You are given a $0$ indexed integer array nums of length n and an integer k.

You are allowed to choose at most one element in nums and replace its value with k. Alternatively, you may choose to leave the array unchanged.

A pivot index pivot defines a valid partition if $1 \leq$ pivot $< n$ and the sum of the prefix subarray nums from index $0$ to pivot $- 1$ is equal to the sum of the suffix subarray nums from index pivot to n $- 1$.

Return the maximum number of valid partitions you can obtain after modifying at most one element.

Constraints:

• n $==$ nums.length

• $2 \leq$ n $\leq 10^5$

• $-10^5 \leq$ k, nums[i] $\leq 10^5$

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.