$$f(x,y)=\frac{2}{x^2+(y-1)^2+1}-\frac{1}{x^2+(y+1)^2+1}$$
will do. 

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Below are the calculations, in Mathematica:

[![enter image description here][1]][1]
[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/LAsPA.png
  [2]: https://i.sstatic.net/P8cgD.png