Given the nodes and adjacency list of a graph, calculate the adjacency matrix for the it.

You have a graph with n nodes indexed from 0 to n-1. You are also given the adjacency list for each node.

You have to return the adjacency matrix for the given graph.

Example

Testing

Input Format

The first line contains an integer T denoting the number of test cases.

For each test case, the input has the following lines:

• The first line contains the integer n.
• The next n lines descibes the adjacent nodes for the i^th node.
  • The first integer m denotes the number of adjacent nodes.
  • The next m integers denote adjacent nodes.

Output Format

For each test case, the output has n lines denoting the adjacency matrix of the graph.

Sample Input

2
4
3 1 2 3
1 0
2 0 3
2 0 2
4
3 1 2 3
1 0
2 0 3
3 0 2 3

Expected Output

0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 0
0 1 1 1
1 0 0 0
1 0 0 1
1 0 1 1

Constraints

1 <= T <= 10
1 <= n <= 500
0 <= m <= n