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 MAXN = 1e5 + 10;
const int MAXM = 1e5 + 10;
struct Edge {
  int to, next, cap;
  int id;
} edge[MAXM];
int tot, head[MAXN];
inline void init() {
  tot = 0;
  memset(head, -1, sizeof(head));
}
inline void add_edge(int u, int v, int w, int id = -1) {
  edge[tot] = (Edge){v, head[u], w, id};
  head[u] = tot++;
  edge[tot] = (Edge){u, head[v], 0, -1};
  head[v] = tot++;
}
int dep[MAXN];
bool bfs(int s, int t) {
  memset(dep, -1, sizeof(dep));
  dep[s] = 0;
  queue<int> Q;
  Q.push(s);
  while (!Q.empty()) {
    int u = Q.front();
    Q.pop();
    for (int i = head[u]; ~i; i = edge[i].next) {
      int v = edge[i].to;
      if (dep[v] == -1 && edge[i].cap) {
        dep[v] = dep[u] + 1;
        Q.push(v);
      }
    }
  }
  return ~dep[t];
}
int cur[MAXN];
int dfs(int u, int t, int r) {
  if (u == t || r == 0) return r;
  int flow(0), f;
  for (int &i = cur[u]; ~i; i = edge[i].next) {
    int v = edge[i].to;
    if (dep[v] == dep[u] + 1 && (f = dfs(v, t, min(r, edge[i].cap))) > 0) {
      edge[i].cap -= f;
      edge[i ^ 1].cap += f;
      flow += f;
      if (!(r -= f)) break;
    }
  }
  return flow;
}
int dinic(int s, int t) {
  int maxflow(0);
  while (bfs(s, t)) {
    memcpy(cur, head, sizeof(head));
    maxflow += dfs(s, t, INF);
  }
  return maxflow;
}
int n1, n2, m, u, v;
int deg[MAXN];
vector<int> output[MAXN];
int main() {
  init();
  memset(deg, 0, sizeof(deg));
  scanf("%d%d%d", &n1, &n2, &m);
  for (int i = 1; i <= m; ++i) {
    scanf("%d%d", &u, &v);
    ++deg[u];
    ++deg[v + n1];
    add_edge(u, v + n1, 1, i);
  }
  int minD = INF;
  for (int i = 1; i <= n1 + n2; ++i) minD = min(minD, deg[i]);
  int s = 0, t = n1 + n2 + 1;
  for (int i = 1; i <= n1; ++i) add_edge(s, i, deg[i] - minD);
  for (int i = n1 + 1; i <= n1 + n2; ++i) add_edge(i, t, deg[i] - minD);
  for (int k = minD; k >= 0; --k) {
    dinic(s, t);
    for (int u = 1; u <= n1; ++u) {
      for (int i = head[u]; ~i; i = edge[i].next) {
        if (edge[i].id != -1 && edge[i].cap) output[k].push_back(edge[i].id);
      }
    }
    for (int i = head[s]; ~i; i = edge[i].next) ++edge[i].cap;
    for (int i = head[t]; ~i; i = edge[i].next) ++edge[i ^ 1].cap;
  }
  for (int i = 0; i <= minD; ++i) {
    int cnt = output[i].size();
    printf("%d", cnt);
    for (int j = 0; j < cnt; ++j) {
      printf(" %d", output[i][j]);
    }
    puts("");
  }
  return 0;
}