An organization wants to implement a full mesh FC SAN. The following is the specification of servers, storage systems, and switches involved in the design:

Number of hosts = 30. Each host has two single-port HBAs

Number of storage arrays = 4. Each array has eight front-end ports.

Available switching elements:

a. Modular FC switches with minimum 16 ports. The number of ports in a switch can be increased up to 32 ports by adding additional port cards. Each port card includes 8 ports.

b. At least two inter-switch links (ISLs) must exist between any two switches to ensure high availability.

At a minimum, how many switches are required to meet the given requirements? Justify the number of ports in each FC switch considering cost optimization.