Count Unique Records With Multiple Criteria With Formula

Count unique records in Column B where.

1.)
... Column H >=A1 and <=A2

2.)
... Column H <>"" and Column I <>"expired" and <>"" and Column I >=A1 and <=A2

3.)
... Column H <>"" and Column I ="expired" and Column H+120 >=A1 and <=A2

4.)
... Column H <>"" and Column I >=A1 and <=A2 and Column J =""

A1 - user defined (start) Date 1
A2 - user defined (end) Date 2
Column B - 6 digit number (or blank)
Column H - Date 3 (or blank)
Column I - Date 4 (or "expired" or blank)
Column J - Date 5 (or blank)