Neighbors

Consider a rectangle on the Cartesian plane with vertices at $(0,0)$ and $(w,h)$, where $w$ and $h$ are positive integers. Within this rectangle, there are $N$ mountain peaks located at grid points, which are points with integer coordinates. Each person wants to build a house, but the following rules apply:

• Only one house can be built at each grid point.

• Houses cannot be built on mountain peaks.

Thus, there are (w+1)\times(h+1)-N possible locations for houses. Some locations are more desirable than others. A grid point $(x,y)$ is said to have a northern neighbor if there is a peak at (x, y+d), where $d$ is a positive integer. Similarly, southern, eastern, and western neighbors are defined. Therefore, each grid point that is not a peak can have between $0$ and $4$ neighbors. The more neighbors a location has, the more desirable it is. Your task is to count how many grid points (excluding peaks) have exactly $0$, $1$, $2$, $3$, or $4$ neighbors.

Write a program that:

• Reads the terrain description from standard input.

• Calculates the number of grid points with exactly $0$, $1$, $2$, $3$, and $4$ neighbors.

• Outputs the result to standard output.