Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. Some houses have gates opening towards the north and some towards t...

Eleven houses A, B, C, D, E, F, P, Q, R, S, and T are arranged in a straight line. Some houses have gates opening 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 fourth 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 opens 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 of the ends.
  Question: What is the position of House E with respect to House P?