A square column with a solid cross section is placed in a building to support a load of $5MN.$ The maximum allowable stress in the column is $350$MPa. The column reacts linearly to all loads. If the contractor is permitted to load the column anywhere in the central one$-$flfth of the column's cross section, what are most nearly the smallest possible dimensions of the column?

$($A$)12cm12cm$

$($B$)14cm14cm$

$($C$)16cm16cm$

$($D$)18cm18cm$