JustPaste.it

Task:

You are given an undirected unweighted graph and one of its vertexes.

Count the number of its connected components.


Input:

The first line contains a natural n (1 ≤ n ≤ 100) – the quantity of the graph’s vertexes.

The next n lines contain the adjacency matrix of the graph (0 means no edge, 1 means the edge exists).


Output:

The first line should contain the number of connected components.

The next each line should contain the length of a connected component, then the component itself.


Example:

Input

Output

4

0 1 1 0

1 0 0 0

1 0 0 0

0 0 0 0

2

3 1 2 3

1 4