# KroneckerProduct with arbitrary number of Pauli matrices

I want define a function of n variables as follows $$f(x_1, ..., x_n)= KroneckerProduct[\sigma^{x_1}, ..., \sigma^{x_n}]$$ where $$\sigma^{x_i}=PauliMatrix[x_i]$$. Given a number $$n$$, I can explicitly write down an expression. For example, for $$n=3$$, I can write down

f[i1_, i2_, i3_] :=KroneckerProduct[PauliMatrix[i1], PauliMatrix[i2],PauliMatrix[i3]];


However, how to write down a generic expression in terms of arbitrary $$n$$, so that I don't have to rewrite the expression for every choice of $$n$$? Thanks!

f[i__] := KroneckerProduct @@ PauliMatrix[{i}]