logic – How many surjective functions satisfies the given property?

I’ve been struggling on this problem for quite a bit and was wondering if someone could help me.
The question goes as follows:
$X$ is a finite set with $|X|=n$ and $n$ is a odd number. How many surjective functions $f:Xrightarrow{0,1}$ are they with the property: $$|f^{-1}(0)|<|f^{-1}(1)|$$
If someone knows the answer please tell me how you got to your answer so I can understand it.

My thougts: I thougth of $arcsin(x)$ because $arcsin(0)$ < $arcsin(1)$, and $arcsin(x)$ is a inverse function, but how could I possibly find all functions?

Thanks in advance 🙂

PS: could someone also explain to me what they exactly mean with $|X|=n$, do they just mean absolute value?