Where are all 8 red coins on super Mario DS?

There is one red coin behind the killer piano. Move slowly so that you don't wake it up. If you do wake it up, move as fast as possible. Go through the door to the library. There is a red coin on top of each bookshelf. There is a red coin beside the boo on the last door on the right. Climb up the stairs, and go in the first door on the left. Jump over the hole, and grab the coin. Go out, enter the first door on your right, and you will face a giant eye. Defeat him, and move on to the room with the tombstones in it. One red coin is under the left middle tombstone. The other is under the closest tombstone to the right. Enter the final door on the right, and avoid the two books that come from the bookcase. Go around the bookcase, avoiding the center of the floor, because it tilts. Collect the red coin, and go back out the way you came. Go to the left of the stairs, and get the star.