King Cnut of the North Sea Empire wishes to see his Jomsvikings, a special viking force, train on a field next to his palace in Denmark. His military advisor, Godwin of Essex, wants to keep most of the Jomsvikings stationed in England where Godwin currently resides. Cnut has a strict requirement, $23$ of the vikings must all be training at most within $6$ feet of each other (i.e. the pairwise distance between them is at most $6$ feet) and if not, then $23$ of the vikings must all be training more than $3$ feet apart from each other. Assume the vikings are points on a plane; they have no areas. Godwin cannot get the vikings to coordinate and achieve this, but wants to send as few as possible. Let the minimum number of vikings that need to be sent to guarantee Cnut’s requirement is satisfied be $n$, enter $n$.