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 mod = 1e9 + 7;
const int maxn = 5005;
struct edge {
  int to, cap, rev;
};
vector<edge> G[maxn];
int level[maxn];
int iter[maxn];
void gInit() {
  for (int i = 0; i < maxn; i++) G[i].clear();
}
void add_edge(int from, int to, int cap) {
  G[from].push_back((edge){to, cap, (int)G[to].size()});
  G[to].push_back((edge){from, 0, (int)G[from].size() - 1});
}
bool bfs(int s, int t) {
  memset(level, -1, sizeof(level));
  queue<int> que;
  level[s] = 0;
  que.push(s);
  while (!que.empty()) {
    int v = que.front();
    que.pop();
    for (int i = 0; i < (int)G[v].size(); i++) {
      edge &e = G[v][i];
      if (e.cap > 0 && level[e.to] < 0) {
        level[e.to] = level[v] + 1;
        que.push(e.to);
      }
    }
  }
  return level[t] != -1;
}
int dfs(int v, int t, int f) {
  if (v == t) return f;
  for (int &i = iter[v]; i < (int)G[v].size(); i++) {
    edge &e = G[v][i];
    if (e.cap > 0 && level[v] < level[e.to]) {
      int d = dfs(e.to, t, min(f, e.cap));
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
int max_flow(int s, int t) {
  int flow = 0, cur_flow;
  while (bfs(s, t)) {
    memset(iter, 0, sizeof(iter));
    while ((cur_flow = dfs(s, t, mod)) > 0) flow += cur_flow;
  }
  return flow;
}
int dl[maxn], dr[maxn];
pair<int, int> w[maxn];
struct node {
  vector<int> id;
  int pre, k;
  void add(int x) { id.push_back(x); }
  int ff(int c) {
    if (pre != c) {
      pre = c;
      k = 0;
    }
    return id[k++];
  }
} q[2005][2005];
int main() {
  int nl, nr, m, i, u, v;
  scanf("%d%d%d", &nl, &nr, &m);
  for (i = 1; i <= m; i++) {
    scanf("%d%d", &u, &v);
    w[i] = pair<int, int>(u, v);
    dl[u]++;
    dr[v]++;
    q[u][v].add(i);
  }
  for (u = 2000, i = 1; i <= nl; i++) u = min(u, dl[i]);
  for (i = 1; i <= nr; i++) u = min(u, dr[i]);
  for (v = 0; v <= u; v++) {
    gInit();
    for (i = 1; i <= nl; i++) add_edge(0, i, dl[i] - v);
    for (i = 1; i <= m; i++) add_edge(w[i].first, w[i].second + nl, 1);
    for (i = 1; i <= nr; i++) add_edge(i + nl, nl + nr + 1, dr[i] - v);
    i = m - max_flow(0, nl + nr + 1);
    printf("%d", i);
    for (i = 1; i <= nl; i++) {
      for (auto e : G[i]) {
        if (e.to != nl + nr + 1 && e.to && e.cap == 1)
          printf(" %d", q[i][e.to - nl].ff(v));
      }
    }
    puts("");
  }
  return 0;
}