Authors of the new, all-in-one encyclopedia have organized the titles in the order they consider most appropriate for their readers. It's not always alphabetical, because they want to observe some peculiar relationships between them. However, they still want to allow users to look up titles quickly.
They achieve this by adding a carefully calculated number of spaces before every title in the list of titles. They call this structure a dictionary.
A dictionary is represented by a list of words with some number of spaces before certain words. Dictionary format can be described as a set of constraints on sequences of consecutive words starting with the same letter. Any maximal sequence of consecutive words starting with the same letter should satisfy the following rules:
- The first word in the group has no spaces before it. Every subsequent word in the group has at least one leading space.
- If
- the first word of the group is deleted and
- one space is deleted before every remaining word and
- the first letter is deleted from every remaining word
then resulting sequence is a dictionary.
The authors don't feel like giving you a more detailed explanation of what a dictionary is, so they have included an example (see sample input and output) that clarifies their definition.
Your task is to write a program that will convert a given list of words into a dictionary by adding some number of spaces before certain words and preserving the original order of the words.