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>
#pragma comment(linker, "/STACK:536870912")
#pragma warning(disable : 4996)
using namespace std;
const int N = 1e5, S = N - 2, T = N - 1;
vector<pair<int, int>> v[N];
vector<int> ans[N];
int cap[N], pt[N], fl[N], d[N];
int ce = 0, n1, n2, m;
void add_edge(int a, int b, int c) {
  cap[ce] = c;
  v[a].push_back({b, ce++});
  v[b].push_back({a, ce++});
}
bool bfs() {
  queue<int> q;
  q.push(S);
  memset(d, 0, sizeof(d));
  ;
  d[S] = 1;
  while (!q.empty()) {
    int node = q.front();
    q.pop();
    for (auto p : v[node]) {
      int to = p.first, num = p.second;
      if (!d[to] && cap[num] - fl[num] > 0) {
        d[to] = d[node] + 1;
        q.push(to);
      }
    }
  }
  return d[T];
}
int dfs(int node, int flow) {
  if (node == T || !flow) return flow;
  for (int &i = pt[node]; i < v[node].size(); i++) {
    int to = v[node][i].first, num = v[node][i].second;
    if (d[node] + 1 == d[to]) {
      int ret = dfs(to, min(flow, cap[num] - fl[num]));
      if (ret) {
        fl[num] += ret;
        fl[num ^ 1] -= ret;
        return ret;
      }
    }
  }
  return 0;
}
int flow = 0;
void dinic() {
  while (bfs()) {
    memset(pt, 0, sizeof(pt));
    ;
    int ret;
    while (ret = dfs(S, 1e9)) flow += ret;
  }
}
int main() {
  scanf("%d%d%d", &n1, &n2, &m);
  for (int i = 0; i < m; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    a--, b--;
    add_edge(a, b + n1, 1);
  }
  int minDeg = 1e9;
  for (int i = 0; i < n1; i++) minDeg = min(minDeg, (int)v[i].size());
  for (int i = 0; i < n2; i++) minDeg = min(minDeg, (int)v[i + n1].size());
  for (int i = 0; i < n1; i++) add_edge(S, i, v[i].size() - minDeg);
  for (int i = 0; i < n2; i++) add_edge(i + n1, T, v[i + n1].size() - minDeg);
  for (int i = 0; i < minDeg + 1; i++) {
    dinic();
    for (int j = 0; j < m; j++) {
      if (fl[j * 2] == 0) {
        ans[i].push_back(j + 1);
      }
    }
    for (int j = 0; j < n1; j++) {
      cap[(j + m) * 2]++;
      cap[(j + m) * 2 + 1]--;
    }
    for (int j = 0; j < n2; j++) {
      cap[(j + m + n1) * 2]++;
      cap[(j + m + n1) * 2 + 1]--;
    }
  }
  for (int i = minDeg; i >= 0; i--) {
    printf("%d ", ans[i].size());
    for (int j : ans[i]) printf("%d ", j);
    printf("\n");
  }
  return 0;
}