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F. Minimal k-covering
time limit per test
1.5 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a bipartite graph G = (U, V, E), U is the set of vertices of the first part, V is the set of vertices of the second part and E is the set of edges. There might be multiple edges.

Let's call some subset of its edges k-covering iff the graph has each of its vertices incident to at least k edges. Minimal k-covering is such a k-covering that the size of the subset is minimal possible.

Your task is to find minimal k-covering for each , where minDegree is the minimal degree of any vertex in graph G.

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 ui and vi (1 ≤ ui ≤ n1, 1 ≤ vi ≤ n2) — the description of the i-th edge, ui is the index of the vertex in the first part and vi 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 cntk of the k-th line is the number of edges in minimal k-covering of the graph. Then cntk 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.

Examples
Input
3 3 7
1 2
2 3
1 3
3 2
3 3
2 1
2 1
Output
0 
3 3 7 4
6 1 3 6 7 4 5
Input
1 1 5
1 1
1 1
1 1
1 1
1 1
Output
0 
1 5
2 4 5
3 3 4 5
4 2 3 4 5
5 1 2 3 4 5