Develop a finite state machine to recognize an octal (base 8) number N whose remainder over 5 is 2, i.e., N%5=2, the octal sequence is terminated by a dollar sign $.

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Problems on Growing Functions

For a given set of functions f and g, the growth of functions states that the function g grows as fast as the function f. The growth rate of algorithms helps determine the algorithm's efficiency and compare its performance to other algorithms.