26. (GBR 2) ${ }^{\mathrm{IMO} 3} \mathrm{~A}$ function $f$ defined on the positive integers (and taking positive integer values) is given by  $$ \begin{aligned} f(1) & =1, \quad f(3)=3 \\ f(2 n) & =f(n) \\ f(4 n+1) & =2 f(2 n+1)-f(n) \\ f(4 n+3) & =3 f(2 n+1)-2 f(n) \end{aligned} $$  for all positive integers $n$. Determine with proof the number of positive integers less than or equal to 1988 for which $f(n)=n$.