Algorithms and Data Structures

# Remove the Vertex From the Graph

Given an undirected graph with `v` vertices and `e` edges, you are asked to print the “importance” of each vertex. To do that for each of the vertices, you should remove all the edges connected to them and print the adjacency matrix after removing the edges connected to that vertex. The importance of different vertices should be independent. So, removing the edges for one vertex shouldn't affect the edges for another.

#### Input

The first line of the input contains two integers `v` (1 ≤ v ≤ 50) and `e` (1 ≤ e ≤ 200).
The following `e` lines contain pairs of integers `v1`, `v2` (1 ≤ v1, v2 ≤ v) which means that the vertex `v1` is connected to the vertex `v2`.

#### Output

The program should print `v` adjacency matrices each separated by a newline. The adjacency matrices should represent the resulting connectivity of the graph after removing the corresponding vertex. The adjacency matrices should be ordered by the number of the vertex.

#### Examples

 Input Output 3 3 1 2 2 3 3 1 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0

#### Explanation

``````# The initial adjacency matrix
0 1 1
1 0 1
1 1 0

# After removing vertex 1
0 0 0
0 0 1
0 1 0

# After removing vertex 2
0 0 1
0 0 0
1 0 0

# After removing vertex 3
0 1 0
1 0 0
0 0 0``````

#### Constraints

Time limit: 1 seconds

Memory limit: 512 MB

Output limit: 1 MB