You are given a $0$ indexed integer array nums.

A triplet of indices (i, j, k) is called a mountain triplet if:

• i $<$ j $<$ k

• nums[i] $<$ nums[j] and nums[k] $<$ nums[j]

Return the minimum possible sum of a mountain triplet in nums. If no mountain triplet exists, return $-1$.

Constraints:

• $3 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^8$

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.