Validated String Array

You are given an array of strings. Your task is to determine whether the array is valid according to the following four conditions:

• The array must not be empty.
• All strings must have the same length.
• If each string is interpreted as an integer, then they must form a strictly increasing sequence, i.e. $$a_1 < a_2 < \cdots < a_n.$$
• No string should start with a zero unless the string is exactly "0".

If all conditions are satisfied, print Valid. Otherwise, print Invalid.

inputFormat

The input is given from standard input and consists of multiple lines:

1. The first line contains an integer n indicating the number of strings.
2. The following n lines each contain one non-empty string composed of digits.

outputFormat

Output a single line to the standard output: either Valid if the array of strings satisfies the criteria, or Invalid otherwise.

3
123
234
345

Valid