Let $\mathrm{a}, \mathrm{b}, \mathrm{c} \in\{1,2,3,4\}$. If the probability, that $\mathrm{a} x^2+2 \sqrt{2} \mathrm{~b} x+\mathrm{c}>0$ for all $x \in \mathbf{R}$, is $\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to $\_\_\_\_$ .