How many solutions in this Statue Park (Loop)?

Question

Rules of Statue Park (Loop), from GM Puzzles

Place each of the twelve pentominoes into the grid once, with rotations and reflections allowed. No two pentominoes can overlap or be orthogonally adjacent, and all cells not occupied by the pentominoes must be traversed by a single, closed loop (connecting cells horizontally or vertically). The black circles indicate some cells that must be covered by pentominoes, white circles indicate spaces that may not be contained in pentominoes and must be part of the loop.

The puzzle intentionally has no black or white circles; it is a blank 14x14 grid. Does this puzzle have no solutions, one solution (up to rotation/reflection), or multiple solutions - and if so, how many?

P.S. this puzzle is meant for those who haven't done this genre before, so if experienced solvers could hold off posting answers that would be nice :)

Answer 1

Zero. If I understand correctly, the U pentomino leaves a hole that can't be filled by another pentomino (because they can't be adjacent) or be part of the loop (because it's only adjacent to at most one other empty square).