RIOPLATENSE 2018 Problem 6

A company has $n$ employees. It is known that each of the employees works at least one of the $7$ days of the week, with the exception of an employee who does not work any of the $7$ days. Furthermore, for any two of these $n$ employees, there are at least $3$ days of the week in which one of the two works that day and the other does not (it is not necessarily the same employee who works those days). Determine the highest possible value of $n$ .