How to count the number of employees in different months based on the start and end times

I currently have an Employee Dimension, consisting of four columns:

Employee ID | Office | Contract Start Date | Contract End Date

I would like to use this to calculate the number of employees in each month, grouped by different offices, as shown in the following figure.

The pseudocode would be something like: 

Count(Employee.EmployeeID, Date.Month > Employee.ContractStartDate && Date.Month < Employee.ContractEndDate)

Do you know how to implement this calculation?

Thank you in advance!