Problem $3$ Push$-$Relabel algorithm $[10$ marks$]$

Trace the Push$-$Relabel algorithm on the following graph and show the residual network after each augmentation $($show height and excess of all nodes$).$ In the case of multiple vertices with positive excess and maximum height, choose the one who comes first in the alphabet. Similarly, in the case of multiple downhill edges, choose the one whose other endpoint come first in the alphabetic order.