Construct a BNF for each of the following languages. Is your grammar ambiguous? If yes, rewrite it to be non-ambiguous. Give an input string of the language and draw the parse tree and AST for your input.

1. The set of all expressions over { id, num, <<, +, (, ) } where << and + are binary operators, id stands for an arbitrary identifier (variable name), num stands for an arbitrary integer number, and () are used for grouping purposes. Both << and + are left-associative. Further, << has lower precedence than +.