Given $n$ cities, some are directly connected, and others are not. You are given an $n \times n$ matrix called cities, where cities[i][j] $= 1$ means city $i^{th}$ and city $j^{th}$ are directly connected, and cities[i][j] $= 0$ means they are not directly connected.

Note: If city $A$ is directly connected to city $B$ and city $B$ is directly connected to city $C$, then city $A$ is indirectly connected to city $C$.

The task is to return the total number of groups of connected cities directly or indirectly. These groups are referred to as provincesA province is a group of directly or indirectly connected cities with no other cities outside of the group..

Constraints:

• $1\leq$ $n$ $\leq200$

• $n ==$ cities.length

• $n ==$ cities[i].length, where $0\leq$ $i$ $\leq n$

• cities[i][j] is either $0$ or $1$.

• cities[i][i] $== 1$

• cities[i][j] $==$ cities[j][i]