magnetic chessboard magnets

I am making a magnetic chessboard (the kind where you have magnets inside individual squares and the pieces, eventually maybe just steel pieces in the board for cost efficiency) and have been trying to figure out what magnets to use. The pieces will be made of pinewood shafts with the diameter of 2cm and height of 3, 4 and 5 cm (basically pretty light) and the space between the magnets in the pieces and magnets (or steel pieces) in the board should be about 3-4mm. I can't find anything on the internet about what magnets are suitable for similar applications and how strong the magnets should be. I'm hoping someone has experience they're willing to share. Thanks in advance to anyone who responds.