A square concrete pile of $10\: m$ length is driven into a deep layer of uniform homogeneous clay. Average unconfined compressive strength of the clay, determined through laboratory tests on undisturbed samples extracted from the clay layer, is $100$ $\text{kPa}$. If the ultimate compressive load capacity of the driven pile is $632$ $\text{kN}$, the required width of the pile is________________ $\text{mm}$. (in integer)
(Bearing capacity factor $N_{c} = 9$; adhesion factor $\alpha = 0.7$)