Seven persons A, B, C, D, P, R, and S are related to Q and seated around a circular table. Some face inside, others outside. Each has a unique profess...

Seven persons A, B, C, D, P, R, and S are related to Q and seated around a circular table. Some face inside, others outside. Each has a unique profession among Banker, Writer, Singer, Doctor, Nurse, Dancer, Engineer, and Teacher. No more than four face the same direction. Given the following clues:

• The Singer sits second to the right of Q.
• Three persons sit between A (who does not sit next to the Banker) and the Nurse.
• D is an Engineer.
• P sits opposite Q, who is the Banker.
• C is female but not a Dancer.
• The Teacher and Writer face inside.
• The Brother of Q sits second to the left of the Banker.
• Two persons sit between S (Doctor and brother of Q) and D.
• D is the mother of Q and sits opposite S.
• D's daughter sits third to the left of D.
• A is the father of Q, who is female.
• Both C and R are children of P, who is married to Q.
• B and R are male.
• B faces inside and sits opposite the Dancer.
• The Writer sits second to the right of the Dancer.
• The Singer is married to the Doctor.
• S is the sister-in-law of Q.
• R does not sit immediately to the left of S.

Question: How many persons sit between the Doctor and Engineer when counted from the right of the Engineer?