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 MAXN = 10000, INF = 1e8;
int N1, N2, M;
int A[MAXN], B[MAXN];
struct edge {
  int v;
  int flow, cap;
  int rev, id;
};
int lev[MAXN], start[MAXN];
vector<edge> adj[MAXN];
int deg[MAXN];
void addedge(int u, int v, int c, int i) {
  edge euv = {v, 0, c, int(adj[v].size()), i};
  edge evu = {u, 0, 0, int(adj[u].size()), i};
  adj[u].push_back(euv);
  adj[v].push_back(evu);
}
bool dinic_bfs(int src, int dest, int *dist) {
  for (int i = 0; i <= N1 + N2 + 1; i++) {
    dist[i] = -1;
  }
  dist[src] = 0;
  queue<int> que;
  que.push(src);
  while (!que.empty()) {
    int u = que.front();
    que.pop();
    for (edge e : adj[u]) {
      if (dist[e.v] < 0 && e.flow < e.cap) {
        dist[e.v] = dist[u] + 1;
        que.push(e.v);
      }
    }
  }
  return dist[dest] >= 0;
}
int dinic_dfs(int *ptr, int *dist, int dest, int u, int f) {
  if (u == dest) {
    return f;
  }
  for (; ptr[u] < adj[u].size(); ptr[u]++) {
    edge &e = adj[u][ptr[u]];
    if (dist[e.v] == dist[u] + 1 && e.flow < e.cap) {
      int df = dinic_dfs(ptr, dist, dest, e.v, min(f, e.cap - e.flow));
      if (df > 0) {
        e.flow += df;
        adj[e.v][e.rev].flow -= df;
        return df;
      }
    }
  }
  return 0;
}
int dist[MAXN];
int ptr[MAXN];
int maxflow(int src, int dest) {
  int flow = 0;
  for (int i = 0; i <= N1 + N2 + 1; i++) {
    dist[i] = 0;
  }
  while (dinic_bfs(src, dest, dist)) {
    for (int i = 0; i <= N1 + N2 + 1; i++) {
      ptr[i] = 0;
    }
    while (true) {
      int df = dinic_dfs(ptr, dist, dest, src, INF);
      if (df == 0) {
        break;
      }
      flow += df;
    }
  }
  return flow;
}
vector<int> go(int d) {
  for (int i = 0; i <= N1 + N2 + 1; i++) {
    adj[i].clear();
  }
  for (int i = 1; i <= N1; i++) {
    addedge(0, i, deg[i] - d, -1);
  }
  for (int i = N1 + 1; i <= N1 + N2; i++) {
    addedge(i, N1 + N2 + 1, deg[i] - d, -1);
  }
  for (int i = 1; i <= M; i++) {
    addedge(A[i], B[i], 1, i);
  }
  maxflow(0, N1 + N2 + 1);
  vector<int> ans;
  for (int i = 1; i <= N1; i++) {
    for (edge e : adj[i]) {
      if (N1 + 1 <= e.v && e.v <= N1 + N2 && !e.flow) {
        ans.push_back(e.id);
      }
    }
  }
  return ans;
}
int main() {
  scanf("%d %d %d", &N1, &N2, &M);
  for (int i = 1; i <= M; i++) {
    scanf("%d %d", &A[i], &B[i]);
    B[i] += N1;
    deg[A[i]]++;
    deg[B[i]]++;
  }
  int mndeg = *min_element(deg + 1, deg + N1 + N2 + 1);
  for (int i = 0; i <= mndeg; i++) {
    vector<int> ans = go(i);
    printf("%lu", ans.size());
    for (int x : ans) {
      printf(" %d", x);
    }
    puts("");
  }
}