Given a 0-indexed integer array heights, where heights[i] represents the elevation of checkpoint i on a trail, find a local peak and return its index. If the trail contains multiple local peaks, return the index of any one of them.

A local mountain peak is a checkpoint whose height is strictly greater than its immediate neighboring checkpoints.

For an index i, heights[i] is a local mountain peak if:

heights[i] > heights[i - 1] and heights[i] > heights[i + 1]

For boundary indices, the missing outside neighbor is treated as -∞.

You must write an algorithm that runs in O(log n) time.

Example 1:

Input: heights = [1, 3, 5, 4, 2, 6, 7, 4]
Output: 2
Explanation: Both indexes 2 and 6 are valid answers.
At index 2, the height is 5. Since 5 is strictly greater than both neighboring 
heights, 3 and 4, index 2 is a valid local mountain peak: 5 > 3 and 5 > 4
There is another valid peak at index 6, where the height is 7: 7 > 6 and 7 > 4

Example 2:

Input: heights = [2, 4, 6, 8, 10]
Output: 4
Explanation: The array is strictly increasing, so the last checkpoint is 
the local mountain peak. 10 > 8 and 10 > -∞

Example 3:

Input: heights = [3]
Output: 0
Explanation: According to the constraints, if heights.length = 1, index 0 is 
considered a peak. Using the boundary convention, both outside neighbors are 
treated as -∞, so 3 > -∞ on the left and 3 > -∞ on the right.

Constraints

1 <= heights.length <= 1000

−2³¹ <= heights[i] <= 2³¹ − 1

heights[i] != heights[i + 1] for every valid index i, where 0 <= i < heights.length - 1

A valid peak is guaranteed to exist.

If heights.length = 1, index 0 is considered a peak.

An element is always considered to be strictly greater than a neighbor that is outside the array.
- heights[-1] = -∞
- heights[n] = -∞

For boundary checkpoints, only the existing neighbor needs to be considered:
- i = 0: heights[0] > heights[1]
- i = n - 1: heights[n - 1] > heights[n - 2]

54. Find Mountain Peak