Consider a CNN architecture with $10$ layers below.

$\backslash$table$[[$No$.,$Layer,Kernel,Padding,Stride,Output Channel$],[1,$Convolution,$5\backslash$times $5,2,2,16],[2,$Max Pooling,$2\backslash$times $2,-,2,16],[3,$Convolution,$5\backslash$times $5,2,1,32],[4,$Convolution,$5\backslash$times $5,1,1,32],[5,$Max Pooling,$2\backslash$times $2,-,2,32],[6,$Convolution,$3\backslash$times $3,,1,64],[7,$Convolution,$3\backslash$times $3,,1,128],[8,$Max Pooling,$5\backslash$times $5,-,2,128],[9,$Fully$-$connected,$-,-,-,256],[10,$Fully$-$connected,$-,-,-,10]]$

$(6$points$)$ Compute the total number of the parameters of the CNN$.$

$(20$points$)$ Suppose that the size of the input is $1351353($Height $x$ Width $x$ Channel$).$ Compute the size of the output of each layer.

$(6$points$)$ Modify the CNN by replacing the $6$th convolutional layer with a depth$-$wise convolution layer including a series of $33$ filters and $11$ filters. Compute the total number of the parameters of the modified CNN$.$