Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. The gates of some houses open towards the north and some towards th...

Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. The gates of some houses open towards the north and some towards the south, with no two adjacent houses having gates opening in the same direction. The following conditions apply:

• House B is not adjacent to House A. - House Q is immediately to the left of House B. - House P is located four houses to the right of House D. - House D is immediately to the left of House R. - The number of houses to the left of House P is one more than the number of houses between House R and House P. - Exactly two houses are to the left of House A. - The number of houses between House P and House A is one less than the number of houses between House T and House C. - House T is adjacent to House P. - Exactly one house is between House F and House Q, and neither of their gates open south. - Exactly one house is between House E and House S, and House S is not adjacent to House C. - House D is second from one end of the row.
  Question: How many houses are located between House A and House B?