A hexagon of which all angles are 120° is called “*diaoable hexagon*”.

Now Orz pandas have 6 segments and they want to create a room to live in with those segments.

Orz pandas wants the room to be diaoable and as large as possible.

In order to be Orzed you should help them determine the maximum area of *diaoable hexagon* you can construct.

There are multiple test cases(not more than 7000).

Each line will contain 6 integers indicating the length of each segment. Process to end of file.

1 ≤ *length* ≤ 10000

For each test case, output the the maximum area of *diaoable hexagon* you can construct in one line(if no *diaoable hexagons* can be constructed, “0” should be printed).

Note that you should round the answer to the nearest number with exactly two digits after the decimal point (0.005 rounds up to 0.01).