It's a mountainous region so there are height differences. Going north and then west might take you to a steeper part of the mountain and then when going south the height where you are must be lower than at your starting position. This is because the rate of change for your coordinates is different depending on your location. Your position probably can be thought to be a function f(x, y, z) and the rate of change as the partial derivative of f depending on which directions you examine.

My scala code passes all the tests expect when n=100000 since answer is too large to be displayed as an integer. Can someone explain how you're supposed to return an integer that is too large to be returned?

The description asks to return false when s is empty but in the tests "" is the required return value