In this question, three statements are given, followed by two conclusions numbered I and II. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follows/follow from the statements.

Statements:
All bottles are bags.
Some bags are pencils.
Some pencils are sharpeners.

Conclusions:
I. Some sharpeners are bottles.
II. Some bottles are pencils.