Evaluate Mathematical Expression

Given a mathematical expression as a string, your task is to evaluate its value and output the result as a floating point number. The expression may contain integers, floating-point numbers, and the operators \( + \), \( - \), \( \times \) (or \( * \)), \( \div \) (or \( / \)), as well as parentheses \( ( \) and \( ) \). Operator precedence must be correctly observed: multiplication and division have higher precedence than addition and subtraction, and parentheses override the default precedence.

Note: You are not allowed to use the built-in eval function or similar utilities.

Examples:

• Input: 3 + 5 → Output: 8.0
• Input: 10 + 2 * 6 → Output: 22.0
• Input: (10 + 2) * 6 → Output: 72.0

inputFormat

The input consists of a single line containing a valid mathematical expression.

outputFormat

Output a single floating point number which is the result of evaluating the expression. The result should be printed on stdout.

3 + 5

8.0