Number of Provinces

There are n cities. Some of them are connected, while some are not. If city a is connected directly with city b, and city b is connected directly with city c, then city a is connected indirectly with city c.

A province is a group of directly or indirectly connected cities and no other cities outside of the group.

You are given an n x n matrix isConnected where isConnected[i][j] = 1 if the ith city and the jth city are directly connected, and isConnected[i][j] = 0 otherwise.

Return the total number of provinces.

Examples

Example 1:

Input: isConnected = [[1,1,0],[1,1,0],[0,0,1]]

Output: 2

Explanation: Cities 0 and 1 are connected to each other, forming one province. City 2 is on its own, forming a second province.

Example 2:

Input: isConnected = [[1,0,0],[0,1,0],[0,0,1]]

Output: 3

Explanation: No cities are connected to each other, so each city is its own province.

Example 3:

Input: isConnected = [[1,1,0],[1,1,1],[0,1,1]]

Output: 1

Explanation: All three cities are connected (directly or indirectly), forming one province.

Constraints

• 1 <= n <= 200
• n == isConnected.length
• n == isConnected[i].length
• isConnected[i][j] is 1 or 0
• isConnected[i][i] == 1
• isConnected[i][j] == isConnected[j][i]