There are $6$ tape drives for a computer system, with n processes vaying for them. There may be $3$ tape drives required for every operation. The full value of n for which a deadlock$-$free device is guaranteed to be $\_\_\_.11$a$\mathrm{.}1$b$\mathrm{.}4$c$\mathrm{.}2$d$\mathrm{.}3$