Time Limit: 2000/1000MS (Java/Others) Memory Limit: 128000/64000KB (Java/Others)

#### Problem Description

Consider N different circles on the plane. They divide it to several parts, you have to find the number of these parts.

For the purpose of this problem the circle of radius r with center (x_{0}, y_{0}) is the set of points

#### Input

The first line of each test case contains N - the number of circles (1 <= N <= 50). Next N lines contain three integer numbers x0, y0, and r each - the coordinates of the center and the radius of the circle. All coordinates do not exceed 10^{3} by their absolute value, all radii are positive and do not exceed 10^{3}. No two circles coincide.

#### Output

For each test case, output K - the number of parts circles divide the plane to, in a single line.

Due to floating point precision losses possible, do not consider parts with area not exceeding 10^{-10}.

#### Sample Input

#### Sample Output

#### Source

Andrew Stankevich Contest 4

#### Manager