Suppose that three switches are used to connect 10 hosts (h_0, h_1, ..., h_9). Assume switch s_1 is connected to h_0, h_1, h_2, h_3 and switch s_2 (using interfaces 1 to 5 respectively); s_2 is connected to hosts h_4, h_5, h_6 and switch s_1 and s_3 (via interfaces 1 to 5 respectively); and s_3 is connected to hosts h_7, h_8, h_9, and switch s_2 (via interfaces 1 to 4 respectively). Consider the transmission of a frame from host h_(X+Y mod 10) to host h_(X+Y+6 mod 10) and a reply back to the source.

Assuming the switch tables start empty, simulate the execution of the self-learning forwarding protocol by representing each transmission with the following notation: Ti: sender -> (dest1, dest2, ...) where sender is the sending host or switch, dest1destn are the set of destinations to which the message is sent, and T0, T1, T2, . etc. indicate increasing time steps. For example, a first transmission from h_0 to s_1 would be indicated with: T0: h_0 -> (s_1).

h_(0+6 mod 10) = 6

h_(0+6+6 mod 10) = 2

T₀: h_6 - (S2)

T_1: S2 -(h_4, h_5, h_6, S1)

T_2: S1-(h_0, h_1, h_2, h_3)

T_3: h_2 -(S1)

T_4: S1 - (S2)

T_5: S2 - (h_6)

Show the content of the tables in the three switches at the end of the execution, with the notation S_i = {(host1,interf1,T1), (host2, interf2, T2), ...}. For example, s_1 = {(h_0,1,T0)} indicates that switch s_1 has learnt that host h_0 is reachable through interface 1 at time T0.