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 = 2000 * 2 + 5;
const int INF = int(1e9) + 5;
namespace Dinic {
struct Edge {
  int from, to, cap, flow;
};
bool operator<(const Edge &a, const Edge &b) {
  return a.from < b.from || (a.from == b.from && a.to < b.to);
}
int n, m, s, t;
vector<Edge> edges;
vector<int> G[maxn];
vector<Edge> edges_copy;
void copy() { edges_copy = edges; }
void recover() { edges = edges_copy; }
bool vis[maxn];
int d[maxn], cur[maxn];
void init(int n) {
  for (int i = 0; i < n; i++) {
    G[i].clear();
  }
  edges.clear();
}
void add_edge(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));
  queue<int> Q;
  Q.push(s);
  vis[s] = 1;
  d[s] = 0;
  while (!Q.empty()) {
    int x = Q.front();
    Q.pop();
    for (int i = 0; i < (int)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 < (int)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 max_flow(int s, int t) {
  memset(d, 0, sizeof(d));
  Dinic::s = s, Dinic::t = t;
  int flow = 0;
  while (bfs()) {
    memset(cur, 0, sizeof(cur));
    flow += dfs(s, INF);
  }
  return flow;
}
}  // namespace Dinic
int u[maxn], v[maxn];
int deg[maxn];
int main() {
  int n1, n2, m;
  scanf("%d%d%d", &n1, &n2, &m);
  int s = 0, t = n1 + n2 + 1;
  for (int i = 0; i < m; i++) {
    scanf("%d%d", u + i, v + i);
    deg[u[i]]++;
    deg[n1 + v[i]]++;
    Dinic::add_edge(u[i], n1 + v[i], 1);
  }
  int min_deg = INF;
  for (int i = 1; i <= n1 + n2; i++) {
    min_deg = min(deg[i], min_deg);
  }
  Dinic::copy();
  for (int flow = 0; flow <= min_deg; flow++) {
    for (int i = 1; i <= n1; i++) {
      Dinic::add_edge(s, i, deg[i] - flow);
    }
    for (int i = 1; i <= n2; i++) {
      Dinic::add_edge(n1 + i, t, deg[n1 + i] - flow);
    }
    printf("%d", m - Dinic::max_flow(s, t));
    for (int i = 0; i < m; i++) {
      auto &e = Dinic::edges[i * 2];
      if (e.flow == 0 and e.from != s and e.to != t) {
        printf(" %d", i + 1);
      }
    }
    putchar('\n');
    Dinic::recover();
  }
}