Formula for calculating patient days with selected date range

I have been struggling with a formula. I have a spreadsheet where I need to calculate the number of days between two dates. However that calculation of days should only be calculated if the dates fall within a specific date range.

For instance, I need to calculate the Length of Stay (LOS) for each patient whose date range falls within date range of example:
Admit Date 03/01/2014
Discharge Date 03/31/2014
Where the date of discharge is not counted unless the patient was only admitted for one day.

Patient Name Admit Date Discharge Date Length of Stay
Patient A 02/28/2014 03/01/2014 0 (This day would be counted in February)
Patient B 03/01/2014 03/03/2014 2
Patient C 03/05/2014 03/12/2014 7
Patient D 03/31/2014 04/01/2014 1
Patient E 02/27/2014 03/02/2014 3
Patient F 03/29/2014 04/03/2014 3

Any assistance would be appreciated.

Thank you,

HospitalOfficer