# Amazon Online Assessment (OA) - Friend Circles

There are `N` students in a class. Some of them are friends, while some are not. Their friendship is transitive in nature.

For example, if `A` is a direct friend of `B`, and `B` is a direct friend of `C`, then `A` is an indirect friend of `C`. And we defined a friend circle is a group of students who are direct or indirect friends.

Given a `N*N` matrix `M` representing the friend relationship between students in the class. If `M[i][j] = 1`, then the `i`th and `j`th students are direct friends with each other, otherwise not. And you have to output the total number of friend circles among all the students.

### Examples

#### Example 1:

##### Input:
``````1[[1,1,0],
2[1,1,0],
3[0,0,1]]``````
##### Explanation :

The `0`th and `1`st students are direct friends, so they are in a friend circle.

The `2`nd student himself is in a friend circle. So return `2`.

#### Example 2:

##### Input:
``````1[[1,1,0],
2[1,1,1],
3[0,1,1]]``````
##### Explanation :

The `0`th and `1`st students are direct friends, the `1`st and `2`nd students are direct friends,

so the `0`th and `2`nd students are indirect friends. All of them are in the same friend circle, so return `1`.

#### Constraints:

• `1 <= N <= 200`
• `M[i][i] == 1`
• `M[i][j] == M[j][i]`

## Title

### Script

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2  >>> a[-1]
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