You are given an integer array nums of length n.

A subarray nums[l...r] is called trionic if there exist two indices p and q with $0 \leq$ l $<$ p $<$ q $<$ r $<$ n such that:

• nums[i] $<$ nums[i + $1$] for all l $\leq$ i $<$ p

• nums[i] $>$ nums[i + $1$] for all p $\leq$ i $<$ q

• nums[i] $<$ nums[i + $1$] for all q $\leq$ i $<$ r

Return the maximum possible sum of any trionic subarray in nums.

Constraints:

• $4 \leq n =$ nums.length $\leq 10^5$

• $-10^9 \leq$ nums[i] $\leq 10^9$

• It is guaranteed that at least one trionic subarray exists.

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.