Knife to me

Birthday cake was very good, tender coffee cake with layers of cream, filled with white chocolate - a miracle of culinary art. But there is a problem: cake is shaped like a prism whose base is the regular N-angled polygon - just as the number of guests, and arrival of Sasha complicated the situation. Now, the cake should be divided into N+1 part.

— Who of us likes geometry? — Well, you studied at math faculty, didn't you?. — Amazing arrogance. You're to blame - and you are gonna take the knife. — Then, I propose to make vertical cuts. — Well, you're right, Captain Obvious. — It's not all. Divide evenly on the N+1 parts so that the volumes of all pieces of the same. — Well, ok. — It's still not all. Divide so that the surface area, filled with chocolate,on all the pieces, was the same. — It was easier to cut on my own.

We consider the projection of the cake on the table. It turns a regular polygon centered at (0, 0) with one vertex at the point (1, 0). The required pieces must be convex polygons such that no three vertices of a piece lie on a straight line. The plan must satisfy the cutting conditions, regardless of the height of the cake. Recall that the chocolate is only on the outer surface of the cake, meaning the upper and side faces.

Input

The number N (3 ≤ N ≤ 100) — the number of guests except for Sasha.

Output

Print exactly N+1 block, each of which describes a single piece. The description of a piece begins with K_i (3 ≤ K_i ≤ 100) — number of vertices. In the next K_i lines, print vertices in the anti-clockwise order, one vertex per line, with possible inaccuracy not greater than 10^{-8}.

Examples