You are given an integer array nums.

You start by picking a starting position curr such that nums[curr] = 0 and choosing a direction: left or right.

The process then proceeds as follows:

• If curr goes out of bounds, meaning curr $< 0$ or curr $\geq$ nums.length, the process finishes.

• If nums[curr] = 0, continue moving in the current direction by one index (decrement curr if moving left, or increment curr if moving right).

• If nums[curr] > 0, decrease nums[curr] by $1$, reverse the current direction, and take one step in the new direction.

A choice of starting index curr and initial direction is considered valid if every element in nums becomes $0$ when the process finishes.

Return the total number of valid selections.

Constraints:

• $1 \leq$ nums.length $\leq 100$

• $0 \leq$ nums[i] $\leq 100$

• There is at least one element i where nums[i] == 0.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.