You are given a $0$ indexed integer array stones sorted in strictly increasing order, representing the positions of stones in a river.

A frog starts at the first stone, travels to the last stone, and then returns to the first stone. The frog can visit each intermediate stone at most once across the entire round trip.

The length of a jump between stones[i] and stones[j] is equal to $|$stones[i] $-$ stones[j]$|$. The cost of a path is defined as the maximum jump length taken during the journey.

Return the minimum possible cost of a valid round trip path.

Constraints:

• $2 \leq$ stones.length $\leq 10^5$

• $0 \leq$ stones[i] $\leq 10^9$

• stones[0] $= 0$

• stones is sorted in a strictly increasing order.

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.