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 INF = 0x3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-6;
struct Edge {
  int from, to, cap, flow;
  Edge(int u, int v, int c, int f) : from(u), to(v), cap(c), flow(f) {}
};
const int maxn = 1 << 12;
struct Dinic {
  int n, m, s, t;
  vector<Edge> edges;
  vector<int> G[maxn];
  bool vis[maxn];
  int d[maxn];
  int cur[maxn];
  void init(int n) {
    this->n = n;
    for (int i = 0; i < n; i++) G[i].clear();
    edges.clear();
  }
  void AddEdge(int from, int to, int cap) {
    edges.push_back(Edge(from, to, cap, 0));
    edges.push_back(Edge(to, from, 0, 0));
    m = edges.size();
    G[from].push_back(m - 2);
    G[to].push_back(m - 1);
  }
  bool BFS() {
    memset(vis, 0, sizeof(vis));
    memset(d, 0, sizeof(d));
    queue<int> q;
    q.push(s);
    d[s] = 0;
    vis[s] = 1;
    while (!q.empty()) {
      int x = q.front();
      q.pop();
      for (int i = 0; i < G[x].size(); i++) {
        Edge& e = edges[G[x][i]];
        if (!vis[e.to] && e.cap > e.flow) {
          vis[e.to] = 1;
          d[e.to] = d[x] + 1;
          q.push(e.to);
        }
      }
    }
    return vis[t];
  }
  int DFS(int x, int a) {
    if (x == t || a == 0) return a;
    int flow = 0, f;
    for (int& i = cur[x]; i < G[x].size(); i++) {
      Edge& e = edges[G[x][i]];
      if (d[x] + 1 == d[e.to] && (f = DFS(e.to, min(a, e.cap - e.flow))) > 0) {
        e.flow += f;
        edges[G[x][i] ^ 1].flow -= f;
        flow += f;
        a -= f;
        if (a == 0) break;
      }
    }
    return flow;
  }
  int Maxflow(int s, int t) {
    this->s = s;
    this->t = t;
    int flow = 0;
    while (BFS()) {
      memset(cur, 0, sizeof(cur));
      flow += DFS(s, INF);
    }
    return flow;
  }
  vector<int> get_answer(int k, int n, int m) {
    vector<int> ans;
    for (int i = 1; i <= n; i++) {
      for (auto& id : G[i]) {
        Edge& e = edges[id];
        if (e.to == 0 || e.to == n + m + 1) continue;
        if (e.cap == e.flow) continue;
        ans.push_back((id >> 1) + 1);
      }
    }
    if (k) {
      for (auto& id : G[s]) edges[id].cap++;
      for (auto& id : G[t]) edges[id ^ 1].cap++;
    }
    return ans;
  }
} gao;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n, m, q;
  cin >> n >> m >> q;
  vector<int> deg(n + m + 1);
  deg[0] = INF;
  gao.init(n + m + 2);
  int s = 0, t = n + m + 1;
  while (q--) {
    static int u, v;
    cin >> u >> v;
    gao.AddEdge(u, n + v, 1);
    ++deg[u], ++deg[n + v];
  }
  int k = *min_element(deg.begin(), deg.end());
  for (int i = 1; i <= n; i++) gao.AddEdge(s, i, deg[i] - k);
  for (int i = 1; i <= m; i++) gao.AddEdge(n + i, t, deg[n + i] - k);
  vector<vector<int> > ans(k + 1);
  for (int i = k; ~i; i--) {
    int flow = gao.Maxflow(s, t);
    ans[i] = gao.get_answer(i, n, m);
  }
  for (int i = 0; i <= k; i++) {
    cout << ans[i].size();
    for (auto& t : ans[i]) cout << " " << t;
    cout << endl;
  }
  return 0;
}