A motorist traveling at $100$ km/h on a highway needs to take the next exit, which has a speed limit of $50$ km/h. The section of the roadway before the ramp entry has a downgrade of $3 \%$ and coefficient of friction $(f)$ is $0.35$. In order to enter the ramp at the maximum allowable speed limit, the braking distance (expressed in m) from the exit ramp is __________