Subtask 1

This subtask was meant for contestants to try and solve $1\le N\le 8$ by hand.

Subtask 2

There are numerous ways to solve this problem. The intended solution will be described here. Each index $i$ has $i$ subarrays ending there, and we will make those subarrays all nonnegative or all negative. It is always possible to partition the integers $1,2,...,n$ into two sets with a difference in sum of at most $1$. Let $i$ represent $i$ nonnegative sum subarrays ending at index $i$, and $-i$ represent $i$ negative sum subarrays ending at index $i$. For even $N$, we use the pattern $1,-2,-3,4$ with signs repeating$\mathrm{mod}4$ which has a difference of at most $1$ at each even index. For odd $N$, we use the pattern $1,2,-3,-4$ with signs repeating$\mathrm{mod}4$ which has a difference of at most $1$ at each odd index. The implementation to create this array is left as an exercise to a reader.