Seven square prisms, each with a height of $1$ unit, and whose base areas are $1,4,9,16,25,36,$ and $49$ square units, are stacked vertically to form a tower in which the base areas of the prisms decrease from bottom to top. Except for the bottom prism, the bottom face of each prism lies completely on top of the prism below it. What is the total surface area of the tower (including the bottom) in square units?