Problem: You are given an undirected bipartite graph without multiple edges. You should paint the edges of graph to minimal number of colours, so that no two adjacent edges have the same colour.

Input

The first line contains three integers a, b, m (1 ≤ a, b ≤ 1000, 0 ≤ m ≤ 105), a is the size of the first part, b is the size of the second part, m is the number of edges in the graph.

Each of the next m lines contains two integers x, y (1 ≤ x ≤ a, 1 ≤ y ≤ b), where x is the number of the vertex in the first part and y is the number of the vertex in the second part. It is guaranteed that there are no multiple edges.

Output

In the first line print integer c — the minimal number of colours. The second line should contain m integers from 1 to c — the colours of the edges (in the order they appear in the input).

If there are several solutions, you can print any one of them.

Examples

Input

4 3 5
1 2
2 2
3 2
4 1
4 3


Output

3
1 2 3 1 2

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using std::pair;
using std::vector;
using Node = size_t;
using Edge = pair<Node, Node>;
using EdgeList = vector<Edge>;
using Color = size_t;
using Coloring = vector<Color>;
pair<EdgeList, size_t> ReadInput(std::istream& in_stream = std::cin);
void WriteAnswer(const Coloring& coloring,
                 std::ostream& out_stream = std::cout);
Coloring ColorEdges(const EdgeList& edges, const size_t nodes);
int main() {
  std::ios_base::sync_with_stdio(false);
  std::cin.tie(nullptr);
  auto input = ReadInput();
  auto coloring = ColorEdges(input.first, input.second);
  WriteAnswer(coloring);
  return 0;
}
using EdgeNumber = size_t;
using NodeColoring = vector<pair<pair<Node, EdgeNumber>, bool>>;
Color GetMinColor(const NodeColoring& fst, const NodeColoring& snd);
bool SwapColors(const NodeColoring& fst, const NodeColoring& snd,
                pair<Color, Color>* result);
void SwapColors(Node a, Color fst, Color snd,
                vector<NodeColoring>* node_by_color);
Coloring ColorEdges(const EdgeList& edges, const size_t nodes) {
  Coloring coloring(edges.size());
  vector<NodeColoring> node_by_color(nodes);
  auto resize_node = [&node_by_color](Node node, size_t size) {
    auto current_size = node_by_color[node].size();
    size = std::max(size, current_size);
    node_by_color[node].resize(size);
  };
  auto color_edge = [&node_by_color, &resize_node](Edge edge, EdgeNumber num,
                                                   Color color) {
    Node a = edge.first, b = edge.second;
    resize_node(a, color + 1);
    resize_node(b, color + 1);
    assert(node_by_color[a][color].second == false &&
           node_by_color[b][color].second == false);
    node_by_color[a][color] = {{b, num}, true};
    node_by_color[b][color] = {{a, num}, true};
  };
  for (EdgeNumber edge_num = 0; edge_num < edges.size(); ++edge_num) {
    const Edge& edge = edges[edge_num];
    Node a = edge.first, b = edge.second;
    pair<Color, Color> swapable;
    Color color;
    if (SwapColors(node_by_color[a], node_by_color[b], &swapable)) {
      SwapColors(a, swapable.first, swapable.second, &node_by_color);
      color = swapable.first;
    } else {
      color = GetMinColor(node_by_color[a], node_by_color[b]);
    }
    color_edge(edge, edge_num, color);
  }
  for (Node node = 0; node < nodes; ++node) {
    for (size_t color = 0; color < node_by_color[node].size(); ++color) {
      auto& edge = node_by_color[node][color];
      if (edge.second) {
        auto edge_number = edge.first.second;
        coloring[edge_number] = color;
      }
    }
  }
  return coloring;
}
void SwapColors(Node node, Color fst, Color snd,
                vector<NodeColoring>* node_by_color) {
  auto free_way = [&node_by_color](Node node, Color color) {
    return node_by_color->at(node).size() <= color ||
           node_by_color->at(node)[color].second == false;
  };
  auto resize_node = [&node_by_color](Node node, size_t size) {
    auto current_size = node_by_color->at(node).size();
    size = std::max(size, current_size);
    node_by_color->at(node).resize(size);
  };
  resize_node(node, std::max(fst, snd) + 1);
  if (!free_way(node, fst)) {
    SwapColors(node_by_color->at(node)[fst].first.first, snd, fst,
               node_by_color);
  }
  std::swap(node_by_color->at(node)[fst], node_by_color->at(node)[snd]);
}
bool SwapColors(const NodeColoring& fst, const NodeColoring& snd,
                pair<Color, Color>* result) {
  Color fst_color, snd_color;
  auto free_color = [](Color color, const NodeColoring& smth) {
    return color >= smth.size() || (!smth[color].second);
  };
  auto busy_color = [](Color color, const NodeColoring& smth) {
    return color < smth.size() && smth[color].second;
  };
  for (fst_color = 0; fst_color < fst.size(); ++fst_color) {
    if (busy_color(fst_color, fst) && free_color(fst_color, snd)) {
      break;
    }
  }
  for (snd_color = 0; snd_color < snd.size(); ++snd_color) {
    if (busy_color(snd_color, snd) && free_color(snd_color, fst)) {
      break;
    }
  }
  if (fst_color == fst.size() || snd_color == snd.size()) {
    return false;
  }
  if (result != nullptr) {
    *result = {fst_color, snd_color};
  }
  return true;
}
Color GetMinColor(const NodeColoring& fst, const NodeColoring& snd) {
  Color color;
  for (color = 0; color < fst.size() || color < snd.size(); ++color) {
    bool flag = 1;
    if (color < fst.size()) {
      flag = flag && (!fst[color].second);
    }
    if (color < snd.size()) {
      flag = flag && (!snd[color].second);
    }
    if (flag) {
      break;
    }
  }
  return color;
}
pair<EdgeList, size_t> ReadInput(std::istream& in_stream) {
  size_t nodes_a, nodes_b, edges_size;
  in_stream >> nodes_a >> nodes_b >> edges_size;
  EdgeList edges(edges_size);
  for (auto& edge : edges) {
    in_stream >> edge.first >> edge.second;
    --edge.first, --edge.second;
    edge.second += nodes_a;
  }
  return {edges, nodes_a + nodes_b};
}
void WriteAnswer(const Coloring& coloring, std::ostream& out_stream) {
  if (coloring.empty()) {
    out_stream << 0;
    return;
  }
  auto max_color = *std::max_element(coloring.begin(), coloring.end());
  out_stream << max_color + 1 << std::endl;
  for (auto color : coloring) {
    out_stream << color + 1 << ' ';
  }
}