A bird is resting on a point $\mathrm{P}$ at a height of $8 \mathrm{~m}$ above the Mean Sea Level (MSL). Upon hearing a loud noise, the bird flies parallel to the ground surface and reaches a point $\mathrm{Q}$ which is located at a height of $3 \mathrm{~m}$ above MSL. The ground surface has a falling gradient of $1$ in $2$. Ignoring the effects of curvature and refraction, the horizontal distance (in meters) between points $\mathrm{P}$ and $\mathrm{Q}$ is $\_\_\_\_\_\_$ (in integer).