Check Mathematical Expressions

You are given a series of simple arithmetic expressions. Each expression is composed only of non‐negative integers and the binary operators +, -, *, and /. There are no spaces in the expressions. An expression is considered valid if and only if:

• It contains only digits and the allowed operators.
• Operators do not appear consecutively.
• During evaluation, no division by zero occurs.

If the expression is valid, output Valid. If an expression contains any illegal characters or if two operators appear consecutively, output Invalid. If the expression triggers a division by zero during evaluation, output Division by zero.

For example, consider the following expressions:

• 3+5 evaluates correctly → Valid
• 8/0 attempts a division by zero → Division by zero
• 5+*7 has consecutive operators → Invalid

Note: All evaluation is done using standard operator precedence. All expressions are assumed to be written without spaces.

inputFormat

The first line of input contains a single integer T (T ≥ 1) which indicates the number of expressions. The following T lines each contain a single arithmetic expression.

For example:

3
3+5
8/0
5+*7

outputFormat

For each expression, output the result on a new line. The result is one of the following strings:

• Valid if the expression is mathematically correct.
• Invalid if the expression contains non-digit characters or consecutive operators or any format issues.
• Division by zero if the expression attempts to divide by zero during evaluation.

For the sample input above, the output would be:

Valid
Division by zero
Invalid

## sample

3
3+5
8/0
5+*7

Valid
Division by zero
Invalid

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