The function $$f$$, defined on the set of ordered pairs of positive integers, satisfies the following properties: $$\begin{eqnarray*}f(x,x) &=& x,\\ f(x,y) &=& f(y,x),\quad\text{and}\\ (x+y) f(x,y) &=& yf(x,x+y).\end{eqnarray*}$$ Calculate $$f(14,52)$$.

(第六届AIME1988 第8题)