Expression Evaluator

You are given a string that represents a mathematical expression. The expression may contain integers or floating‐point numbers, the arithmetic operators +, -, *, /, the exponentiation operator **, and parentheses ( and ). Your task is to evaluate the expression and print the result.

If the expression is evaluated successfully, print the result. If a division by zero occurs, print the error message Error: Division by zero.. For any other invalid input, print Error: Invalid input..

The evaluation should follow the standard operator precedence rules. In mathematical notation, the exponentiation operator is given by \( a^{b} \) (i.e. a ** b in the input).

inputFormat

The input consists of a single line from stdin containing a mathematical expression. The expression may include numbers, operators +, -, *, /, ** and parentheses. Extra spaces may appear between tokens.

outputFormat

Output to stdout the evaluated result. If the expression is invalid or if a division by zero occurs, output the corresponding error message:

• Error: Division by zero.
• Error: Invalid input.

If the result is an integer, print it without a decimal point; otherwise, print the floating‐point result.

## sample

3 + 5 * 2

13

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