You are given a $0$ indexed integer array nums whose length is a power of $2$.

Apply the following algorithm on nums:

1. If the length of nums is equal to $1$, stop the process and return nums[$0$].

2. Create a new $0$ indexed integer array newNums of length nums.length $/ 2$.

3. For every even index i where $0 \leq$ i $<$ nums.length $/ 2$, assign newNums[i] $= \min($nums[$2 imes$ i], nums[$2 imes$ i $+ 1$]).

4. For every odd index i where $0 \leq$ i $<$ nums.length $/ 2$, assign newNums[i] $= \max($nums[$2 imes$ i], nums[$2 imes$ i $+ 1$]).

5. Replace the array nums with newNums.

6. Repeat the entire process from step $1$.

Return the final remaining value in nums after applying the algorithm.

Constraints:

• $1 \leq$ nums.length $\leq 1024$

• $1 \leq$ nums[i] $\leq 10^9$

• nums.length is a power of $2$.

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.