Score : $600$ points
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 $x$.
Input is given from Standard Input in the following format:
$N$ $A_1$ $...$ $A_N$
Print the maximum possible sum of the chosen elements.
6 1 2 3 4 5 6
12
Choosing $2$, $4$, and $6$ makes the sum $12$, which is the maximum possible value.
5 -1000 -100 -10 0 10
0
Choosing $-10$ and $10$ makes the sum $0$, which is the maximum possible value.
10 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000
5000000000
Watch out for overflow.
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
295