Problem 3: (5 2 points) In a city, there are n streets going from east to west and numbered from south to north (so, the first street is the southmost one). There are also m avenues going from south to north and numbered from east to west (so, the first avenue is the eastmost one). Design an algorithm that takes a list of dangerous crosses and computes the number of paths going always west or north from the corner of the first street and the first avenue to the corner of the n-th street and the m-th avenue such that the path does not go through dangerous crosses. The complexity of the algorithm should be O(mn)