Let (a, b, c, d) be an ordered quadruple of not necessarily distinct integers, each one of them in the set \{0,1,2,3\}. For how many such quadruples is it true that a \cdot d-b \cdot c is odd? (For example, (0,3,1,1) is one such quadruple, because 0 \cdot 1-3 \cdot 1=-3 is odd.)
Answer Choices
A. 48
B. 64
C. 96
D. 128
E. 192