Heat (Hard)
— The boatswain must have overheated in this heat....
— Or the compote in the galley has soured from the heat and started fermenting...
From the conversation between the captain and the navigator
The heat was becoming unbearable... The boatswain had run out of handkerchiefs, and now, along with the jibs, he was distributing to the sailors not the usual neat handkerchiefs, but ones still in triangular form, likely made from material not originally intended for the jibs.
Seva decided once more to cover the porthole in his cabin with this thick fabric to reduce the sunlight entering. Meanwhile, the curious sailor pondered the same question: What is the maximum area of the porthole that can be covered this way?
Help Seva solve this seemingly simple problem, which he has been unable to figure out on his own.
Input
The input consists of a single line containing four natural numbers: r, a, b, and c (0 < r ≤ 100, 0 < a, b, c ≤ 200). Here, r is the radius of the porthole, and a, b, and c are the lengths of the sides of the handkerchief. It is guaranteed that the handkerchief has a non-zero area.
Output
Output a single number representing the maximum area of the porthole that can be covered, with a precision of at least 3 decimal places.