Given: an undirected graph.
How many edges must you remove to make it a tree? (Or a forest of trees?)

Input Specification

~N \le 1\,000~, the number of vertices.
An adjacency matrix, ~N~ rows with ~N~ numbers (0 or 1).
The matrix will be symmetrical (it is undirected!).

Output Specification

The minimum number of edges you have to remove.

Sample Input

3
0 1 1
1 0 1
1 1 0

Sample Output

1