We investigated a program which is probably used as one component of a bigger password breaking algorithm. We determined that the program can input arbitrary N-bit queue and for actual N-bit input also the program output will be always N bits long. Additionally we noticed that the longer program input is, the longer will be the output calculating time. After performing some repeating tests we also determined that the program working time depends only and exactly on input length, not on the input itself. Finally we fixed some actual working times:

-for N=10 - 10.576 seconds;

-for N=20 - 11.087 seconds;

-for N=25 - 13.544 seconds;

-for N=30 - 27.442 seconds;

-for N=35 - 1 minute 46.059 seconds;

-for N=40 - 9 minutes 10.784 seconds.

Task:

a) Find the program working time for N=50.

b) Please derive the mathematical formula using which is possible to calculate actual working time for arbitrary N.