Bonxie attack P47175

Assume an infinite flat world. There, we have n bonxies, each protecting a disc of radius r_i centered at (x_i, y_i). Please compute a point protected by the maximum number of bonxies.

Input

Input is all integer numbers, and consists of several cases, each one with n followed by the n triples x_i y_i r_i. You can assume 1 ≤ n ≤ 1000, that all coordinates are at most 10⁹ in absolute value, that all radii are between 1 and 10⁹, that each pair of circles of the discs either do not intersect, or intersect at exactly two points, and that there is no point in the plane with more than two circles on it. The input cases have no precision issues.

Output

For every case, print the maximum number of bonxies that can protect a point.

Hint

The expected solution has cost Θ(n² logn).