The numbers 1,2, \cdots , 9 are randomly placed into the 9 squares of a 3 \times 3 grid. Each square gets one number, and each of the numbers is used once. What is the probability that the sum of the numbers in each row and column is odd.

**Answer Choices**

A. $\dfrac{1}{21}$

B. \$\dfrac{1}{14}\$
C. $\dfrac{5}{63}$

D. \$\dfrac{2}{21}\$
E. $\dfrac{1}{7}$