Suppose ${\mathrm{A}}_1, {\mathrm{A}}_2----, {\mathrm{A}}_{30}$ are thirty sets each with five elements and ${\mathrm{B}}_1, {\mathrm{B}}_2, \dots , {\mathrm{B}}_{\mathrm{n}}$ are n sets each with three elements such that $\underset{\mathrm{i}=1}{\overset{30}{\cup }} {\mathrm{A}}_{\mathrm{i}}=\underset{\mathrm{J}=1}{\overset{\mathrm{n}}{\cup }} {\mathrm{B}}_{\mathrm{J}}=\mathrm{S}$. If each element of S belongs to exactly ten of the A_i'S and exactly 9 of the B_J'S then the value of n is