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Problems

Connected components

Connected components

Time limit 1 second
Memory limit 128 MiB

The undirected unweighted graph is given. Find the number of its connected components.

Input data

The first line contains the number of vertices n\:(n \le 100) in the graph. Then, in n lines, an n by n matrix is given — the adjacency matrix of the graph. In the i-th row, at the j-th position, there is a 1 if vertices i and j are connected by an edge, and 0 if there is no edge between them. The main diagonal of the matrix contains zeroes. The matrix is symmetric with respect to the main diagonal.

Output data

Print the number of connected components in a graph.

Examples

Input example #1
6
0 1 1 0 0 0
1 0 1 0 0 0
1 1 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 0 0 0
Output example #1
3
Source 2011 Summer school, Sevastopol, August 8, Day 1, League 1