You are given a graph that has $9$ nodes, numbered $1$ to $9,$ and the following edges in sorted order by weight:

$(2,9),(1,3),(4,6),(2,8),(3,6),(5,6),(3,4),(2,7),(7,9),(1,6),(4,5).$

Run Kruskal's algorithm using a union$-$find array and update that array by processing the edges in the order received. When merging union$-$find "trees", connect the representative $($root$)$ of the lighter tree $($the one with the smaller number of nodes$)$ to the heavier tree $($the one with the larger number of nodes$).$ If the two trees have the same number of nodes, then connect the representative node with the larger value$/$index to the one with the smaller value$/$index$.$

Representative nodes will have initial values of $\text{'}0\text{'},$ meaning that every entry in the union$-$find array will be initialized to zero. Write below the contents of the union$-$find array once all edges have been processed.