Let T_{1} be a triangle with sides 2011,2012 , and 2013. For n \geq 1, if T_{n}=\triangle A B C and D, E, and F are the points of tangency of the incircle of \triangle A B C to the sides A B, B C, and A C, respectively, then T_{n+1} is a triangle with side lengths A D, B E, and C F, if it exists. What is the perimeter of the last triangle in the sequence \left(T_{n}\right) ?
Answer Choices
A. \dfrac{1509}{8}
B. \dfrac{1509}{32}
C. \dfrac{1509}{64}
D. \dfrac{1509}{128}
E. \dfrac{1509}{256}