You are given two circles. One has a radius 1 and is centered at \((0, 1)\) in the Cartesian plane. The other has a radius 2 and is centered at \((2, 0)\). If the area of intersection of the circles is \( \mathfrak{E} \), then find \( \left \lfloor 1000 \mathfrak{E} \right \rfloor \).

**Notation**: \( \lfloor \cdot \rfloor \) denotes the floor function.

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