You can create a closed curve of length \(l\) by drawing any path of length \(l\) that connects to its start. Some examples are given above.

Let the maximum area for a closed curve of length 1 be \(A\). Find \(\lfloor1000A\rfloor\).

Clarification: the symbol \(\lfloor x \rfloor\) denotes the largest integer less than or equal to \(x\).

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