Let S ={( m, n ): m, n ∈{1,2,3, ….., 50}}. If the number of elements (m, n) in S such that 6^m +9^n is a multiple of 5 is p and the number of…

Let $\displaystyle \mathrm{S}=\{(\mathrm{m}, \mathrm{n}): \mathrm{m}, \mathrm{n} \in\{1,2,3, \ldots . ., 50\}\}$. If the number of elements (m, n) in S such that $\displaystyle 6^{\mathrm{m}}+9^{\mathrm{n}}$ is a multiple of $\displaystyle 5$ is p and the number of elements (m, n) in S such that m+n is a square of a prime number is q , then $\displaystyle \mathrm{p}+\mathrm{q}$ is equal to $\displaystyle \_\_\_\_$.