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;
struct node {
  int to, cap, flow;
  int revInd, ind;
  node() {}
};
vector<node> neigh[4042];
int n1, n2, m;
int source, sink;
int deg[4042];
vector<int> ans[4042];
bool used[4042];
int flow(int x) {
  if (x == sink) {
    return 1;
  }
  used[x] = 1;
  for (int i = 0; i < neigh[x].size(); i++) {
    if (neigh[x][i].cap - neigh[x][i].flow == 0) {
      continue;
    }
    if (used[neigh[x][i].to]) {
      continue;
    }
    if (flow(neigh[x][i].to)) {
      neigh[x][i].flow++;
      neigh[neigh[x][i].to][neigh[x][i].revInd].flow--;
      return 1;
    }
  }
  return 0;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n1 >> n2;
  cin >> m;
  int minDeg = 1 << 20;
  source = n1 + n2;
  sink = n1 + n2 + 1;
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    b += n1;
    node crr;
    crr.flow = 0;
    crr.cap = 1;
    crr.ind = i;
    crr.to = b;
    crr.revInd = neigh[b].size();
    neigh[a].push_back(crr);
    crr.to = a;
    crr.cap = 0;
    crr.revInd = neigh[a].size() - 1;
    neigh[b].push_back(crr);
    deg[a] = neigh[a].size();
    deg[b] = neigh[b].size();
  }
  for (int i = 0; i < n2 + n1; i++) {
    minDeg = min(minDeg, deg[i]);
  }
  for (int i = 0; i < n1; i++) {
    node crr;
    crr.cap = deg[i] - minDeg;
    crr.flow = 0;
    crr.ind = -1;
    crr.to = i;
    crr.revInd = neigh[i].size();
    neigh[source].push_back(crr);
    crr.to = source;
    crr.cap = 0;
    crr.revInd = neigh[source].size() - 1;
    neigh[i].push_back(crr);
  }
  for (int i = n1; i < n1 + n2; i++) {
    node crr;
    crr.cap = 0;
    crr.flow = 0;
    crr.ind = -1;
    crr.to = i;
    crr.revInd = neigh[i].size();
    neigh[sink].push_back(crr);
    crr.to = sink;
    crr.cap = deg[i] - minDeg;
    crr.revInd = neigh[sink].size() - 1;
    neigh[i].push_back(crr);
  }
  for (int k = minDeg; k >= 0; k--) {
    while (flow(source)) {
      for (int i = 0; i < n1 + n2 + 3; i++) {
        used[i] = 0;
      }
    }
    for (int i = 0; i < n1 + n2 + 3; i++) {
      used[i] = 0;
    }
    for (int i = 0; i < n1; i++) {
      for (int j = 0; j < neigh[i].size(); j++) {
        if (neigh[i][j].cap - neigh[i][j].flow == 0 && neigh[i][j].ind != -1) {
          ans[k].push_back(neigh[i][j].ind);
        }
      }
    }
    for (int i = 0; i < n1; i++) {
      node crr;
      crr.cap = 1;
      crr.flow = 0;
      crr.ind = -1;
      crr.to = i;
      crr.revInd = neigh[i].size();
      neigh[source].push_back(crr);
      crr.to = source;
      crr.cap = 0;
      crr.revInd = neigh[source].size() - 1;
      neigh[i].push_back(crr);
    }
    for (int i = n1; i < n1 + n2; i++) {
      node crr;
      crr.cap = 0;
      crr.flow = 0;
      crr.ind = -1;
      crr.to = i;
      crr.revInd = neigh[i].size();
      neigh[sink].push_back(crr);
      crr.to = sink;
      crr.cap = 1;
      crr.revInd = neigh[sink].size() - 1;
      neigh[i].push_back(crr);
    }
  }
  for (int i = 0; i <= minDeg; i++) {
    sort(ans[i].begin(), ans[i].end());
    cout << m - ans[i].size() << " ";
    int s = 0;
    for (int j = 0; j < m; j++) {
      if (s < ans[i].size() && ans[i][s] == j) {
        s++;
      } else {
        cout << j + 1 << " ";
      }
    }
    cout << "\n";
  }
  return 0;
}