402656: GYM100834 E Polycarp and Arcolygon

Polycarp has got a plane with N circles on it and an infinitely long thread. Each circle i is discribed using the centerpoint coordinates x_i and y_i and the radius r_i. Polycarp uses the thread to swift all the circles so that all of them are inside the figure, formed by the thread. However, the thread can not be cut.

Polycarp is eager to know what the shortest length the tread should be to be able to swift the circles and what area the resulting figure will have.

The first line contains the only integer N, 2 ≤ N ≤ 100.

Next N lines contain integer triplet x_i, y_i, r_i. The numbers are separated by whitespaces,  - 1000 ≤ x_i, y_i ≤ 1000, 1 ≤ r_i ≤ 100. It is insured that the circles do not intersect and contact with each other.

Output two numbers — thread length and figure area. You may assume that answers is coparated with the precision of 10^- 6.

2
0 0 1
99 99 100

670.80969437 33561.73030009

2
10 0 4
-10 0 4

65.13274123 210.26548246

5
0 100 10
-100 -20 10
100 -20 10
-50 40 10
50 40 10

575.24184011 17438.25913572