A closed$-$tube barometer has a height of $664$ mm when placed in a room at $\mathrm{.}88$ atm $($recall $1$ atm $=1\mathrm{.}01$x$105$ N$/$m$2)$ of pressure. If mercury has a density of $13,600$ kg$/$m$3,$ how tall would the barometer need to be if the liquid used inside it were honey $($density $1400$ kg$/$m$3)?$