Janitor Troubles#9887
While working a night shift as a janitor at the university, you absent-mindedly erase a blackboard covered with equations, only to realize afterwards that these were no ordinary equations! They were the notes of the venerable Professor E. I. N. Stein, who earlier that day had solved the elusive maximum quadrilateral problem! Quick, you have to redo his work before anyone notices what happened.
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 a quadrilateral that can be constructed with these side lengths. A quadrilateral is a polygon with four vertices.
Four positive integers s_1, s_2, s_3 and s_4 — the side lengths.
It is guaranteed that 1 \le s_i \le 1000 and 2 s_i < \sum\limits_{j=1}^{4} s_j for all .
Print a single floating-point number — the maximum area described above. Your answer must have an absolute or relative error of at most 10^{-6}.
Example 1
Example 2
Example 3