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A single vertical friction pile of diameter $500$ mm and length $20$ m is subjected to a vertical compressive load. The pile is embedded in a homogeneous sandy stratum where; angle of internal friction $(\phi)=30^{\circ}$, dry unit weight $(\gamma_d)=20 \: kN/m^3$ and angle of wall friction $(\delta)=2 \phi /3$. Considering the coefficient of lateral earth pressure $(K)=2.7$ and the bearing capacity factor $(N_q)=25$, the ultimate bearing capacity of the pile (in kN) is ________
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