A positive point charge is placed a certain perpendicular distance from the axis of a uniformly charged cylinder and experiences a certain force. Assume the cylinder is long enough to be approximated as infinitely long. Now suppose this experiment is repeated. Suppose you want to make changes to cause the magnitude of the force to be decreased by a factor of $3.$ If the charge per unit length of the cylinder is increased three$-$fold then by what number would the charge of the point charge have to be multiplied? Assume all other parameters are fixed.