$($Zegbee WSN$)$ The figure below is showing a two clusters and a sink of a wireless sensor network.

$1-$ Identify the two cluster's node sets, the head of each cluster and the sink $($PAN coordinator$).$Each node is adopting three states: Transmit $($T$),$ Receive$($R$)$ and Sleep $($S$).$ The access in each cluster is in TDMA mode between cluster head and end$-$devices. Show in a table of $9$ time slots the status of each node in each.

$2-$ Determine the duty cycle of each node $($power saving rate$).$

$3-$ As each transmission is one time$-$slot duration, determine the latency of any end device data to reach the sink if only one super$-$frame is sent between F$-$E and D$-$E after collecting all end devices' frames.

$4-$ What is the power cost of each transmission from end device to sink$,$ if the transmission between a cluster head and the sink is having a cost of $3$ as indicated in the figure? Please note that $\frac{x}{Y}$ means $x$ is latency and $Y$ is the power cost of the link.