2219. Trees in a Wood

The saying “You can’t see the wood for the trees” is not only a cliche, but is also incorrect. The real problem is that you can’t see the trees for the wood. If you stand in the middle of a wood, the trees tend to obscure each other and the number of distinct trees you can actually see is quite small. This is especially true if the trees are planted in rows and columns, because they tend to line up. The purpose of this problem is to find how many distinct trees one can see if one were standing on the position of a tree in the middle of the wood.

For a mathematically more precise description we assume that you are situated at the origin of a coordinate system in the plane.Trees are planted at all positions {x,y}∈ Z×Z \ {(0,0)},with |x| <=a and|y|<=b.