Suppose $A_1,A_2,\mathrm{...},A_{30}$   are thirty sets each with five elements and  $B_1,B_2,\mathrm{...},B_n$  are $n$   sets each with three elements such that  $\underset{i=1}{\overset{30}{\cup }}{A}_i=\underset{j=1}{\overset{n}{\cup }}{B}_j=S.$  If each element of  $S$  belongs to exactly ten of the  $A_i\text{'}s$ and exactly 9 of the  $B_j\text{'}s$, then the value of  $n$  is