Given a matrix sized m x n, we define an O-region as a non-empty sub-block with another non-empty sub-block inside removed, such that the removed sub-block has no common boundaries with the outside. That is, the leftmost column of the removed sub-block must be different from the leftmost column of the outer sub-block, and similarly the rightmost columns, topmost rows, and bottommost rows are different. The removal of the inner sub-block leaves a region which looks like the letter O.

Let X be the set of all integers between 0 and n-1. Suppose we have a collection S₁, S₂, ..., S_m of subsets of X. Say an atom A is a subset of X such that for each S_i we have either A is a subset of S_i or A and S_i do not have any common elements.

The Chef likes to stay in touch with his staff. So, the Chef, the head server, and the sous-chef all carry two-way transceivers so they can stay in constant contact. Of course, these transceivers have a limited range so if two are too far apart, they cannot communicate directly.

Recently Johnny have learned bogosort sorting algorithm. He thought that it is too ineffective. So he decided to improve it. As you may know this algorithm shuffles the sequence randomly until it is sorted. Johnny decided that we don't need to shuffle the whole sequence every time. If after the last shuffle several first elements end up in the right places we will fix them and don't shuffle those elements furthermore. We will do the same for the last elements if they are in the right places.