子瓷砖

Place an integer between 1 and 17 into some of the empty cells in the grid. When completed, the grid should have one 1, two 2’s, etc., up to seventeen 17’s. Furthermore, for all: N larger than 1, the squares marked N must form a connected N-omino whose shape “contains” the (N −1)-omino determined by the (N −1)’s. (Reflections and rotations are allowed. Some of the cells have already been labeled.

The answer to this puzzle is the product of the areas of the empty regions in the completed grid.