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 such triplet exists, return $-1$.

Constraints:

• $3 \leq$ nums.length $\leq 50$

• $1 \leq$ nums[i] $\leq 50$

Input: nums = [2, 5, 3]-List[int]
Output: 10-int
Explanation: The triplet with values 2, 5, and 3 satisfies the mountain conditions, and its sum is 10.

Input: nums = [4, 4, 4]-List[int]
Output: -1-int
Explanation: No mountain triplet exists because no element is strictly greater than both a preceding and a following element.

Input: nums = [7, 1, 5, 2, 6, 4]-List[int]
Output: 8-int
Explanation: The triplet with values 1, 5, and 2 is a mountain triplet with sum 8, which is the minimum possible sum.

Input: nums = [12, 3, 9, 8, 11, 2, 10]-List[int]
Output: 13-int
Explanation: The triplet with values 3, 8, and 2 satisfies the mountain conditions and has sum 13, the minimum possible sum.

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.