The figure below shows two $3$x$3$ sub$-$windows representing the

gradient of the corresponding sub$-$window of an input image in

the $$ and $$ directions, respectively. These values are calculated

as the first step of the Harris corner detection algorithm:

$021$

$1101$

$2101$

$$

$012$

$01010$

$122$

$$

Given the above values for $$ and $$ calculate the corresponding

auto$-$correlation matrix.