A child has an empty box that measures 4 inches by 6 inches by 3 inches. View the figure. A right rectangular prism is shown. The length is labeled l equals six inches. The width is labeled w equals four inches. The height is labeled h equals three inches. The diagonal of the base is labeled s. The interior diagonal is labeled r.

What is the length of the longest pencil that will fit into the box, given that the length of the pencil must be a whole number of inches? Do not round until your final answer.

Enter the correct answer in the box.