Private language depends on public language and vice versa.
Private language works with public language and vice versa.
A public language with no private languages feeding into it does not exist.
A private language with no input from public language cannot exist except in very rare & unusual circumstances.
Any individual’s private language must seek expression in public language through communication with others, at least one other, at the very least an imaginary other, including an imaginary self.
A public language is dead without private speakers.