BTW, increasing max_e and max_pi to 3, and even to 4 leads to some surprising results. For instance, try chekio(pi) with those values at least 3. More

This solution is way faster than the recursive one. A good family of tests is running on n*[n], with n even. The recursive one churns answers up to n=18, and dies miserably with n= 20. This one has no problem with n=30, and could probably go further. More

Why speedy? Lots of constant time simpler, and probably faster, solutions. More

You should learn what a stack is. More

Never mind this wasteful and slow solution, look at the Recursive one, under Speedy. More

Plain solution, not very pythonic. More