Inn on trail up Mt. Fuji--question

When I climbed Mt. Fuji in 1957, we stayed in an inn on the cinder trail,
about three-quarters of the way up, I think. The sleeping room was a tatami
floor, no furnishings whatsoever. We were wedged tightly side by side and
head to feet. We got up in darkness and climbed the rest of the way so we
would be at the top for sunrise.

Does anyone recall whether the sleeping arrangements at the inn in the 1950s
or thereabouts was (1) everyone in one room, or (2) men in one room and
women in another.

Is the inn still there? If so, please describe it. Many thanks.

HH