LogiQuest

289. Friend Circles

EasyDFSAdjacency Matrix

M[i][j] = 1 means person i and j are friends (the matrix is symmetric with 1s on the diagonal). Print the number of friend circles (connected groups).

Input format

Line 1: n Next n lines: n values

Output format

The number of circles.

Example 1

Input

3
1 1 0
1 1 0
0 0 1

Output

2

Example 2

Input

3
1 0 0
0 1 0
0 0 1

Output

3

Constraints

1 ≤ n ≤ 200

Read input from standard input and print the answer to standard output. Your code is judged against 3 test cases, most of them hidden.

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