Consider a square with vertices at \((1,1);(-1,1);(-1,-1);(1,-1)\). Let \(S\) be the region consisting of all points inside the square which are nearer to the origin than to any edge. The area of \(S\) is \({\frac{A}{B}(C\sqrt{D}-E)}\)

where \(A,B,C,D,E\) are integers,_need not be distinct and \(D\) is square free and \(A,B\) are co prime.

Find \(A+B+C+D+E\)

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