## Circle Packing II

### Problem 476

Let `R`(`a`, `b`, `c`) be the maximum area covered by three non-overlapping circles inside a triangle with edge lengths `a`, `b` and `c`.

Let `S`(`n`) be the average value of `R`(`a`, `b`, `c`) over all integer triplets (`a`, `b`, `c`) such that 1 ≤ `a` ≤ `b` ≤ `c` < `a` + `b` ≤ `n`

You are given `S`(2) = `R`(1, 1, 1) ≈ 0.31998, `S`(5) ≈ 1.25899.

Find `S`(1803) rounded to 5 decimal places behind the decimal point.