Let the boys be A, B,~C and D and their gifts be 1, 2, 3 and 4. List down all possible arrangements:  (A2, B1, C4, D3), (A2, B3, C4, D1), (A2, B4, C1, D3), (A3, B1, C4, D2), (A3, B4, C2, D1), (A3, B4, C1, D2), (A4, B1, C2, D3), (A4, B3, C2, D1), (A4, B3, C1, D2)  There are \textbf{9} possible arrangements. 
Four boys each prepared $1$ gift for a party. How many ways can these $4$ gifts be \textsubscript{} distributed among the $4$ kids so that no one receives his own gift? 
a: $$12$$ 
b: $$9$$ 
c: $$6$$ 
d: $$1$$ 
e: None of the above 