Write a function solution that, given two integers a and b, returns the maximum number of repeated square root operations that can be performed using the numbers from the interval [a..b](both ends included) as starting points. square root operations can be performed as long as the result is still an integer.
for example, given a = 10, b = 20, the function should return 2. starting with the integer 16, two square root operations can be performed: sqrt(16) = 4 and then sqrt(4) = 2.
given a = 6000 and b = 7000, the function should return 3. starting with integer 6561, three square root operations can be performed: sqrt(6561) = 81, sqrt(81) = 9 and sqrt(9) = 3.

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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: