I am looking for a function that takes $n$ parameters $ x_1, x_2, ... x_n $, such that, if and only if any $i$th parameters are equal, then the outputs are equal. Mathematicaly, $$ f:R^n \rightarrow R,\ \forall (i = 1,2,...n) ({x_i}_1={x_i}_2 \leftrightarrow f(...{x_i}_1...)=f(...{x_i}_2...)) $$
Could we generalize this idea for $n$ parameters? I am looking for a mathematical expression of this function, only satisfying this property. Any operator is plausible as long as it is in mathematical concept (logical, modula , arithmetic etc.).