Max Volume

Time limit1sMemory limit128 MB

Summary

Compute the volume of each cone, cylinder, and sphere with pi as 3.14159 and print the largest value rounded to three decimals.

Level: Easy1 of 10
Topics: Math, Implementation
Solved: No attempts yet

Problem

Find the largest volume among the given three dimensional figures. There are three kinds of figures: a cone, a cylinder, and a sphere.

The volume $V$ of each figure comes from these formulas.

Cone: $V = \frac{1}{3} \pi r^2 h$
Cylinder: $V = \pi r^2 h$
Sphere: $V = \frac{4}{3} \pi r^3$

Use $\pi = 3.14159$ in the calculation.

Input

The first line contains the number of figures $n$ ( $1 \le n \le 100$ ). Each of the next $n$ lines describes one figure. A cone starts with the letter C, followed by the radius $r$ and the height $h$ . A cylinder starts with the letter L, followed by the radius $r$ and the height $h$ . A sphere starts with the letter S, followed by the radius $r$ alone.

Output

Print the largest volume among the given figures, rounded to three decimal places. No volume in the input lands exactly on a rounding boundary.

Examples2

Example 1

Input

5
S 3.0
C 2.5 3
S 1.79
L 2.78 1.4
C 1.15 2.36

Expected output

113.097

Example 2
Input
```
3
C 10 10
L 5 12
S 6
```
Expected output
```
1047.197
```