a$)$ We want to build a wireless sensor network monitoring the occurrence of lighting in storms$$by means of light sensors$.$ Sensor nodes are thereby placed on roof tops of different buildings. Readings are propagated to a base station using multi$-$hop Zigbee$$mesh communication. Not all nodes are equipped with a light sensor; some solely serve as communication relays $($Routers$).$ Furthermore, all devices are battery driven. The system should run for several months without human intervention. Message delay is not of primary importance.

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Consider the maximum number of children $($Cm$)$ of a ZigBee router, the maximum number of child routers $($Rm$)$ of a parent node, and the depth of the network $($Lm$)$ are $6,5,$ and $4$ respectively.

i$.$ Calculate the maximum number of end nodes in this network.

ii$.$ Calculate different CSkip$$of the network.