Description

Recnetly, chen_h has fell in love with a new game called “destroy the farmland”. The rules of the game are very simple. Throw a bomb on the farmland, and then it would explode at the landing point (suppose the explosive range is a circle). Since the explosive power is different to each one, the explosive area is necessarily different. Here we provide the explosive power for a bomb is 0 if transmitted into the water.

To simpilify the question, the farm can be simplified into a two-dimensional plane. The landing point is (X,Y), and the explosive area is simplified into a circle. Of course, bomb power factor could be represented with a variable R which is equal to the radius of a circle.

Input

The first line is one integer n indicates the number of the bombs(0<n<1000). Then follows n lines every line has three integers X, Y, R. (|X|, |Y|, |R|<=1000)

Output

The total destroyed area that these N circles with 3 digits after decimal point.

Sample

Input

3
0 0 1
0 0 1
100 100 1

Output

6.283