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Backbone Fast is used to recover from indirect link failure and for a fast convergence in the backbone

Switch B Connected to Switch A (Root Switch)
Switch C Connected to Switch A (Root Switch)
When Backbone fast enabled and indirect link failure
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When Backbone fast enabled, Non designated port will accept the inferior BPDU
If we enable backbone fast it will skip the max age timer
so we can save 20 seconds of time.( 30 seconds of delay)
When backbone fast enabled and due to indirect link failure
Switch C when receives a inferior BPDU , it will send a Root Link Query (RLQ)---for finding alternate path to root bridge
On both Non designated Port and Root Ports
Now Switch C receives a reply for RLQ from root bridge and will now skip the max age timer (20 seconds)
Interface will go from listening to learning and learning to forwarding (30 seconds)