Mountains or Valleys

A mountain is a list with exactly one peak.

• All numbers to the left of the peak are increasing.
• All numbers to the right of the peak are decreasing.
• The peak CANNOT be on the boundary.

A valley is a list with exactly one trough.

• All numbers to the left of the trough are decreasing.
• All numbers to the right of the trough are increasing.
• The trough CANNOT be on the boundary.

Some examples of mountains and valleys:

Mountain A:  [1, 3, 5, 4, 3, 2]   # 5 is the peak
Mountain B:  [-1, 0, -1]   # 0 is the peak
Mountain B:  [-1, -1, 0, -1, -1]   # 0 is the peak (plateau on both sides is okay)

Valley A: [10, 9, 8, 7, 2, 3, 4, 5]   # 2 is the trough
Valley B: [350, 100, 200, 400, 700]  # 100 is the trough

Neither mountains nor valleys:

Landscape A: [1, 2, 3, 2, 4, 1]  # 2 peaks (3, 4), not 1
Landscape B: [5, 4, 3, 2, 1]  # Peak cannot be a boundary element
Landscape B: [0, -1, -1, 0, -1, -1]  # 2 peaks (0)

Based on the rules above, write a function that takes in a list and returns either "mountain", "valley", or "neither".

Examples

landscape_type([3, 4, 5, 4, 3]) ➞ "mountain"

landscape_type([9, 7, 3, 1, 2, 4]) ➞ "valley"

landscape_type([9, 8, 9]) ➞ "valley"

landscape_type([9, 8, 9, 8]) ➞ "neither"

Notes

• A peak is not exactly the same as the max of a list. The max is a unique number, but a list may have multiple peaks. However, if there exists only one peak in a list, then it is true that the peak = max.
• See comments for a hint.