Brahma and Shiva

**This in an interactive problem** Brahma created a bidimensional world, he started from a giant circle and placed $2 \cdot N$ points (numbered $1$ through $2 \cdot N$) in clockwise order on the circumference. Then Brahma created many regions by consecutively taking two of the points and slicing the circle with a line segment connecting them. The slices are such that the following conditions are