Column ABC has a uniform rectangular cross section with $b=12mm$ and $d=22mm.$ The column is braced in the $xz$ plane at its midpoint $C$ and carries a centric load $P$ of magnitude $3\mathrm{.}8$ kN $.$ Knowing that a factor of safety of $3\mathrm{.}2$ is required, determine the largest allowable length $L.$ Use $E=200$GPa. Neglect the rotational stiffness of the bracing in the $xz$ plane and the lateral stiffness of the bracing in the $yz$ plane. $($Round the final answer to the nearest whole number.$)$

The allowable length $L$ is $$ mm $.$