Once upon a time, there lived a migrant barbarian tribe. Every time it settled down, a tent was set for the chief of the tribe. First, an area was selected and divided into NxM squares with side lengths of 1 unit. Then, they chose a site for the tent in such a way that every vertex of its base coincided with some vertex of one of the squares. According to an ancient tradition, the base had to be a rhomb. For example, there are all 6 different possible sites for the tent in a 2x2 area:
An example of a tent in a 4x2 area:
For a given N and M, return the number of different possible sites for the chief's tent. Two sites are different if there is at least one vertex which belongs to one site but not the other.