Data abstraction and problem solving with c++ in mythology, the hydra was a monster with many heads. every time the hero chopped off a head, two smaller heads would grow in its place. fortunately for the hero, if the head was small enough, he could chop it off with out two more growing in its place. to kill the hydra, all our hero needed to do was to chop off all the heads. write a program that simulates the hydra. instead of heads, we will use strings. a bag of strings, then, represents the hydra. every time you remove a string from the bag, delete the fi rst letter of the string and put two copies of the remaining string back into the bag. for example, if you remove hydra, you add two copies of ydra to the bag. if you remove a one-letter word, you add nothing to the bag. to begin, read one word from the keyboard and place it into an empty bag. the hydra dies when the bag becomes empty. using big o notation, predict the time requirement for this algorithm in terms of the number n of charac ters in the initial string. then time the actual execution of the program for various values of n and plot its per formance as a function of n.