How do I get into Baba Yaga's hut?

Hint 1 of 4:

You need the skull to lower the gate first.

Hint 2 of 4:

The thief outside of the town or Zara at the magic shop will tell you about
this hut.

Hint 3 of 4:

You need to say a rhyme to get in.

Hint 4 of 4:

You should have talked to the skull before you gave him the gem.