The assignment needs to be modified.  The recursive function should read one
character per call (an entire line is read in each recursive chain).

The program should not use strings - here it's a complication.  The recursive
function should have a single char variable.  

The writing of the entire palindrome should be done recursively -- not just
the backward part or just the forward part.  Each call of the recursive
function that writes part of the forward portion should also write the
corresponding part of the backwards portion.