The moon has been opened up, and land can be obtained for free, but there is a catch. You have to build a wall around the land that you stake out, and building a wall on the moon is expensive. Every country has been allotted a $500\mathrm{m}$ by $500\mathrm{m}$ square area, but they will possess only that area which they wall in. $251001$ posts have been placed in a rectangular grid with $1$ meter spacing. The wall must be a closed series of straight lines, each line running from post to post.

The bigger countries of course have built a $2000\mathrm{m}$ wall enclosing the entire $250000{\mathrm{m}}^2$ area. The Duchy of Grand Fenwick, has a tighter budget, and has asked you (their Royal Programmer) to compute what shape would get best maximum enclosed-area/wall-length ratio.

You have done some preliminary calculations on a sheet of paper. For a $2000$ meter wall enclosing the $250000{\mathrm{m}}^2$ area the enclosed-area/wall-length ratio is $125$.
Although not allowed , but to get an idea if this is anything better: if you place a circle inside the square area touching the four sides the area will be equal to $\pi \times {250}^2{\mathrm{m}}^2$ and the perimeter will be $\pi \times 500\mathrm{m}$, so the enclosed-area/wall-length ratio will also be $125$.

However, if you cut off from the square four triangles with sides $75\mathrm{m}$, $75\mathrm{m}$ and $75\sqrt{2}\mathrm{m}$ the total area becomes $238750{\mathrm{m}}^2$ and the perimeter becomes $1400+300\sqrt{2}\mathrm{m}$. So this gives an enclosed-area/wall-length ratio of $130.87$, which is significantly better.

Find the maximum enclosed-area/wall-length ratio.
Give your answer rounded to $8$ places behind the decimal point in the form abc.defghijk.