You are given a $0$-indexed integer array nums of size $n$.

You need to apply $n - 1$ operations sequentially to the array. In the $i^{th}$ operation, where $0 \leq i < n - 1$:

• If nums[i] == nums[i + 1], multiply nums[i] by $2$ and set nums[i + 1] to $0$.

• Otherwise, skip this operation.

After performing all operations, shift all $0$’s to the end of the array while maintaining the relative order of the non-zero elements.

Return the modified array.

Constraints:

• $2 \leq$ nums.length $\leq 2000$

• $0 \leq$ nums[i] $\leq 1000$

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.