Given circles in a plane, you need to draw a circle, and find the maximum number of given circles it can intersect with.
Two circles intersect with each other if and only if they share at least one common point. It is guaranteed that any two given circles do not share a common point and do not contain each other. The circle you draw may degenerate into a line (a circle with infinite radius) or a point.

The first line contains an integer , indicating the number of circles.
Each of the next  lines contains three integers  and , indicating the coordinates and the radius of a circle.

Output an integer indicating the maximum number of intersected circles.

4
-3 1 1
6 0 2
0 -4 2
1 0 1

3

5
1 4 1
-1 2 1
1 0 1
-1 -2 1
1 -4 1

5