Question $7$ Assume an open addressing hash table implementation, where the size of the array is N$=19,$ and that double hashing is performed for collision handling. The second hash function is defined as: d$($k$)=$q$-$k modq $,$ where k is the key being inserted in the table and the prime number q is $=7.$ Use simple modular operation $($kmodN$)$ for the first hash function. i$)$ Show the content of the table after performing the following operations, in order: put$(45),$ put$(25),$ put$(12),$ put$(61),$ put$(38),$ put$(88),$ remove$(12),$ put$(39),$ remove$(61),$ put$(18),$ put$(29),$ put$(29),$ put$(35).$ i$)$ What is the size of the longest cluster caused by the above insertions? ii$)$ What is the number of occurred collisions as a result of the above operations? iii$)$ What is the current value of the table's load factor?