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 $\text{[math]}$ k-covering iff the graph $\text{[math]}$ 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 $\text{[math]}$ is minimal possible.

Your task is to find minimal k-covering for each $\text{[math]}$ , 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 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 $\text{[math]}$ 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.

Minimal k-covering

Examples