You are given a rectangular grid of $0$s and $1$s$,$ where the $0$s represent water and the $1$s represent land. A land$-$cell

is connected to another if the two are adjacent $($horizontally$,$ vertically and diagonally$).$ All the land$-$cells that are

connected in this manner form an island and the number of land$-$cells in the island define the island size. In the

following example, there are a total of $6$ islands, their sizes being $2,4,5,7,11$ and $12.$

Every island is connected via bridges to the smallest island larger than itself and to the largest island smaller

than itself. In addition, there is a bridge between two islands if their sizes have the same sum$-$of$-$digits. In the

example, there are bridges between the islands