Problem: 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 <image> k-covering iff the graph <image> 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 <image> is minimal possible.

Your task is to find minimal k-covering for each <image>, 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 <image> 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 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int N = 4040, INF = 2e4;
struct Edge {
  int from, to, flow;
};
struct MaxFlow {
  int B[N], qu[N];
  vector<Edge> E;
  vector<int> Adj[N];
  void Add(int v, int u, int cap) {
    Adj[v].push_back(E.size());
    E.push_back(Edge{v, u, cap});
    Adj[u].push_back(E.size());
    E.push_back(Edge{u, v, 0});
  }
  bool BFS(int s, int t) {
    memset(B, -1, sizeof(B));
    B[s] = -2;
    int l = 0, r = 0;
    qu[r++] = s;
    while (r - l) {
      int nw = qu[l++];
      if (nw == t) return (1);
      for (int i = 0; i < Adj[nw].size(); ++i) {
        Edge& edge = E[Adj[nw][i]];
        if (edge.flow && B[edge.to] == -1)
          B[edge.to] = Adj[nw][i], qu[r++] = edge.to;
      }
    }
    return (0);
  }
  int GetMaxFlow(int s, int t) {
    int Flow = 0;
    while (BFS(s, t)) {
      int nw = t, _Flow = INF;
      while (B[nw] != -2) {
        Edge& edge = E[B[nw]];
        _Flow = min(_Flow, edge.flow), nw = edge.from;
      }
      nw = t;
      while (B[nw] != -2) {
        Edge &edge = E[B[nw]], &edge2 = E[B[nw] ^ 1];
        edge.flow -= _Flow;
        edge2.flow += _Flow;
        nw = edge.from;
      }
      Flow += _Flow;
    }
    return (Flow);
  }
};
int n1, n2, m, Mnd = INF, D[N];
vector<int> Res[N];
int32_t main() {
  MaxFlow G;
  scanf("%d%d%d", &n1, &n2, &m);
  for (int i = 1, a, b; i <= m; i++)
    scanf("%d%d", &a, &b), D[a]++, D[n1 + b]++, G.Add(a, n1 + b, 1);
  for (int i = 1; i <= n1 + n2; i++) Mnd = min(Mnd, D[i]);
  for (int i = 1; i <= n1; i++) G.Add(0, i, D[i] - Mnd);
  for (int i = n1 + 1; i <= n1 + n2; i++) G.Add(i, n1 + n2 + 1, D[i] - Mnd);
  for (int t = Mnd; t; t--) {
    G.GetMaxFlow(0, n1 + n2 + 1);
    for (int i = 1; i <= n1; i++)
      for (auto X : G.Adj[i])
        if (G.E[X].to && G.E[X].flow) Res[t].push_back((X + 2) >> 1);
    for (int i = 1; i <= n1; i++) G.Add(0, i, 1);
    for (int i = n1 + 1; i <= n1 + n2; i++) G.Add(i, n1 + n2 + 1, 1);
  }
  for (int i = 0; i <= Mnd; i++) {
    printf("%d", Res[i].size());
    for (auto X : Res[i]) printf(" %d", X);
    puts("");
  }
  return (0);
}