//type Pos = (Int, Int)    // a position on a chessboard 
//type Path = List[Pos]    // a path...a list of positions

def count_all_tours_urban(dim: Int) = {
  for (i <- (0 until dim).toList; 
       j <- (0 until dim).toList) yield count_tours(dim, List((i, j)))
}


assert(count_all_tours_urban(1) == List(1))
assert(count_all_tours_urban(2) == List(0, 0, 0, 0))
assert(count_all_tours_urban(3) == List(0, 0, 0, 0, 0, 0, 0, 0, 0))
assert(count_all_tours_urban(4) == List(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0))
assert(count_all_tours_urban(5) == List(304, 0, 56, 0, 304, 0, 56, 0, 56, 0, 56, 0, 64, 0, 56, 0, 56, 0, 56, 0, 304, 0, 56, 0, 304))