Evaluate Mathematical Expression

You are given a string representing a mathematical expression that consists of positive integers, the binary operators +, -, *, and /, and possibly nested parentheses. The expression should be evaluated according to the standard operator precedence rules: multiplication and division have higher precedence than addition and subtraction. All divisions are integer divisions, meaning the result of e.g. $8/4$ is 2 and $2-3/5$ is 2 (since $3/5=0$ in integer division).

For example, the expression $3+5*2$ should be evaluated as $3+(5\times2)=13$, and the expression $100*(2+12)/14$ results in 100.

Your task is to implement a function that parses and evaluates such expressions correctly.

inputFormat

The input consists of a single line containing the mathematical expression (as a string). The expression will only contain positive integers, the operators +, -, *, /, and parentheses. There will be no invalid characters.

outputFormat

Output a single integer, which is the evaluation result of the expression.

3+5

8