1. Consider the following grammar:

   btree : NIL | LPAREN btree COMMA value COMMA btree RPAREN value : digit | digit value digit : 0|1|2|3|4|5|6|7|8|9 

   Some examples of binary trees are:

   (NIL,12,NIL) ((NIL,12,NIL),20,(NIL,15,NIL)) ((NIL,3,NIL),8,((NIL,12,NIL),20,(NIL,15,NIL))) 

   Augment this grammar with attributes and the attribute computation functions and predicates to accept binary trees that are "balanced". A balanced binary tree is one in which the heights of the subtrees at each interior node are within one of each other.