COUNTIF Dates within dates plus condition.

Hi, 

I´m struggling a bit with the formula to calculate my conditions. I´ve attached an example file to giv an understanding. 

My conditions are two date columns (A & B) and one date row (H6:ID6). I have four hypothetical sales persons (C6:F6) whom get marked with an "x" (C7:F7 and down) if they do a sale within the given date range in my columns. 

My headache is how to calculate the number of "ongoing sales" per day each salesman have (HI:ID4). 

So the critera of an "x" within a date range needs to meet that the dates in the date row occurs during the range and then calcuate the number of occurrences of "x" during that specific date. 

Anyone that has some valuable input on how to build this formula? 

Kind regards,

Viktor