Question $1$

A hash table with $10$ buckets uses the hash function f$($x$)=$ x $\%10,$ and linear probing to resolve collisions. If the keys

$[$

$8$

$,$

$165$

$,$

$232$

$,$

$213$

$,$

$197$

$]$

$[8,165,232,213,197]$

are inserted in that order into the hash table, what is the greatest number of steps a key can be from its natural position in the table?