// Part 1 about finding and counting Knight's tours//==================================================type Pos = (Int, Int) // a position on a chessboard type Path = List[Pos] // a path...a list of positions//(1a) Complete the function that tests whether the position // is inside the board and not yet element in the path.def is_legal(dim: Int, path: Path)(x: Pos): Boolean = ...//(1b) Complete the function that calculates for a position // all legal onward moves that are not already in the path. // The moves should be ordered in a "clockwise" order.def legal_moves(dim: Int, path: Path, x: Pos): List[Pos] = ...//assert(legal_moves(8, Nil, (2,2)) == // List((3,4), (4,3), (4,1), (3,0), (1,0), (0,1), (0,3), (1,4)))//assert(legal_moves(8, Nil, (7,7)) == List((6,5), (5,6)))//assert(legal_moves(8, List((4,1), (1,0)), (2,2)) == // List((3,4), (4,3), (3,0), (0,1), (0,3), (1,4)))//assert(legal_moves(8, List((6,6)), (7,7)) == List((6,5), (5,6)))//(1c) Complete the two recursive functions below. // They exhaustively search for open tours starting from the // given path. The first function counts all possible open tours, // and the second collects all open tours in a list of paths.def count_tours(dim: Int, path: Path): Int = ...def enum_tours(dim: Int, path: Path): List[Path] = ...