Problem Statement

Write a program that evaluates a given arithmetic expression represented as a string. The expression may contain non-negative integers, the operators +, -, *, /, and parentheses ( and ). The operators should follow the standard precedence rules (i.e., multiplication and division have higher precedence than addition and subtraction) and parentheses should override the default precedence.

Requirements

• You may not use any built-in functions or libraries that can directly evaluate the expression (such as eval in various languages). The parsing and evaluation logic must be implemented manually.
• The expression input will always be valid, but it can include whitespace, nested parentheses, and numbers with multiple digits.
• Perform integer division when evaluating division expressions (truncate any decimals).

Example

For example, given the input string:

"2 * (3 + 4) - 5 / 2"

The expected output is:

13

Instructions

Implement a function that takes an arithmetic expression string as input and returns its evaluated result as an integer. Ensure that your solution handles nested parentheses and adheres strictly to the operator precedence rules.