def add_pair(x: Pos)(y: Pos): Pos = 

def is_legal(dim: Int, path: List[Pos])(x: Pos): Boolean = 

  0 <= x._1 && 0 <= x._2 && x._1 < dim && x._2 < dim && !path.contains(x)

def moves(x: Pos): List[Pos] = {

  List(( 1,  2),( 2,  1),( 2, -1),( 1, -2),

       (-1, -2),(-2, -1),(-2,  1),(-1,  2)).map(add_pair(x))

}

def legal_moves(dim: Int, path: List[Pos], x: Pos): List[Pos] = {

  moves(x).filter(is_legal(dim, path))

/*

def tour(dim: Int, path: List[Pos]): List[List[Pos]] = {

  if (path.length ==  dim * dim) // && moves(n)(path.head).contains(path.last)) 

    List(path)

    (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).flatten

}

*/

def tour(dim: Int, path: List[Pos]): Int = {

  if (path.length == dim * dim) 1

  else 

    (for (x <- legal_moves(dim, path, path.head)) yield tour(dim, x::path)).sum

//println(tour(n, List((0, 0))))

for (d <- 1 to 6) {

  println(s"${d} x ${d} " + (for (i <- 0 until d; j <- 0 until d) yield tour(d, List((i, j)))).sum)

}