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: Time Limit Exceeded)

inf = float('inf')
N = int(input())
A = list(map(int, input().split()))
dp0=[[-inf]*(2+N//2) for _ in range(N+1)]
dp1=[[-inf]*(2+N//2) for _ in range(N+1)]
dp0[0][0] = 0

for i, x in enumerate(A):
    j = i//2
    for n in (j, j + 1):
        dp0[i+1][n] = max(dp0[i][n], dp1[i][n])
        dp1[i+1][n] = dp0[i][n - 1] + x
    #print(dp0)
    #print(dp1)

print(max(dp0[N][N//2], dp1[N][N//2]))