With the introduction of Large Language Models (LLMs), Alex began to actively use them for various purposes: to explain an incomprehensible topic on the subject, make a training plan, and even write a birthday greeting to his friends. To use LLM, you need to write a lead-in called prompt. The aim of the prompt is to explain to the model what is to be done and what is expected as a response. Thus the whole question cannot consist of a prompt only. The prompt usually looks like this:

You work as a proofreader for educational books. Rewrite the following text, correcting grammatical, punctuation, and semantic errors.

Alex's friends also began using LLMs and actively sharing their generation results. Alex decided to make a collection of successful prompts to use them more actively later. A prompt is considered successful if the result of most generations with this prompt is considered successful.

Alex has a set of questions that he and his friends have asked LLM. He came up with the following algorithm to find all the prompts from a set of questions:

1. At the beginning, all questions are divided into two non-empty sequences of words called the prefix and suffix of the string. If you write all the words from the prefix and suffix sequentially with a space, you will get the original question. Then only the prefixes are processed.
2. Next, two random prefixes $$$q_i$$$ and $$$q_j$$$ are taken. If these prefixes have the largest common non-zero prefix $$$q^{*}$$$ such that $$$q_i = q^{*} + q_i^{+}$$$ and $$$q_j = q^{*} + q_j^{+}$$$, then $$$q_i$$$ and $$$q_j$$$ are replaced by $$$q^{*}$$$ and are not processed further (By $$$q+$$$ we mean a non-empty subsequence of words from $$$q$$$).
3. Step 2 is repeated as long as it is possible to replace prefix pairs by the largest common non-zero prefixes.

At the end of this algorithm, we obtain the set of all prompts for the questions.

Help Alex: find all the successful prompts from the questions Alex and his friends asked LLM.