You will write a program that given some English word finds other valid English words that have exactly the same letters. For example given the word cat the program finds the word act which is another word with the same letters. The program relies on an English dictionary to verify whether or not a string is a valid English word. Part 1: You plan to make a set of all the words in the dictionary (all converted to lowercase). Then, given a word, you plan to make words from all the combinations of the letters and check whether each is in the set. If yes, it is a valid English word and you add it to the result. For example, for the word cat, the combinations are act, atc, cat, cta, tac, tca. act is in the dictionary and thus valid. Analyze the runtime and memory footprint of this algorithm and give the big O. Write your brief and clear answer in the report. No code to write at all.