Sum of neighbors

In a square area of size n \times n, the cells are numbered consecutively from $0$ to n^2 - 1, from top to bottom and from left to right in each row.

Nyasyr stands in the cell numbered $k$ in this area and wants to find the sum of the numbers of all neighboring cells. Help Nyasyr with this task.

Note that each cell can have no more than $4$ neighbors directly above, below, to the left, and to the right.

Below is an example with n = 4 and k = 11.

Here Nyasyr stands on the cell with number $11$, and neighboring cells are marked with circles. In this case, there is no neighbor on the right.