For a complex number z, let Re(z) denote the real part of z. Let S be the set of all complex numbers z satisfying z⁴ − |z|⁴ = 4iz², where i = √−1. Then the minimum possible value of |z₁ − z₂|², where z₁, z₂ ∈ S with Re(z₁) > 0 and Re(z₂) < 0, is _____.