Evaluate a Mathematical Expression

Given a string representing a mathematical expression, you are required to compute its value by simulating a simple parser. The expression may contain non-negative integers, the operators +, -, *, / (where / is integer division), and parentheses ( ). Operator precedence follows the standard rules:

• Multiplication and division have higher precedence than addition and subtraction.
• Operators with the same precedence are evaluated from left to right (associativity).

The answer should be computed using the algorithm similar to the Shunting Yard algorithm.

Note: All divisions are integer divisions, meaning that the result of 7/2 is 3 because it discards the remainder.

inputFormat

The input is given via standard input (stdin) as a single line representing the mathematical expression. The expression will only contain non-negative integers, the operators +, -, *, /, and possibly parentheses.

outputFormat

Output the evaluated result as an integer via standard output (stdout).

3+5*2

13