Chino's Latte Art

While looking for heart shapes in Chino's Latte Art (Hard), Cocoa wondered: can a latte art that is both a polygon and heart-shaped be made very small and delicate? Help Cocoa answer her question.

A polygon is defined as heart-shaped if there exist polygon vertices $A$ and $B$ such that all of the following conditions hold.

• The interior angle at $A$ is less than $180$ degrees, and the interior angle at $B$ is greater than $180$ degrees.
• The given polygon is symmetric about the line $AB$.
• When the given polygon is split by the segment $AB$, both resulting parts are convex polygons.

A single value $N$ ($N=100\,000$) is given.

Print the coordinates of the vertices of a polygon representing the latte art, starting from any vertex and listing them in clockwise order. On the $i$-th line, print the $x$ and $y$ coordinates of the $i$-th point, in that order.

The polygon must satisfy the following conditions.

• It must be a simple polygon with exactly $N$ vertices.
• No vertex may have an interior angle of exactly $180$ degrees.
• Every vertex $(x,y)$ must have integer coordinates satisfying $-2\,000\,000\le x,y\le 2\,000\,000$.
• It must satisfy the heart-shape conditions defined above.