$$\mathfrak{U} = \left(\begin{matrix}
x_{11} & x_{12} & x_{13} \\
x_{21} & x_{22} & x_{23} \\
x_{31} & x_{32} & x_{33}
\end{matrix}\right)$$
$$\begin{align}
f(\mathfrak{U}) & = \left(\begin{matrix}
\underbrace{(x_{11} + x_{12} + x_{13})}_\cdot \\
\overbrace{\underbrace{(x_{21} + x_{22} + x_{23})}}_\cdot \\
\overbrace{(x_{31} + x_{32} + x_{33})} \\
\end{matrix}\right) \\
& = (x_{11} + x_{12} + x_{13}) \cdot (x_{21} + x_{22} + x_{23}) \cdot (x_{31} + x_{32} + x_{33})
\end{align}$$
$$\begin{matrix}
40 & 30 & 42 & 22 & 74 \\
294 & 97 & \color{red} {35} & \color{red}{272} & \color{red}{167} \\
52 & 8 & \color{red}{163} & \color{red}{270} & \color{red}{242} \\
247 & 130 & \color{red}{216} & \color{red} {68} & \color{red}{266} \\
283 & 245 & 164 & 53 & 148 \\
\end{matrix}$$
The part highlighted in red is the part where the value of the function
\$f(\mathfrak{U})\$ is largest for the entire grid:
(35 + 272 + 167) ⋅ (163 + 270 + 242) ⋅ (216 + 68 + 266) = 175972500\$(35 + 272 + 167) ⋅ (163 + 270 + 242) ⋅ (216 + 68 + 266) = 175972500\$
Output is the result of the function \$f(\mathfrak{U})\$ for the 3×3 sub-grid that
gives the largest result. In above example this would have been
175972500\$175972500\$.
