Imagine you are developing a personalized text suggestion system that predicts the most likely next letter$($s$)$ based on your typing history. This system analyzes past usage to provide tailored suggestions, reducing errors and improving the overall typing experience. Unlike existing systems, which complete entire words, your system focuses on suggesting only the most probable next letter$($s$),$ ensuring better flexibility and precision. This program will simulate a text prediction engine capable of learning from user input and responding to queries with suggestions. It offers the following functionalities: $1.$ Adding words and their usage frequencies to the system$$s dictionary. $2.$ Respond to queries by predicting the most likely next letter based on the provided prefix. The program will appropriately inform the user if no words match a given prefix. Example: Suppose your dictionary contains the following data: $$ "hello" used $50$ times $$ "help" used $30$ times $$ "heat" used $20$ times $$ "hero" used $10$ times If you query with the prefix, $$he$,$ the system will analyze the words starting with $"$he$"$ and suggest the most likely next letter$($s$)$: $\text{'}$l$\text{'}$ appears in "hello" and "help" a total of $50+30=80$ times. $\text{'}$a$\text{'}$ appears in "heat" a total of $20$ times. $\text{'}$r$\text{'}$ appears in "hero" a total of $10$ times. Thus, the most likely next letter is l$.$ If you query with the prefix ho$,$ since no word starts with ho$,$ the program will respond appropriately, indicating that no matching prefix exists in the dictionary. The Problem You are tasked with designing a system that answers queries about the most likely next letter based on a list of words and their usage frequencies. Your program will process a series of operations, which include adding words to a dictionary and querying for prefixes.

The Input $($to be read from standard console input $($not file i$/0.$ Any file i$/$o in the code will get zero$))$ The input begins with a single positive integer, n$,$ which specifies the number of commands your program needs to process. Each of the following n lines contains one command, in one of two formats: $$ Insert Command A command that starts with the integer $1,$ followed by a word and a frequency: $$ Query Command A command that starts with the integer $2,$ followed by a prefix: The Output $($to be printed to standard console output $($no file i$/$o$.$ Any file i$/$o in the code will get zero$))$ For each query command, your program must produce exactly one line of output: $1.$ If the prefix is a proper prefix for one or more words in the dictionary at the time of the query: o Print all the letters that are the most likely to come next, in alphabetical order, without space between them. $2.$ If the prefix is not a proper prefix for any word in the dictionary: o Print the string "unrecognized prefix" on a line by itself. Implementation Restrictions You are required to implement a trie data structure to manage all input words and handle queries. Each trie node should include the following information: $1.$ Node Frequency: The frequency of the string represented by this node $($i$.$e$.,$ how many times this specific string has been added to the dictionary$).2.$ Sum Prefix Frequency: The total frequency of all words in the dictionary that have this string as a prefix, including the string itself. $3.$ Maximum Child Frequency: The highest frequency among all child nodes of the current node. For example, if the node represents "app" and there are currently $25$ occurrences of words starting with "appl" and $20$ with "appy," this value should be $25.4.$ Children Pointers: An array of $26$ pointers, each representing one of the possible next letters $(\text{'}$a$\text{'}$ to $\text{'}$z$\text{'}).$ A pointer should be NULL if no words in the dictionary continue along that path. Typically, only a subset of these pointers will be active. Implementation Details $$ Type $1$ Commands: Use the trie's insert function to add words to the dictionary. Since words may appear multiple times in the input, ensure your insert function is designed to update existing nodes instead of creating duplicates unnecessarily. $$ Type $2$ Commands: Implement a custom function for handling prefix queries. While this function will be similar to the standard search function in a trie, it must include additional logic to determine and return the required output $($e$.$g$.,$ the most likely next letter or a list of letters$).$ Additional Requirement: You must read data from the standard console input and print the output in the standard console as well. No file i$/$o should be used in the code. write code in c