Dean has been using computers for some time now, but he is unfamiliar with a number of utility programs. In order to better maintain his computer, he decides to ask his coworker Andrea for advice on basic utility programs. Andrea tells Dean that he should periodically perform on his computer to optimize the hard drive so that it works more efficiently. This process works by rearranging the data on the hard drive so all files are stored in contiguous locations.

Write a program that performs a simple n-body simulation, called "jumping leprechauns." this simulation involves n leprechauns, numberd 1 to n. it maintains a gold value g_i for each leprechaun i, which begins with each leprechaun starting out with a million dollars worth of gold, that is, g_i = 1000000 for each i = 1,. in addition, the simulation also maintains, for each leprachaun, i, a place on the horizon, which is represented as a double-precision floating point number, x_i. in each iteration of the simulation, the simulation processes the leprachauns in order. processing a leprachaun i during its iteration begins by computing a new place on the horizon for i, which is determined by the assignment: