Aliens

To make contact with aliens, huge structures visible from space were built across the Earth. After 15 years and ten quadrillion kuna, a team of scientists concluded that showing there is intelligent life on Earth calls for symmetry in how the structures are placed. The first step of the plan is to make the layout symmetric about a line parallel to the $y$ axis of the Cartesian coordinate system that holds the structure locations.

For a real number $c$, the layout is symmetric about the line $x = c$ when every occupied coordinate $(x, y)$ has a structure at $(2c - x, y)$ as well.

The budget ran out long ago, so the symmetry has to be reached while building as few new structures as possible. Find the smallest number of new structures and their locations.

The first line contains the number of existing structures $N$. ($1 \le N \le 1000$)

Each of the next $N$ lines contains two integers $X$ and $Y$, the coordinates of one structure. Both values are smaller than $10^8$ in absolute value. No two structures share the same coordinates.

On the first line, print the smallest number $R$ of new structures.

On each of the next $R$ lines, print the coordinates of one new structure.

Several answers can reach the minimum, so pick one by the following rule. A new structure also has integer coordinates, so $s = 2c$ is an integer for the axis $x = c$. If more than one $s$ reaches the smallest $R$, take the smallest such $s$. For that axis, print the new coordinates in increasing order of $x$, breaking ties by increasing $y$.