In the vertexes of a regular $ 100$-gon we place the numbers from $ 1$ to $ 100$ , in some order, every number appearing exactly once. We say that an arrangment of the numbers is happy if for every simmetry axis of the polygon, the numbers which are from one side of the axis are greater that their respective simmetrics (we don't take into consideration the numbers which are on the axis) Find all happy arrangments (If two happy arrangments are the same under the rotation they are considered as only one)