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ZOJ Problem Set - 2518
Wrapping Pillar

Time Limit: 2 Seconds      Memory Limit: 65536 KB

An ellipse can be determined by a pair of a and b, the half lengths of its horizontal and vertical axes, respectively. CYJJ loves ellipses so much that she plans to build a pillar with ellipse base at the center of her living room. She is to wrap the pillar by some wall-paper and you are supposed to tell her the minimum area of paper she has to buy.

Input
The input consists of several test cases, each occupies a line with 3 positive numbers: H, a and b, where H is the height of the pillar, a and b are the half lengths of the horizontal and vertical axes of the ellipse base.

Output
For each test case, output in a line the minimum area of paper that can wrap the pillar.

Sample Input:
100 10 10
10 5 10
Sample Output:
6283.19
484.42


Author: CHEN, Yue
Source: CYJJ's Funny Contest #2, Relaxing on Math
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