Define a context-free grammar in BNF capable of generating only balanced strings of (nested or flat) matched parentheses. The empty string is not in this language.

For instance, the strings (), ()(), (()), (()())(), and ((()())()) are sentences in this language, while the strings )(, )(), )()(, (()(), ())((, and ((()()) are not. Note that not all strings with the same number of open and close paren- theses are in this language (e.g., the strings )( and )()( are not sentences in this language).