In the language Lisp, each of the four basic arithmetic operators appears before an arbitrary number of operands, which are separated by spaces. The resulting expression is enclosed in parentheses. The operators behave as follows:

(+ a b c ...) returns the sum of all the operands, and (+) returns 0.

(- a b c ...) returns a - b - c - ..., and (- a) returns -a. The minus operator must have at least one operand.

(* a b c ...) returns the product of all the operands, and (*) returns 1.

(/ a b c ...) returns a / b / c / ..., and (/ a) returns 1 / a. The divide operator must have at least one operand.

You can form larger arithmetic expressions by combining these basic expressions using a fully parenthesized prefix notation. For example, the following is a valid Lisp expression:

(+ (- 6) (* 2 3 4) (/ (+ 3) (*) (- 2 3 1)))

This expression is evaluated successively as follows:

(+ (- 6) (* 2 3 4) (/ 3 1 -2))

(+ -6 24 -1.5)

16.5

Design and implement an algorithm that uses any stack implementation (e.g. java.util.Stack ) to evaluate a legal Lisp expression composed of the four basic operators and integer values. Write a program that reads such expressions and demonstrates your algorithm.

Precondition :You can assume opening and closing parenthesis are all balanced in any given expression. Also you can assume all numbers are integer.

Demonstrate your implementation with the following expressions:

Expression (+ (- 6) (* 2 3 4) (/ (+ 3) (*) (- 2 3 1))) evaluates to 16.5 Expression (+ (- 632) (* 21 3 4) (/ (+ 32) (*) (- 21 3 1))) evaluates to -378.11764705882354 Expression (+ (/ 2) (* 2) (/ (+ 1) (+) (- 2 1 ))) evaluates to Infinity

Hint: You may use more than one stack if needed.