Date Range between Variable Dates

I am trying to create a formula to determine number of weeks between 2 days, but only including those days within a specified time period. For example, each row shows a start date and an end date, and I want to know how many of those days fall within a specified range. Here is an example,

Start Date: 1/1/20
End Date: 12/30/20
Time Period: 4/3/20-8/3/20

Start Date: 5/18/20
End Date: 11/30/20
Time Period: 4/3/20-8/3/20

Start Date: 6/5/20
End Date: 7/5/20
Time Period: 4/3/20-8/3/20

Start Date: 6/5/50
End Date: 10/20/20
Time Period: 4/3/20-8/3/20

As you can see, I have multiple rows with a start date and an end date, and I am trying to determine how many days during the time period fall within the start date and the end date for each row. Any ideas? I know how to calculate days between events, but am not sure how to find how many days fall within the time period. Thank you!

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