Using the separability property where appropriate, write the minimum total number of arithmetic operations $($number of additions and multiplications summed together$)$ per sample needed to filter a $2$D image with each of the given filters.

Assume that the size of the filtered $2$D image is

$$

$\backslash$times

$$

N$\backslash$times N$,$ where

$$

N is very large.

Write the minimum number of arithmetic operations separated by a space, from the one corresponding to the filter

$$

$1$

f

$1$

$$

to the one corresponding to

$$

$4$

f

$4$

$$

$.$

For example, if

$$

$1$

f

$1$

$$

required $1$ addition and $1$ multiplication per sample,

$$

$2$

f

$2$

$$

$2$ additions and $2$ multiplications per sample,

$$

$3$

f

$3$

$$

$3$ additions and $3$ multiplications per sample, and

$$

$4$

f

$4$

$$

$4$ additions and $4$ multiplications per sample, the correct answer would be: