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>
const int N = 4000 + 10;
const int M = 1e6 + 10;
int n, m, e, s, t;
int pre[M], to[M], f[M], head[N], wcnt = 1;
int deg[N];
int pid[N];
int dep[N], cur[N];
bool vis[2010][2010];
inline void addedge(int u, int v, int w) {
  wcnt++;
  pre[wcnt] = head[u];
  head[u] = wcnt;
  to[wcnt] = v;
  f[wcnt] = w;
}
inline void add1edge(int u, int v, int w) {
  addedge(u, v, w);
  addedge(v, u, 0);
}
bool bfs() {
  static int q[N], ql, qr;
  int i, u;
  memset(dep, 0, sizeof(dep));
  memcpy(cur, head, sizeof(head));
  q[ql = qr = 1] = s;
  dep[s] = 1;
  while (ql <= qr) {
    u = q[ql++];
    for (i = head[u]; i; i = pre[i]) {
      if (f[i] and !dep[to[i]]) {
        dep[to[i]] = dep[u] + 1;
        q[++qr] = to[i];
      }
    }
  }
  return dep[t];
}
int maxflow(int u, int lim) {
  int i, tot = 0, flow;
  if (u == t) return lim;
  for (i = cur[u]; i; i = pre[i]) {
    cur[u] = i;
    if (f[i] and dep[u] + 1 == dep[to[i]]) {
      flow = maxflow(to[i], std::min(lim - tot, f[i]));
      f[i] -= flow;
      f[i ^ 1] += flow;
      tot += flow;
      if (tot == lim) break;
    }
  }
  return tot;
}
int dinic() {
  int ans = 0;
  while (bfs()) ans += maxflow(s, 0x3f3f3f3f);
  return ans;
}
int main() {
  int i, j, mindeg, u, v, cnt;
  scanf("%d %d %d", &n, &m, &e);
  s = n + m + 1;
  t = s + 1;
  for (i = int(1); i <= int(e); i++) {
    scanf("%d %d", &u, &v);
    add1edge(u, v + n, 1);
    deg[u]++;
    deg[v + n]++;
  }
  mindeg = deg[1];
  for (i = int(1); i <= int(n + m); i++) mindeg = std::min(mindeg, deg[i]);
  for (i = int(1); i <= int(n); i++) {
    pid[i] = wcnt + 1;
    add1edge(s, i, deg[i] - mindeg);
  }
  for (i = int(n + 1); i <= int(n + m); i++) {
    pid[i] = wcnt + 1;
    add1edge(i, t, deg[i] - mindeg);
  }
  for (i = int(mindeg); i >= int(0); i--) {
    dinic();
    for (j = int(1); j <= int(e); j++) vis[i][j] = f[j << 1];
    for (j = int(1); j <= int(n + m); j++) f[pid[j]]++;
  }
  for (i = int(0); i <= int(mindeg); i++) {
    cnt = 0;
    for (j = int(1); j <= int(e); j++) cnt += vis[i][j];
    printf("%d", cnt);
    for (j = int(1); j <= int(e); j++)
      if (vis[i][j]) printf(" %d", j);
    putchar('\n');
  }
  return 0;
}