maximize (2/r)^r*(1/(-4+4r))^(-2+2r)*(1/(4-2r))^(1-r/2)*(1/(-1+2r))^(-1/2+r)*(-2+3r)^(-2+3r)*(0.5+0.5*r)^(0.5+0.5*r) where 1 <= r <= 2

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