# Bonxie attack P47175

Statement

thehtml
When walking on the remote isle of Foula, professor Oak was dive-bombed by many bonxies that were protecting their territories. Those (fortunately, failed) attacks inspired this problem.

Assume an infinite flat world. There, we have n bonxies, each protecting a disc of radius ri centered at (xi, yi). 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 xi yi ri. 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).

Public test cases
• Input

```5  0 0 5  0 -6 2  2 0 2  -1 1 3  9 9 1
2  1000000000 -1000000000 1000000000  500000000 -500000000 42
```

Output

```3
2
```
• Information
Author
Ivan Geffner
Language
English
Official solutions
C++
User solutions
C++