11.19 Let \( N \) be the set of positive integers, and define the function \( f \) on \( N \) as follows:
(i) \( f(1)=1, \quad f(3)=3 \);
(ii) For \( n \in N \), we have
\[
\begin{array}{l}
f(2 n)=f(n), \\
f(4 n+1)=2 f(2 n+1)-f(n), \\
f(4 n+3)=3 f(2 n+1)-2 f(n) .
\end{array}
\]

Find all \( n \) such that \( n \leqslant 1988 \) and \( f(n)=n \).
(29th International Mathematical Olympiad, 1988)