Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that 2^N<N! is m/n, where m and n are coprime, then 4 m-3 n…

Let N denote the sum of the numbers obtained when two dice are rolled. If the probability that $\displaystyle 2^N<N!$ is $\displaystyle \frac{m}{n}$, where $\displaystyle m$ and $\displaystyle n$ are coprime, then $\displaystyle 4 m-3 n$ is equal to