$79.$ N A jack$-$in$-$the$-$box with a box of mass $\backslash ($ M $\backslash )$ and clown of mass $\backslash ($ m$=200\mathrm{.}0\backslash$mathrm$\{$~g$\}\backslash )$ rests on a horizontal table $($Fig$.$ P$8\mathrm{.}50).$ The clown is attached to the box by means of a lightweight, vertical spring with force constant $\backslash ($ k$=1\mathrm{.}00\backslash$times $10^\{2\}\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash ).$ Zara pushes down on the clown with an additional force of $4$ mg $,$ further compressing the spring. When Zara removes her hand, the clown jumps upward, and the spring lifts the box off the table. What is the maximum value for the mass $\backslash ($ M $\backslash )$ of the box for this action to occur?