Evaluate ${}_{S}f(x,y,z)dS,$ where $f(x,y,z)=x^2+y^2+z^2$ and $S$ is given by $z=x+y,x^2+y^{2}49.$

$2,401$

$2,401\sqrt[\phantom{2}]{3}$

$2,401\sqrt[\phantom{2}]{2}$

$2,401\sqrt[\phantom{2}]{3}$

$2,401$