$)$ Find the shortest path from node $0($source node$)$ to all other nodes using Dijkstra$$s algorithm. Show S$,$ Q$,$ and the distances of all nodes to node $0,$ every time you add a node to S$,$ by filling in the following table.

$$

Q

S

$0$

$1$

$2$

$3$

$4$

$5$

$6$

$7$

$8$

$\{0,1,2,3,4,5,6,7,8\}$

$$

$0$