if i%2 == 0:
                ans1 += a[i]
            else:
                ans2 += a[i]
        ans = max(ans1,ans2)

        cuml = [0] * (n + 1)
        cumr = [0] * (n + 1)

        for i in range(n):
            if i == 0:
                cuml[i + 1] = a[i]
            else:
                cuml[i + 1] = cuml[i - 1] + a[i]
        
        for i in range(n - 1,-1,-1):
            if i == n - 1:
                cumr[i] = a[i]
            else:
                cumr[i] = cumr[i + 2] + a[i]
        
        for i in range(1,n - 2,2):
                ans = max(ans,cuml[i] + cumr[i + 2])
    
    else:
        cuml = [0] * (n + 1)
        cumr = [0] * (n + 1)
        cumr2 = [0] * (n + 1)

        for i in range(n):
            if i == 0:
                cuml[i + 1] = a[i]
            else:
                cuml[i + 1] = cuml[i - 1] + a[i]
        
        for i in range(n - 1,-1,-1):
            if i == n - 1:
                cumr[i] = a[i]
                cumr2[i] = a[i]
            else:
                cumr[i] = cumr[i + 2] + a[i]
                if i%2 == 1:
                    if i == n - 2:
                        continue
                    if i == n - 4:
                        cumr2[i] = cumr2[i + 3] + a[i]
                    else:
                        cumr2[i] = max(cumr2[i + 2],cumr[i + 3]) + a[i]

        cumr.append(0)
        ans = -INF
        for i in range(n):
            ans = max(ans,cuml[i] + cumr[i + 2])
            if i <= n - 6 and i%2 == 1:
                ans = max(ans,cuml[i] + cumr2[i + 2])
            if i <= n - 4 and i%2 == 1:
                ans = max(ans,cuml[i] + cumr[i + 3])
    
    print(ans)

if __name__ =='__main__':
    main()