Minimum Edges to Connect Graph

You are given an undirected graph with n nodes and m edges. Your task is to determine the minimum number of edges that need to be added to make the graph fully connected.

The graph is represented by nodes numbered from 1 to n and a list of m edges, each connecting a pair of nodes. Two nodes are in the same connected component if there is a path between them.

Hint: If there are c connected components, then the minimum number of edges required is c - 1 (i.e. connect every component together).

Mathematically, if we denote the number of connected components as \( c \), the answer is:

[ \text{Answer} = c - 1 ]

inputFormat

The first line of input contains a single integer T representing the number of test cases. The description of each test case follows.

For each test case, the first line contains two integers n and m, where n is the number of nodes and m is the number of edges. The next m lines each contain two integers u and v representing an edge between nodes u and v.

outputFormat

For each test case, output a single integer on a new line which is the minimum number of additional edges required to make the graph fully connected.

## sample

3
5 3
1 2
2 3
4 5
4 0
3 3
1 2
2 3
1 3

1
3
0

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