Suppose we define the Fibolucci numbers by
f0=0, f1=1, f2=1, and in general fn+1 = fn + fn-1 + fn-2 for n greater than 1.
So, the sequence goes 0, 1, 1, 2, 4, 7, 13, 24, 44, 81,... Use the idea of Binary Powering and matrices covered to write a python program which can calculate the nth Fibolucci number (the number n should be read in from the user). You must not use recursion. Test your program by calculating
The 72nd Fibolucci number
The 117th Fibolucci number