Minimal k-covering

Description:

Input:

The first line contains three integers n₁, n₂ and m (1 ≤ n₁, n₂ ≤ 2000, 0 ≤ m ≤ 2000) — the number of vertices in the first part, the number of vertices in the second part and the number of edges, respectively.

The i-th of the next m lines contain two integers u_i and v_i (1 ≤ u_i ≤ n₁, 1 ≤ v_i ≤ n₂) — the description of the i-th edge, u_i is the index of the vertex in the first part and v_i is the index of the vertex in the second part.

Output:

For each print the subset of edges (minimal k-covering) in separate line.

The first integer cnt_k of the k-th line is the number of edges in minimal k-covering of the graph. Then cnt_k integers follow — original indices of the edges which belong to the minimal k-covering, these indices should be pairwise distinct. Edges are numbered 1 through m in order they are given in the input.

Sample Input:

3 3 7
1 2
2 3
1 3
3 2
3 3
2 1
2 1

Sample Output:

0 
3 3 7 4 
6 1 3 6 7 4 5 

Sample Input:

1 1 5
1 1
1 1
1 1
1 1
1 1

Sample Output:

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