Which city is Jinhanju Corporation in?

Time limit1sMemory limit1024 MB

Summary

Given the three distances between capitals of a triangle, find the area shared by three circles, each centered at a capital with radius equal to the opposite distance.

Level: Medium6 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

Jinhanju Corporation is located in which city? Jeonju!

Generally, when people think of the Three Kingdoms period, they picture Goguryeo, Baekje, and Silla. Before them, however, there were the Samhan (Three Han): Jinhan, Mahan, and Byeonhan.

jinhan814 saw their own name and concluded that they descended from Jinhan of the Samhan period, so they founded Jinhan Corporation. They studied the Samhan and found the following facts.

At the time, each of the three states had a capital, and each expanded its territory around its capital. Each state expanded in a circle centered on its capital, and the radius was the distance between the capitals of the other two states.

Territories sometimes overlapped. The region where all three states overlapped was called the battleground.

Jinhan, who was researching at Jinhan Corporation, found the distances between the three capitals. Now Jinhan wants to know the area of the battleground. Help Jinhan find it.

Input

The first line contains three integers $a,b,c(1\le a\le b\le c\le 1\,000$ ; $a+b>c)$ , separated by spaces.

$a$ is the distance between the capital of Jinhan and the capital of Mahan, $b$ is the distance between the capital of Mahan and the capital of Byeonhan, and $c$ is the distance between the capital of Byeonhan and the capital of Jinhan.

Output

Print the area of the battleground on the first line. If there is no battleground, its area is considered $0$ .

An answer is accepted if its absolute or relative error is at most $10^{-6}$ .

When the three states are positioned to satisfy the conditions in the problem, the area of the territories is constant.

Hint

The content above may differ from historical facts.

The title of this problem and the answer to the title were ideas from kidw0124 and w8385.

Examples5

Example 1
Input
```
3 4 4
```
Expected output
```
8.394424
```
Example 2
Input
```
3 4 5
```
Expected output
```
6.641675
```
Example 3
Input
```
3 4 6
```
Expected output
```
2.410185
```
Example 4
Input
```
43 924 925
```
Expected output
```
2789.772940
```
Example 5
Input
```
813 814 815
```
Expected output
```
466974.245538
```