Necessary and sufficient conditions for a Boolean function $f$ in $n$ variables to satisfy $f(x_1,x_2,...,x_n)=f(x_n,...,x_2,x_1)$?

Question

What are necessary and sufficient conditions for a Boolean function $f$ in $n$ variables to satisfy $$f(x_1,x_2,...,x_n)=f(x_n,...,x_2,x_1)?$$

Functions like this may be useful in cryptographic algorithms, so I need a way to search for them.