The cardinal invariant $\mathfrak{hm}$ is defined as the minimum size of a family of $\mathsf{c}_{\mathsf{min}}$-monochromatic sets that cover $2^{\omega}$ (where $\mathsf{c}_{\mathsf{min}}\left( x,y\right)$ is the parity of the biggest initial segment both $x$ and $y$ have in common). We prove that $\mathfrak{hm}=\omega_{1}$ holds in the Shelah's model of $\mathfrak{i< u}$ so the inequality $\mathfrak{hm< u}$ is consistent with the axioms of $\mathsf{ZFC.}$ This answers a question of Thilo Weinert.