Description

User friendships are given for a new SNS service. Users who are directly friends or connected through friends belong to the same group. Find the total number of friend groups.

Input

Output

Constraints

• •1 ≤ N ≤ 200
• •friends[i][i] = 1 (self)
• •friends[i][j] = friends[j][i] (symmetric)

Examples

7
[[1,1,0,0,0,0,0],
 [1,1,1,0,0,0,0],
 [0,1,1,0,0,0,0],
 [0,0,0,1,1,0,0],
 [0,0,0,1,1,0,0],
 [0,0,0,0,0,1,1],
 [0,0,0,0,0,1,1]]

3