You are a white rook in the land of Chessboardia. The evil black queen has decided to pass a bill where white pieces are not allowed to transit over black spaces, which means you can't pass over, or land in any black spaces. As a rook, you can only move to any square in the same row or column you are at, so that you can move horizontally, vertically, but not diagonally.

If you wish to move again, the queen demands that you pay her in "checks", the local currency of Chessboardia. For every black square that you wish to transit, you must pay 20 checks. You get a permit that allows you to transit one black square of your choice as many times as you wish. You want to be able to visit at least every white space on the board, no matter the number of moves. Naturally, you also want to give the queen the lowest amount of checks possible. Assuming Chessboardia is a standard 8x8 chess board, what is the minimum number of black spaces you must pay for so that you can visit every white square on the board as a rook?

As a general problem, how many black squares must you pay for in the case of an nxn chessboard?