Find Number of Days Without Inventory

Hi there. I am trying to find a way to calculate the number of days a business did not have product in stock using multiple dates.

Product Ship Date Sold Date
A 3/28/2016 5/15/2016
A 3/28/2016 6/3/2016
A 3/28/2016 7/15/2016
B 3/29/2016 7/18/2016
A 4/15/2016 7/15/2016
C 4/30/2016 5/5/2016
B 6/30/2016 8/25/2016
A 7/27/2016 8/18/2016
A 7/27/2016 8/26/2016
C 8/11/2016 9/25/2016

I want to calculate the number of days between 4/1/2016 and 9/1/2016 they had zero inventory of Product A, B, and C. The number I am trying to get for Product A is 18, Product B is 7, and Product C is 127.

Attachment is included.

Those numbers equal the number of days when a product was not present in inventory.

I am trying to count the number of days where all of product A is sold, but a new shipment hasn't arrived yet.

Ship date will correspond to the first day it is in inventory and sold date is the date it leaves inventory.

For example, if we are looking at the dates 4/1 to 9/1, there was zero inventory of product A from 7/15 until 7/27 and then again from 8/26 to 9/1.

Please let me know if this helps. Thanks!

In your file date are different then date you describe in #5

Revised file with a color coded explanation of how I am coming up with my numbers. I am using an arbitrary time period of 4/1 to 9/1 even though the earliest ship dates are before that date.

Please let me know if this is more clear. Thank you for all of the help!