You are given an integer array nums of length $3$, where each element represents the length of a side. Determine what kind of triangle these three sides form and return the corresponding string.

Return:

• "equilateral" if all three sides are equal

• "isosceles" if exactly two sides are equal

• "scalene" if all three sides are different

• "none" if the three sides cannot form a valid triangle

A set of side lengths forms a valid triangle if the sum of any two sides is strictly greater than the remaining side.

Note: A triangle is valid only when all three pairwise triangle inequalities hold.

Constraints:

• nums.length == 3

• $1 \leq$ nums[i] $\leq 100$

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.