$1.$ Consider the following hash function. Messages are in the form of a sequence of numbers in Zn$,$M $=($a$1,$ a$2,...,$ at$).$ The hash value h is calculated as $($Pti$=1$ a$2$i $)$ mod n for some predefined value n$.$

$($a$)$ Does this hash function satisfy any of the requirements for a hash function listed bellow? Explain your answer for each case.

$$ It can be applied to a block of data of any size. $(5$ points$)$

$$ It produces a fixed$-$length output. $(5$ points$)$

$$ It is relatively easy to compute for any given input. $(5$ points$)$ Preimage resistance. $(10$ points$)$

$$ Secondary preimage resistance. $(10$ points$)$

$$ Collision resistance. $(10$ points$)$

$($b$)$ Compute the hash for M $=(120,145,224,657)$ for n $=981.(5$ points$)$