$2.$ Consider a processor with a virtually$-$indexed physically$-$tagged $($VIPT$)$ cache. The cache capacity is $64$KB with a block size of $128$B$.$ The page size in the system is $4$KB$.$ You use the standard set indexing scheme on the virtual address, but the tag comes from the physical address as shown:

Virtual Address: set index block offset

Physical Address: tag block offset

VIPT caches may be prone to the synonym problem. Recall that synonyms are virtual addresses that map to the same physical address. If unhandled, a physical block may wrongfully exist in the cache at more than one location at any time, which leads to incorrect behavior $($i$.$e$.,$ one instance of the block becomes stale if the other instance is modified$).$ b$)$ Without changing the VIPT cache capacity $(64$KB$),$ block size $(128$B$)$ and page size $(4$KB$),$ what is the minimum associativity needed such that synonyms would not be a problem?