Counting the number of times a date occurs in multiple start and end date ranges.

Hi,

I have a list of start and end dates and would like to count the number of times each date throughout the year appears in these date ranges so that I can plot them to show the busiest periods.

I have attached an example file. I have been puzzling on this for a while, I was thinking it would be easy to use a COUNTIFS formula to decide whether the date in column D was equal or greater than the date in column B and then if it was equal or less than the date in column C. I have had a brain fade now...I can't remember what I've done now

Could someone please point me back in the right direction with this?

Thanks very much..