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 ⌈ n/5 ⌉ of the given points. Assume 2 ≤ n ≤ 10⁵, and that no given coordinate is larger than 10⁶ 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 ⌈ n/5 ⌉. If there is more than one possible line, choose any one. Follow strictly the format of the sample output.