Function to fatten numbers X50141

In this problem, given any natural number x with n digits x₁ … x_n, we say that y = y₁ … y_n is the result of fattening x if, for every i between 1 and n, y_i = max{x₁, …, x_i}. For instance, if we fatten 7 we get 7, if we fatten 32064781 we get 33366788, and if we fatten 9000000 we get 9999999.

Write a function

to return the result of fattening x.

You cannot use vectors in the code. We suggest to think of a recursive solution. You may implement and use auxiliar procedures.

Your program should follow a right programming style. You should include the appropriate comments.

Precondition

It holds 0 < x < 10⁹.

Observation You only need to submit the required procedure; your main program will be ignored.