Crowded line P68571

You are given $n$ points on the plane. You have the guarantee that there exists at least one line that contains at least $20\%$ of the $n$ given points. Find any such line.

Input

Input consists of several cases, with only integer numbers, each one with $n$, followed by $n$ different pairs $(x, y)$. There is at least one line with at least $\lceil n/5 \rceil$ of the given points. Assume $2 \le n \le 10^5$, and that no given coordinate is larger than $10^6$ in absolute value.

Output

For every case, print information about the line you found: The number $m$ of all the given points that belong to your line, followed by all those $m$ points in any order. The number $m$ must be at least 2 and also at least $\lceil n/5 \rceil$. If there is more than one possible line, choose any one. Follow strictly the format of the sample output.