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There are N students in the class. Some of them are friends and some are not. Their friendship is transitive. If we know that An is a friend of B and B is a friend of C, then we can think that An is also a friend of C. The so-called moments refers to the collection of all friends.

Given a matrix M of N * N, it represents the friend relationship between the middle school students in the class. If M [I] [j] = 1, it means that the I and j students are known to be friends with each other, otherwise they do not know. You must output the total number of known moments among all the students.

Example 1:

Enter:

[[1,1,0]

[1,1,0]

[0,0,1]]

Output: 2

Explanation: it is known that student 0 and student 1 are friends with each other, and they are in a circle of friends.

The second student himself is in a circle of friends. So return 2.

Example 2:

Enter:

[[1,1,0]

[1,1,1]

[0,1,1]]

Output: 1

Explanation: it is known that student 0 and student 1 are friends with each other, and student 1 and student 2 are friends with each other, so student 0 and student 2 are also friends, so the three of them are in a circle of friends and return 1.

Note:

N is within the range of [1200].

For all students, M [I] [I] = 1.

If there is M [I] [j] = 1, then M [j] [I] = 1.

Ideas for solving the problem:

1, because a friend's friend is still a friend, the first thing to think of is depth-first traversal.

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