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.

Input: stones = [0, 1]-List[int]
Output: 1-int
Explanation: The frog jumps from 0 to 1 and back to 0, so the maximum jump length is 1.

Input: stones = [0, 4, 8, 15]-List[int]
Output: 11-int
Explanation: A valid path is 0 → 4 → 8 → 15 → 4 → 0, whose largest jump is from 15 to 4 with length 11.

Input: stones = [0, 2, 3, 10, 12]-List[int]
Output: 9-int
Explanation: A valid path is 0 → 2 → 3 → 10 → 12 → 3 → 0. The largest jump is from 12 to 3 with length 9.

Input: stones = [0, 10, 11, 12, 30, 31]-List[int]
Output: 19-int
Explanation: A valid path is 0 → 10 → 11 → 12 → 30 → 31 → 12 → 10 → 0. The largest jump is from 31 to 12 with length 19.

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