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)




def resolve():
    N = int(input())
    A= list(map(int,input().split()))
    if N % 2 ==0:
        x1 =sum(A[::2])
        x2 =sum(A[1::2])
        print(max(x1,x2))
        return

    inf = -float('inf')
    table = [dict() for i in range(N)]

    table[0][0] = [0,inf]

    table[0][1] =[inf,A[0]]
    print(table[0])
    for i in range(1,N):
        v=A[i]
        i1 = (i-1) // 2
        i2 = (i+1)//2
        print(i1,i2)
        if i % 2 ==1:
            i1 = (i-1) // 2
            i2 = (i+1)//2
            
            table[i][i1] = max(table[i-1][i1])
            table[i][i2] = [max(table[i-1][i2]),table[i-1][i1][0]+v]

        else:
            
            i1 = i // 2
            i0 = i1 - 1
            i2 = (i+2)//2
            
            table[i][i1] = [max(table[i-1][i1]),table[i-1][i0]+v]
            table[i][i2] = [inf,table[i-1][i1][0]+v]


    print(max(table[-1][N//2]))





if __name__ == "__main__":
    resolve()
    #unittest.main()