A 3 \times 3 square is partitioned into 9 unit squares. Each unit square is painted either white or black with each color being equally likely, chosen independently and at random. The square is then rotated 90^{\circ} clockwise about its center, and every white square in a position formerly occupied by a black square is painted black. The colors of all other squares are left unchanged. What is the probability that the grid is now entirely black?

**Answer Choices**

A. \dfrac{49}{512}

B. \dfrac{7}{64}

C. \dfrac{121}{1024}

D. \dfrac{81}{512}

E. \dfrac{9}{32}