N kings are placed on a chessboard, with at most one king on any square. Following standard rules of movement (one square in any direction), every king must be able to reach some edge of the board without ever occupying a square that was already occupied, and every square must be occupied exactly once by some king at some point. At the start, and after each move, no king may occupy a square that is currently adjacent to another king, horizontally or vertically (diagonally adjacent is OK). The kings may play in any order, and a king may exit the board once it reaches any edge. Kings may start on an edge square. What is the maximum N, what is a starting configuration that allows this maximum, and what is the order of play that allows all kings to exit the board?
Update: An edge square means any of the 28 squares on the perimeter of the board.