Problem Description

There are N circles on the plane. Dumbear wants to find a region which is covered by as many circles as possible. But Dumbear is very dumb, so he turns to momodi for help. But momodi is very busy. Can you help him find out the maximum times that a region can be covered? Notice that a point on a circle’s boundary is considered to be covered by this circle.

Input

There are several test cases in the input.

For each case, the first line contains an integer N (1≤ N ≤ 100) denotes the number of circles.
For the next N lines, each line contains three integers X, Y, R denotes a circle whose center is (X, Y) (-10000 ≤ X, Y ≤ 10000) and radius is R (0 < R ≤ 5000).

The input terminates by end of file marker.

Output

For each test case, output a single line contains only a number denotes the maximum times that a region can be covered.

3
0 0 1
1 0 1
2 0 1

3

Author

momodi & Dumbear@WHU