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.

Example

Input: isConnected = [
  [1, 1, 0],
  [1, 1, 0],
  [0, 0, 1],
];
Output: 2;

Solution

/**
 * @param {number[][]} isConnected
 * @return {number}
 */
var findCircleNum = function (isConnected) {};