Consider the function \( f(x) = 234-x \). How many ordered pairs of positive integers \( (x, y) \) are there such that

\[ \begin{cases} x = f(y) \\ y = f(x) \\ \end{cases} \]

**Details and assumptions**

For an **ordered pair of integers** \((a,b)\), the order of the integers matter. The ordered pair \((1, 2)\) is different from the ordered pair \((2,1) \).

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