Given N circles. Calculate the total area that these N circles cover.

Input

First line: N (1 ≤ n ≤ 50)

- In the i-th line of the next n lines contains 3 integers Xi, Yi and Ri, separated by spaces. These are the coordinates of the center and the radius of the i-th circle (-10000 ≤ Yi-Ri, Yi+Ri, Xi-Ri, Xi+Ri ≤ 10000)

Output

The total area that these N circles cover with 5 digits after decimal point

Example

Input:
2
5 6 3
5 5 5
Output:
78.53982