Statement

You are given an integer N. You also have an empty N × N grid of cells, on top of which you can add tetris pieces in the following way: (1) Select 4 cells from the grid which correspond to one of the following 8 shapes: (2) If all 4 selected cells are empty, then a new tetris piece is placed on top of them. Any grid obtained through these operations starting from an empty grid is called a tetris tiling. Find any N × N tetris tiling which uses the maximum possible number of pieces.