Height Map

A height map is a two dimensional matrix of positive integers that describes a polyhedron. A cell holding the value $V$ carries a $1 \times 1 \times V$ rectangular column that rests on one of its $1 \times 1$ faces. All the downward facing $1 \times 1$ faces together make the single bottom face of the solid, and further faces appear on the top and on the sides.

For instance, a $2 \times 2$ matrix whose values are all 2 is a cube of side 2. If one of the values is 1, the solid is that same cube with one corner cut off. The picture below shows both shapes.

Not every polyhedron can be described this way, but many can. Here are some other examples.

Given a height map, count the faces of the solid it describes. Every height is an integer, so the surface of the solid splits into axis parallel unit squares. Two unit squares belong to the same face when they lie on the same plane, point outward in the same direction, and share a side. A face is a maximal set of unit squares linked by that relation. A face with a hole inside it still counts as one face. As the examples show, two different faces on the same plane may share a vertex, a whole side, or part of a side.

The first line contains two integers $R$ and $C$, the number of rows and the number of columns of the height map ($1 \le R, C \le 100$). Each of the next $R$ lines contains $C$ integers. The $j$-th integer on the $i$-th line is the value $V_{i,j}$ in row $i$ and column $j$ ($1 \le V_{i,j} \le 10^9$).

Print one line with the number of faces of the polyhedron described by the height map.