The following state diagram is given as basis for state transition testing and contains only valid transitions:

Explanation of the state diagram: States are depicted as nodes. The initial state is I, the final state is F. A state transition is depicted as a directed arrow with the initiating event as a label, e. g. from I to S1 with event a, and is also written as a triple (I,a,S1). Note: A test case is a sequence of events that initiates the corresponding sequence of state transitions.

The state diagram contains the following 7 state transitions:

(I, a, S1)

(S1, a, S2), (S1, b, S3), (S1, c, F)

(S2, a, S3)

(S3, a, S2), (S3, b, F)

What is the minimum number of test cases to achieve 100% coverage of all valid state transitions in the diagram?