The Mid-Point Squares

The perimeter of a square is $2016\text{ cm}$ . The midpoints of its sides are joined to form a new square. Again,the midpoints of the sides of this new square are joined to form another square. This process is continued till infinity.

Let $\mathbf{S}$ denote the perimeter of all such squares formed(including the original square). Evaluate $\lfloor\mathbf{S}\rfloor$ .