Let α,β,γ∈C be the roots of the polynomial x3−3x2+3x+7. For any complex number z, let f(z) be defined as follows:
f(z)=∣z−α∣+∣z−β∣+∣z−γ∣−2w∈{α,β,γmax}∣z−w∣.
Let A be the area of the region bounded by the locus of all z∈C at which f(z) attains its global minimum. Find ⌊A⌋.