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Problem I
Janitor Troubles
The maximum quadrilateral problem is quite easy to state: given four side lengths $s_1, s_2, s_3$ and $s_4$, find the maximum area of any quadrilateral that can be constructed using these lengths. A quadrilateral is a polygon with four vertices.
Input
The input consists of a single line with four positive integers, the four side lengths $s_1$, $s_2$, $s_3$, and $s_4$.
It is guaranteed that $2s_ i < \sum _{j=1}^4 s_ j$, for all $i$, and that $1 \leq s_ i \leq 1\, 000$.
Output
Output a single real number, the maximal area as described above. Your answer must be accurate to an absolute or relative error of at most $10^{-6}$.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 3 3 3 |
9 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 2 1 1 |
1.299038105676658 |
| Sample Input 3 | Sample Output 3 |
|---|---|
2 2 1 4 |
3.307189138830738 |
