Consider the following simple modification to Protocol ElectMesh: When sending a wake-up message, a node includes the information of whether it is an internal, a border, or a corner node. Then, during the first stage of the election, a border node uses this information if possible to send the election message only along the outer ring (it might not be possible.). Show that the protocol so modified uses at most 4(a +

b) + 5n + k
− 32 messages.