Count number of rows based on multiple criteria

Question

I have a sheet used to calculate work-time for contractors and catch errors. Each row is a time-entry, with columns used to indicate the employee name, campus visited, date, time-in, and time-out.

I'm currently able to count the number of entries per employees per date per campus (i.e. John entered a time log for Campus Alpha 2 times for date 9/1/2018).

This is achieved through the following array formula stored at the top of the O column: =ArrayFormula(IF(ROW(C:C)=1,"Logs/Date",IF(ISBLANK(C:C), "", COUNTIF(D:D&CHAR(9)&N:N&CHAR(9)&C:C, D:D&CHAR(9)&N:N&CHAR(9)&C:C) ))) Where column C is Campus, D is Date, and N is Employee Name.

I would like to extend this slightly, by only counting time-entries which fit the above criteria AS WELL AS have overlapping time. So if time-in and time-out do not overlap then it's not counted, if they do overlap in some way then I want to count the number of affected entries (as it's an error). Time-in is stored in column E and time-out is in column F.

I'm out of ideas on how to add that functionality to the pre-existing formula, any advice is greatly appreciated.

I've attached an example sheet at the following link: https://docs.google.com/spreadsheets/d/1WSZtDWuLrVf8oBbN4i6Y09tJCa2x5DM6EQ2IbcMewHE/edit?usp=sharing The entries highlighted in orange are examples that should be counted as their times overlap. The entries highlighted in green are not problem as their times do not overlap. The values in cell O5 and O6 should be 1 instead of 2.