Given a $4 \times 4$ image, find the $4 \times 4$ enhanced output using the $3 \times 3$ Laplacian sharpening filter with the borders periodically extended.
$$
x(m, n)=\left[\begin{array}{llll}
138 & 163 & 162 & 177 \\
148 & 157 & 167 & 175 \\
153 & 165 & 160 & 178 \\
157 & 162 & 164 & 188
\end{array}\right]
$$