Statement

The mountains around Pisa are a well known hiking destination, with a peculiar terrain shape. In particular, you are interested in a rectangular area of N × M square meters, subdivided into N × M square cells, each with an area of a square meter. Those cells are uniquely identified by their distance from the top and the left sides of the rectangle, with cell (i,j) being at a distance of i meters from the top of the map and j meters from the left side of the rectangle. Each cell (i, j) has an altitude of H_i,j meters, described by two arrays of integers A and B: H_i,j = A_i* B_j. A peak is a cell that has a strictly higher altitude than all the cells that share a side with it. How many peaks are there?