2. (15 pts) Describe an O(n)-time algorithm that checks if brackets in a given arithmetic expression is properly placed, i.e., all left brackets are matched with their right counterparts and there are no unmatched brackets between any pair of matched brackets. Note that there are generally more than one types of brackets and only those of the same type can match against each other. For simplicity, you can assume that all operands are represented as a and addition, +, is the only available operation other than parentheses. See below for examples of expressions, where brackets are improperly used: (a + a) + a) (a + (a +a) Ja + (a + a)( a + {a + (a + a)), a + (a + (a +a] + a) Your algorithm must be non-recursive and may use a stack