A file system implementation has the following characteristics

Block size is $2$k $(2048$ Bytes$)$

Block metadata size is $48$ Bytes

Maximum number of blocks supported is $100$

Four block types $($just like TinyFS$)$: Superblock, Inode, File Extent and Empty

Non$-$contiguous file storage $($none of the inode or file extent blocks need to be next to each other$)$

Inode blocks contain no file content, only file information like name, size, permissions, etc. which together take up only $1000$ Bytes total to store per file.

A number of small log files, $($each of size $12200$ Bytes$)$ are going to be constantly written to the file system or deleted from it$.$

How many total distinct log files can be stored in this system at the same time? $($show your work$)$