You are given an array of integers original of length $n$ and a $2$D integer array bounds of length $n$, where bounds[i] = [u_i, v_i] represents the inclusive range of values copy[i] can take.

An array copy of length $n$ is considered a copy array of original if both of the following conditions are satisfied:

• bounds[i][0] $\leq$ copy[i] $\leq$ bounds[i][1] for every $i$ where $0 \leq i < n$.

• copy[i] - copy[i - 1] is equal to original[i] - original[i - 1] for every $i$ where $1 \leq i < n$.

Return the total number of possible copy arrays.

Constraints:

• $2 \leq n =$ original.length $\leq 10^5$

• $1 \leq$ original[i] $\leq 10^9$

• bounds.length $= n$

• bounds[i].length $= 2$

• $1 \leq$ bounds[i][0] $\leq$ bounds[i][1] $\leq 10^9$

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.