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 N = 5007, M = 2e4 + 7, INF = 1e9;
int edge[M], succ[M], cap[M], ver[N], idx;
int cur[N], dep[N], deg[N], link[M];
int n, m, s, t;
void add(int u, int v, int c) {
  edge[idx] = v;
  cap[idx] = c;
  succ[idx] = ver[u];
  ver[u] = idx++;
}
bool bfs() {
  memset(dep, 0, sizeof dep);
  queue<int> q;
  q.push(s);
  dep[s] = 1;
  cur[s] = ver[s];
  while (!q.empty()) {
    int u = q.front();
    q.pop();
    for (int i = ver[u]; ~i; i = succ[i]) {
      int v = edge[i];
      if (cap[i] && !dep[v]) {
        dep[v] = dep[u] + 1;
        q.push(v);
        cur[v] = ver[v];
        if (v == t) return 1;
      }
    }
  }
  return 0;
}
int dinic(int u, int limit) {
  if (u == t) return limit;
  int flow = 0, k;
  for (int i = cur[u]; ~i && flow < limit; i = succ[i]) {
    cur[u] = i;
    int v = edge[i];
    if (cap[i] && dep[v] == dep[u] + 1) {
      k = dinic(v, min(limit - flow, cap[i]));
      if (!k) dep[v] = -1;
      cap[i] -= k;
      cap[i ^ 1] += k;
      flow += k;
    }
  }
  return flow;
}
int dinic() {
  int res = 0, flow;
  while (bfs())
    while (flow = dinic(s, INF)) res += flow;
  return res;
}
int main() {
  memset(ver, -1, sizeof ver);
  int n1, n2, m;
  scanf("%d%d%d", &n1, &n2, &m);
  s = 0, t = n1 + n2 + 1;
  for (int i = 1; i <= m; ++i) {
    int u, v;
    scanf("%d%d", &u, &v);
    v += n1;
    add(u, v, 1);
    ++deg[v];
    ++deg[u];
    link[i] = idx - 1;
    add(v, u, 0);
  }
  int minDeg = 1e9;
  for (int i = 1; i <= n1 + n2; ++i) minDeg = min(minDeg, deg[i]);
  for (int i = 1; i <= n1; ++i) add(s, i, deg[i] - minDeg), add(i, s, 0);
  for (int i = n1 + 1; i <= n1 + n2; ++i)
    add(i, t, deg[i] - minDeg), add(t, i, 0);
  vector<vector<int>> res;
  for (int _ = 0; _ <= minDeg; ++_) {
    int maxflow = dinic();
    vector<int> op;
    for (int i = 1; i <= m; ++i)
      if (cap[link[i]] == 1) op.push_back(i);
    for (int i = ver[s]; ~i; i = succ[i]) ++cap[i];
    for (int i = ver[t]; ~i; i = succ[i]) ++cap[i ^ 1];
    res.push_back(op);
  }
  for (int i = (int)res.size() - 1; i >= 0; --i) {
    printf("%d ", (int)res[i].size());
    for (auto& p : res[i]) printf("%d ", p);
    puts("");
  }
  return 0;
}