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 = 5010;
struct Edge {
  int to, flow, ridx, i;
  Edge(int to, int flow, int ridx, int i)
      : to(to), flow(flow), ridx(ridx), i(i) {}
};
vector<Edge> G[maxN];
int hit[maxN];
int que[maxN];
int cur[maxN];
inline int& rflow(const Edge& e) { return G[e.to][e.ridx].flow; }
inline void addEdge(int u, int v, int w, int i) {
  const int n = G[v].size();
  const int m = G[u].size();
  G[u].emplace_back(v, w, n, +i);
  G[v].emplace_back(u, 0, m, -1);
}
bool Bfs(int s, int t) {
  memset(hit, -1, sizeof hit);
  int qt = 0, qh = hit[s] = 0;
  for (que[qt++] = s; qt != qh;) {
    const int u = que[qh++];
    for (const Edge& e : G[u]) {
      if (e.flow != 0 && hit[e.to] == -1) {
        hit[e.to] = hit[u] + 1;
        que[qt++] = e.to;
      }
    }
  }
  return hit[t] != -1;
}
int Dfs(int u, int t, int flow) {
  if (u == t) return flow;
  while (cur[u] < G[u].size()) {
    Edge& e = G[u][cur[u]++];
    if (hit[e.to] == hit[u] + 1) {
      if (e.flow == 0) continue;
      int f = min(flow, e.flow);
      if (int res = Dfs(e.to, t, f)) {
        rflow(e) = rflow(e) + res;
        e.flow = e.flow - res;
        return res;
      }
    }
  }
  return 0;
}
int maxflow(int s, int t) {
  int res = 0;
  while (Bfs(s, t)) {
    memset(cur, 0, sizeof cur);
    while (int flow = Dfs(s, t, INF)) res = res + flow;
  }
  return res;
}
int in[maxN];
int main() {
  static int n1, n2, m;
  scanf("%d%d%d", &n1, &n2, &m);
  for (int i = 1; i <= m; i++) {
    static int u, v;
    scanf("%d%d", &u, &v);
    in[u]++;
    in[v + n1]++;
    addEdge(u, v + n1, 1, i);
  }
  const int s = 0, t = n1 + n2 + 1;
  for (int i = 1; i <= n1; i++) addEdge(s, i, n1 < n2 ? INF : 0, -1);
  for (int i = 1; i <= n2; i++) addEdge(i + n1, t, n1 <= n2 ? 0 : INF, -1);
  int k = *min_element(in + 1, in + t);
  for (int i = 0; i <= k; i++) {
    maxflow(s, t);
    vector<int> ans;
    for (const Edge& e1 : G[s]) {
      for (const Edge& e2 : G[e1.to]) {
        if (e2.i == -1 || e2.flow != 0) continue;
        ans.push_back(e2.i);
      }
    }
    printf("%d%c", ans.size(), " \n"[ans.size() == 0]);
    for (const int& i : ans) printf("%d%c", i, " \n"[&i == &ans.back()]);
    for (Edge& e : G[s]) e.flow++;
    for (Edge& e : G[t]) rflow(e)++;
  }
  return 0;
}