Problem p02580 (C++) — buggy submission, verdict: Time Limit Exceeded

#define MOD 1000000007

#if 1
//------------------------------------------------------------
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

template <class T> struct Entry {
  static void Run() { T().Run(); }
};
struct MyMain;

#if defined(TEST)
#include "test.hpp"
#else
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(16);
  Entry<MyMain>::Run();
  return 0;
}
#endif

//------------------------------------------------------------
using ll = long long;
#define int ll

#define FOR(i, s, e) for (ll i = ll(s); i < ll(e); ++i)
#define RFOR(i, s, e) for (ll i = ll(e) - 1; i >= ll(s); --i)
#define REP(i, n) for (ll i = 0, i##_size = ll(n); i < i##_size; ++i)
#define RREP(i, n) for (ll i = ll(n) - 1; i >= 0; --i)

#define INF INT64_MAX

//------------------------------------------------------------
template <class T> struct ContainerHolder {
  bool flag = true;
  T &var;
  ContainerHolder(T &v) : var(v) {}
  operator bool() const { return flag; }
  T *operator->() { return &var; }
};
template <class T> ContainerHolder<T> ContainerHold(T &v) {
  return ContainerHolder<T>(v);
}

#define CFOR(it, container)                                                    \\
  for (auto holder = ContainerHold(container); holder; holder.flag = false)    \\
    for (auto it = holder->begin(), endIt = holder->end(); it != endIt; ++it)

//------------------------------------------------------------
template <class T> struct arr : public vector<T> {
  arr() {}
  arr(initializer_list<T> il) : vector<T>(il) {}
  explicit arr(ll n, T v = T()) : vector<T>(n, v) {}

  T &operator()(int i) { return (*this)[i]; }
  T const &operator()(int i) const { return (*this)[i]; }
  void init(ll n, T v = T()) {
    this->clear();
    this->resize(n, v);
  }
  ll sz() const { return (ll)this->size(); }
  void pb(T v) { this->push_back(v); }
  void sort() { std::sort(this->begin(), this->end()); }
  void sort(function<bool(T, T)> p) {
    std::sort(this->begin(), this->end(), p);
  }
  void rsort() { std::sort(this->begin(), this->end(), greater<T>()); }
  void reverse() { std::reverse(this->begin(), this->end()); }
  void unique_erase() {
    this->erase(std::unique(this->begin(), this->end()), this->end());
  }
  bool next_permutation() {
    return std::next_permutation(this->begin(), this->end());
  }

  // これ以下はソート済み前提
  int lower_bound(T const &v, function<bool(T, T)> p) {
    return std::lower_bound(this->begin(), this->end(), v, p) - this->begin();
  }
  int lower_bound(T const &v) {
    return std::lower_bound(this->begin(), this->end(), v) - this->begin();
  }

  int upper_bound(T const &v, function<bool(T, T)> p) {
    return std::upper_bound(this->begin(), this->end(), v, p) - this->begin();
  }
  int upper_bound(T const &v) {
    return std::upper_bound(this->begin(), this->end(), v) - this->begin();
  }

  int find_nearest(T const &v) {
    int i = this->lower_bound(v);
    if (i >= sz()) {
      --i;
    } else if ((*this)[i] != v) {
      int p = i - 1;
      if (p >= 0) {
        int id = abs((*this)[i] - v);
        int pd = abs((*this)[p] - v);
        if (pd < id) {
          i = p;
        }
      }
    }
    return i;
  }

  // 見つからなければ-1
  int find(T const &v) {
    int i = this->lower_bound(v);
    if (i >= sz()) {
      return -1;
    }
    if ((*this)[i] != v) {
      return -1;
    }
    return i;
  }
};
using ints = arr<ll>;

template <class T> struct que : public queue<T> {
  ll sz() const { return (ll)this->size(); }
  T popfront() {
    T v = this->front();
    this->pop();
    return v;
  }
};

template <class A, class B> struct pr {
  union {
    A a;
    A key;
    A first;
    A x;
  };
  union {
    B b;
    B value;
    B second;
    B y;
  };

  pr() : a(A()), b(B()){};
  pr(A a_, B b_) : a(a_), b(b_) {}
  pr(pr const &r) : a(r.a), b(r.b){};
  pr(pair<A, B> const &r) : a(r.first), b(r.second){};

  bool operator==(pr const &r) const { return a == r.a && b == r.b; }
  bool operator!=(pr const &r) const { return !((*this) == r); }
  bool operator<(pr const &r) const {
    if (a == r.a) {
      return b < r.b;
    }
    return a < r.a;
  }

  pr operator+(pr v) const { return pr(x, y) += v; }
  pr operator-(pr v) const { return pr(x, y) -= v; }

  pr &operator+=(pr v) {
    x += v.x;
    y += v.y;
    return *this;
  }
  pr &operator-=(pr v) {
    x -= v.x;
    y -= v.y;
    return *this;
  }

  void flip() { swap(x, y); }

  friend istream &operator>>(istream &is, pr &p) {
    is >> p.a >> p.b;
    return is;
  }
  friend ostream &operator<<(ostream &os, pr const &p) {
    os << p.a << " " << p.b;
    return os;
  }
};
using pint = pr<ll, ll>;
using pints = arr<pint>;

template <class K, class V> struct dic : public map<K, V> {
  bool get(K const &k, V *v) {
    auto it = this->find(k);
    if (it != this->end()) {
      *v = it->second;
      return true;
    }
    return false;
  }
};

template <class T> struct arr2 {
  vector<T> m_vec;
  int m_width;
  int m_height;

  arr2() : m_width(0), m_height(0) {}
  arr2(int w, int h, T const &value = T()) : m_width(w), m_height(h) {
    m_vec.resize(w * h, value);
  }
  arr2(arr2 const &r) {
    m_vec = r.m_vec;
    m_width = r.m_width;
    m_height = r.m_height;
  }
  arr2(arr2 &&r) {
    m_vec = move(r.m_vec);
    m_width = r.m_width;
    m_height = r.m_height;
  }
  arr2 &operator=(arr2 const &r) {
    m_vec = r.m_vec;
    m_width = r.m_width;
    m_height = r.m_height;
    return *this;
  }
  arr2 &operator=(arr2 &&r) {
    m_vec = move(r.m_vec);
    m_width = r.m_width;
    m_height = r.m_height;
    return *this;
  }

  bool operator==(arr2 const &r) const { return m_vec = r.m_vec; }

  bool operator<(arr2 const &r) const {
    if (m_width != r.m_width) {
      return m_width < r.m_width;
    }
    if (m_height != r.m_height) {
      return m_height < r.m_height;
    }
    REP(i, m_vec.size()) {
      if (m_vec[i] != r.m_vec[i]) {
        return m_vec[i] < r.m_vec[i];
      }
    }
    return false;
  }

  pint size() const { return pint(m_width, m_height); }
  int width() const { return m_width; }
  int height() const { return m_height; }

  void init(int w, int h, T const &value = T()) {
    m_vec.clear();
    m_vec.resize(w * h, value);
    m_width = w;
    m_height = h;
  }
  void init(pint size, T const &value = T()) { init(size.x, size.y, value); }
  T &operator()(int x, int y) { return m_vec[y * m_width + x]; }
  T const &operator()(int x, int y) const { return m_vec[y * m_width + x]; }

  T &operator()(pint p) { return m_vec[p.y * m_width + p.x]; }
  T const &operator()(pint p) const { return m_vec[p.y * m_width + p.x]; }

  T &operator[](pint p) { return m_vec[p.y * m_width + p.x]; }
  T const &operator[](pint p) const { return m_vec[p.y * m_width + p.x]; }

  bool isIn(int x, int y) const {
    return x >= 0 && x < m_width && y >= 0 && y < m_height;
  }
  bool isIn(pint p) const { return isIn(p.x, p.y); }
  bool isOut(int x, int y) const {
    return x < 0 || x >= m_width || y < 0 || y >= m_height;
  }
  bool isOut(pint p) const { return isOut(p.x, p.y); }

  struct iterator {
  private:
    arr2<T> *owner;

  public:
    pint pt;

    iterator(arr2<T> *owner_, pint pt_) : owner(owner_), pt(pt_) {}

    bool operator==(iterator const &r) const { return pt == r.pt; }
    bool operator!=(iterator const &r) const { return !((*this) == r); }
    void operator++() {
      ++pt.x;
      if (pt.x >= owner->width()) {
        ++pt.y;
        pt.x = 0;
      }
    }
    T &operator*() { return (*owner)(pt); }
  };
  iterator begin() { return iterator(this, pint(0, 0)); }
  iterator end() { return iterator(this, pint(0, height())); }

  void disp(ostream &os) {
    REP(y, m_height) {
      REP(x, m_width) { os << setw(2) << (*this)(x, y) << " "; }
      os << endl;
    }
    os << endl;
  }
};

const pints around4 = {pint(-1, 0), pint(0, -1), pint(1, 0), pint(0, 1)};

//------------------------------------------------------------
template <class T> void chmin(T &a, T b) {
  if (b < a) {
    a = b;
  }
}
template <class T> void chmax(T &a, T b) {
  if (b > a) {
    a = b;
  }
}

constexpr int gcd(int a, int b) {
  if (a < 0) {
    a = -a;
  }
  if (b < 0) {
    b = -b;
  }
  if (a == 0) {
    return b;
  }
  if (b == 0) {
    return a;
  }

  while (int c = a % b) {
    a = b;
    b = c;
  }
  return b;
}

constexpr int lcm(int a, int b) { return a * b / gcd(a, b); }

//------------------------------------------------------------
struct bfs {
  ints froms;
  ints steps;

  bfs(int N, int start, function<ints(int)> getAround) {
    froms.init(N, -1);
    steps.init(N, -1);

    que<ll> queue;
    queue.push(start);
    froms[start] = start;
    steps[start] = 0;

    while (queue.empty() == false) {
      ll p = queue.popfront();

      for (ll n : getAround(p)) {
        if (steps[n] != -1) {
          continue;
        }

        froms[n] = p;
        steps[n] = steps[p] + 1;
        queue.push(n);
      }
    }
  }
};

struct BfsResult {
  arr2<pint> froms;
  arr2<int> steps;
};

template <class T>
BfsResult bfs2(arr2<T> const &field, pints const &starts,
               function<bool(T)> canMove) {
  BfsResult result;
  result.froms.init(field.size(), pint(-1, -1));
  result.steps.init(field.size(), -1);

  que<pint> queue;
  for (auto const &start : starts) {
    queue.push(start);
    result.froms(start) = start;
    result.steps(start) = 0;
  }

  while (queue.empty() == false) {
    auto p = queue.popfront();

    for (auto a : around4) {
      pint n = p + a;
      if (field.isOut(n)) {
        continue;
      }
      if (result.steps(n) != -1) {
        continue;
      }
      if (!canMove(field(n))) {
        continue;
      }

      result.froms(n) = p;
      result.steps(n) = result.steps(p) + 1;
      queue.push(n);
    }
  }

  return result;
}

//------------------------------------------------------------
template <int M> struct modint {
  int raw;

  modint() { raw = 0; }
  modint(int v) {
    if (v < 0) {
      raw = (v % M) + M;
    } else if (v >= M) {
      raw = v % M;
    } else {
      raw = v;
    }
  }
  modint operator+(modint v) const { return modint(raw) += v; }
  modint operator-(modint v) const { return modint(raw) -= v; }
  modint operator*(modint v) const { return modint(raw) *= v; }

  modint &operator+=(modint v) {
    raw += v.raw;
    if (raw >= M) {
      raw -= M;
    }
    return *this;
  }
  modint &operator-=(modint v) {
    raw -= v.raw;
    if (raw < 0) {
      raw += M;
    }
    return *this;
  }
  modint &operator*=(modint v) {
    raw = (raw * v.raw) % M;
    return *this;
  }
  modint pow(int n) const { return modint::pow(raw, n); }
  static modint pow(int a, int n) {
    if (n < 0) {
      // not support
      abort();
    }

    int r = 1;
    while (n) {
      if (n & 1) {
        r = (r * a) % M;
      }
      a = (a * a) % M;
      n >>= 1;
    }
    return modint(r);
  }

  modint inv() const {
    int a = raw;
    int b = M;
    int u = 1;
    int v = 0;
    while (b) {
      int t = a / b;
      a -= t * b;
      u -= t * v;
      swap(a, b);
      swap(u, v);
    }
    u %= M;
    if (u < 0) {
      u += M;
    }
    return u;
  }

  friend istream &operator>>(istream &is, modint &m) {
    int v;
    is >> v;
    m = modint(v);
    return is;
  }
  friend ostream &operator<<(ostream &os, modint const &m) {
    return os << m.raw;
  }
};

using mint = modint<MOD>;
using mints = arr<mint>;

//------------------------------------------------------------
struct UnionFind {
  struct Node {
    Node *parent = nullptr;
    int count = 1;

    Node *Root() {
      if (parent == nullptr) {
        return this;
      }
      return parent = parent->Root();
    }
  };
  vector<Node> nodes;

  UnionFind(int count) { nodes.resize(count); }

  void Join(int a, int b) {
    Node *rootA = nodes[a].Root();
    Node *rootB = nodes[b].Root();
    if (rootA == rootB) {
      return;
    }

    if (rootA->count > rootB->count) {
      swap(rootA, rootB);
    }

    rootB->count += rootA->count;
    rootA->parent = rootB;
    rootA->count = 0;
  }

  bool IsReachable(int a, int b) {
    Node *rootA = nodes[a].Root();
    Node *rootB = nodes[b].Root();
    return rootA == rootB;
  }

  int Count(int a) { return nodes[a].Root()->count; }
};

//------------------------------------------------------------
template <class T> struct SumsImpl {
private:
  int N;
  arr<T> S;

public:
  SumsImpl(int N_) : N(N_), S(N + 1, 0) {}
  void Set(int i, T const &value) { S(i + 1) = S(i) + value; }

  // l <= x < r
  T Get(int l, int r) const { return S(r) - S(l); }
};
using Sums = SumsImpl<int>;

template <class T> struct ImosImpl {
private:
  int N;
  arr<T> S;

public:
  ImosImpl() {}
  ImosImpl(int N_) : N(N_), S(N + 1, 0) {}

  void init(int N_) {
    N = N_;
    S.init(N + 1, 0);
  }

  void Add(int i, T const &value) { S(i + 1) += value; }

  void Calc() {
    REP(i, N) { S(i + 1) += S(i); }
  }

  // l <= x < r
  T Get(int l, int r) const { return S(r) - S(l); }

  T Get(int i) const { return S(i); }
};
using Imos = ImosImpl<int>;

template <class T> struct Sums2Impl {
private:
  arr2<T> sums;

public:
  Sums2Impl(int W, int H) : sums(W + 1, H + 1) {}

  void Set(int x, int y, T const &value) {
    T s = value;
    s += sums(x + 1, y);
    s += sums(x, y + 1);
    s -= sums(x, y);
    sums(x + 1, y + 1) = s;
  }

  // l <= x < r
  // t <= y < b
  T Get(int l, int t, int r, int b) const {
    int s = sums(r, b);
    s -= sums(r, t);
    s -= sums(l, b);
    s += sums(l, t);
    return s;
  }
};
using Sums2 = Sums2Impl<int>;

template <class T> struct Imos2Impl {
private:
  arr2<T> sums;

public:
  Imos2Impl(int W, int H) : sums(W + 1, H + 1) {}

  void Add(int x, int y, T const &value) { sums(x + 1, y + 1) += value; }

  void Calc() {
    REP(y, sums.height() - 1) {
      REP(x, sums.width() - 1) {
        T s = 0;
        s += sums(x + 1, y);
        s += sums(x, y + 1);
        s -= sums(x, y);
        sums(x + 1, y + 1) += s;
      }
    }
  }

  // l <= x < r
  // t <= y < b
  T Get(int l, int t, int r, int b) const {
    int s = sums(r, b);
    s -= sums(r, t);
    s -= sums(l, b);
    s += sums(l, t);
    return s;
  }
};
using Imos2 = Imos2Impl<int>;

//------------------------------------------------------------
struct CombiTbl {
  mints fac;
  mints ifac;

  // 重複組み合わせを使う場合は N*2 を指定しないといけない
  CombiTbl(int N) : fac(N), ifac(N) {
    fac[0] = 1;
    ifac[0] = 1;
    FOR(i, 1, N) {
      fac[i] = fac[i - 1] * i;
      ifac[i] = fac[i].inv();
    }
  }

  // a!
  mint Fac(int a) const { return fac(a); }

  // aPb
  mint Perm(int a, int b) const { return fac(a) * ifac(a - b); }

  // aCb
  mint Combi(int a, int b) const { return fac(a) * ifac(b) * ifac(a - b); }

  // aHb（重複組み合わせ）
  mint RepCombi(int a, int b) const { return Combi(a + b - 1, b); }
};

//------------------------------------------------------------
#if defined(TEST)
extern istream &mis;
extern ostream &mos;
#else
istream &mis = cin;
ostream &mos = cout;
#endif

//------------------------------------------------------------

struct OutputStream {
  template <class T>
  friend OutputStream &operator<<(OutputStream &s, T const &v) {
    mos << v << '\\n';
    return s;
  }
} out;

struct PrintStream {
  stringstream ss;

  template <class T> friend PrintStream &operator<<(PrintStream &s, T &&v) {
    s.ss << v << ' ';
    return s;
  }

  PrintStream &operator<<(PrintStream &(*manip)(PrintStream &)) {
    return (*manip)(*this);
  }
} prn;

PrintStream &en(PrintStream &s) {
  string str = s.ss.str();
  s.ss = stringstream();
  if (str.empty() == false) {
    str.pop_back();
  }
  mos << str << '\\n';
  return s;
}

//------------------------------------------------------------

template <class T> struct in_base {
  T value;
  in_base() { mis >> value; }
  operator T() { return value; }
};

struct in_int {
  int value;

  in_int() { mis >> value; }
  in_int(int add) {
    mis >> value;
    value += add;
  }
  operator int() { return value; }
};

template <class A, class B> struct in_pr {
  pr<A, B> value;

  in_pr() { mis >> value.a >> value.b; }
  in_pr(int addA, int addB) {
    mis >> value.a >> value.b;
    value.a += addA;
    value.b += addB;
  }
  in_pr(bool flip) { mis >> value.b >> value.a; }
  in_pr(int addA, int addB, bool flip) {
    mis >> value.b >> value.a;
    value.a += addB;
    value.b += addA;
  }
  operator pr<A, B>() { return value; }
};

template <class T> struct in_arr {
  arr<T> value;

  in_arr(int N) {
    value.init(N);
    REP(i, N) { mis >> value[i]; }
  }
  in_arr(int N, int add) {
    value.init(N);
    REP(i, N) {
      mis >> value[i];
      value[i] += add;
    }
  }
  operator arr<T>() { return value; }
};

template <> struct in_arr<pint> {
  arr<pint> value;

  in_arr(int N) {
    value.init(N);
    REP(i, N) { mis >> value[i]; }
  }
  in_arr(int N, int addA, int addB) {
    value.init(N);
    REP(i, N) {
      mis >> value[i].a >> value[i].b;
      value[i].a += addA;
      value[i].b += addB;
    }
  }
  in_arr(int N, bool flip) {
    value.init(N);
    REP(i, N) { mis >> value[i].b >> value[i].a; }
  }
  in_arr(int N, int addA, int addB, bool flip) {
    value.init(N);
    REP(i, N) {
      mis >> value[i].b >> value[i].a;
      value[i].a += addB;
      value[i].b += addA;
    }
  }
  operator arr<pint>() { return value; }
};

template <class A, class B> struct in_dic {
  dic<A, B> value;

  in_dic(int N) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.first >> pr.second;
      value.insert(pr);
    }
  }
  in_dic(int N, int addA, int addB) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.first >> pr.second;
      pr.first += addA;
      pr.second += addB;
      value.insert(pr);
    }
  }
  in_dic(int N, bool flip) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.second >> pr.first;
      value.insert(pr);
    }
  }
  in_dic(int N, int addA, int addB, bool flip) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.second >> pr.first;
      pr.first += addB;
      pr.second += addA;
      value.insert(pr);
    }
  }
  operator dic<A, B>() { return value; }
};

template <class T> struct in_arr2 {
  arr2<T> value;

  in_arr2(int H, int W) {
    value.init(W, H);
    REP(y, H) {
      REP(x, W) { mis >> value(x, y); }
    }
  }
  in_arr2(int H, int W, int add) {
    value.init(W, H);
    REP(y, H) {
      REP(x, W) {
        mis >> value(x, y);
        value(x, y) += add;
      }
    }
  }

  operator arr2<T>() { return value; }
};

template <class T, class Tuple, size_t... Index>
T MakeFromTupleImpl(Tuple &&t, index_sequence<Index...>) {
  return T(get<Index>(forward<Tuple>(t))...);
}

template <class T, class Tuple> T MakeFromTuple(Tuple &&t) {
  return MakeFromTupleImpl<T>(
      forward<Tuple>(t),
      make_index_sequence<tuple_size<remove_reference_t<Tuple>>::value>{});
}

template <class... ARGS> struct inputWithParam {
  tuple<ARGS...> param;
  inputWithParam() {}
  explicit inputWithParam(tuple<ARGS...> &&param_) : param(param_) {}

  operator int() { return MakeFromTuple<in_int>(param); }
  operator double() { return MakeFromTuple<in_base<double>>(param); }
  operator string() { return MakeFromTuple<in_base<string>>(param); }
  operator char() { return MakeFromTuple<in_base<char>>(param); }

  template <class A, class B> operator pr<A, B>() {
    return MakeFromTuple<in_pr<A, B>>(param);
  }

  template <class T> operator arr<T>() {
    return MakeFromTuple<in_arr<T>>(param);
  }

  template <class A, class B> operator dic<A, B>() {
    return MakeFromTuple<in_dic<A, B>>(param);
  }

  template <class T> operator arr2<T>() {
    return MakeFromTuple<in_arr2<T>>(param);
  }
};

struct input {
  operator int() { return inputWithParam<>(); }
  operator double() { return inputWithParam<>(); }
  operator string() { return inputWithParam<>(); }
  operator char() { return inputWithParam<>(); }

  template <class A, class B> operator pr<A, B>() { return inputWithParam<>(); }

  template <class... ARGS> inputWithParam<ARGS...> operator()(ARGS &&...args) {
    inputWithParam<ARGS...> withParam(forward_as_tuple(args...));
    return withParam;
  }
} in;

//------------------------------------------------------------
#endif

struct MyMain {
  int H = in;
  int W = in;
  int M = in;

  void Run() {
    ints xc(W);
    ints yc(H);
    set<pint> F;
    int maxX = 0;
    int maxY = 0;
    REP(i, M) {
      int y = in(-1);
      int x = in(-1);
      xc(x)++;
      yc(y)++;
      F.insert(pint(x, y));
      chmax(maxX, xc(x));
      chmax(maxY, yc(y));
    }

    int maxXCount = 0;
    int maxYCount = 0;
    REP(x, W) {
      if (maxX == xc(x)) {
        maxXCount++;
      }
    }
    REP(y, H) {
      if (maxY == yc(y)) {
        maxYCount++;
      }
    }
    int left = maxXCount * maxYCount;

    for (auto const &p : F) {
      if (xc(p.x) == maxX && yc(p.y) == maxY) {
        left--;
      }
    }

    int ans = maxX + maxY;
    if (left <= 0) {
      ans--;
    }
    out << ans;
  }
};


Error: TLE

Fixed submission:

#define MOD 1000000007

#if 1
//------------------------------------------------------------
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;

template <class T> struct Entry {
  static void Run() { T().Run(); }
};
struct MyMain;

#if defined(TEST)
#include "test.hpp"
#else
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(16);
  Entry<MyMain>::Run();
  return 0;
}
#endif

//------------------------------------------------------------
using ll = long long;
#define int ll

#define FOR(i, s, e) for (ll i = ll(s); i < ll(e); ++i)
#define RFOR(i, s, e) for (ll i = ll(e) - 1; i >= ll(s); --i)
#define REP(i, n) for (ll i = 0, i##_size = ll(n); i < i##_size; ++i)
#define RREP(i, n) for (ll i = ll(n) - 1; i >= 0; --i)

#define INF INT64_MAX

//------------------------------------------------------------
template <class T> struct ContainerHolder {
  bool flag = true;
  T &var;
  ContainerHolder(T &v) : var(v) {}
  operator bool() const { return flag; }
  T *operator->() { return &var; }
};
template <class T> ContainerHolder<T> ContainerHold(T &v) {
  return ContainerHolder<T>(v);
}

#define CFOR(it, container)                                                    \\
  for (auto holder = ContainerHold(container); holder; holder.flag = false)    \\
    for (auto it = holder->begin(), endIt = holder->end(); it != endIt; ++it)

//------------------------------------------------------------
template <class T> struct arr : public vector<T> {
  arr() {}
  arr(initializer_list<T> il) : vector<T>(il) {}
  explicit arr(ll n, T v = T()) : vector<T>(n, v) {}

  T &operator()(int i) { return (*this)[i]; }
  T const &operator()(int i) const { return (*this)[i]; }
  void init(ll n, T v = T()) {
    this->clear();
    this->resize(n, v);
  }
  ll sz() const { return (ll)this->size(); }
  void pb(T v) { this->push_back(v); }
  void sort() { std::sort(this->begin(), this->end()); }
  void sort(function<bool(T, T)> p) {
    std::sort(this->begin(), this->end(), p);
  }
  void rsort() { std::sort(this->begin(), this->end(), greater<T>()); }
  void reverse() { std::reverse(this->begin(), this->end()); }
  void unique_erase() {
    this->erase(std::unique(this->begin(), this->end()), this->end());
  }
  bool next_permutation() {
    return std::next_permutation(this->begin(), this->end());
  }

  // これ以下はソート済み前提
  int lower_bound(T const &v, function<bool(T, T)> p) {
    return std::lower_bound(this->begin(), this->end(), v, p) - this->begin();
  }
  int lower_bound(T const &v) {
    return std::lower_bound(this->begin(), this->end(), v) - this->begin();
  }

  int upper_bound(T const &v, function<bool(T, T)> p) {
    return std::upper_bound(this->begin(), this->end(), v, p) - this->begin();
  }
  int upper_bound(T const &v) {
    return std::upper_bound(this->begin(), this->end(), v) - this->begin();
  }

  int find_nearest(T const &v) {
    int i = this->lower_bound(v);
    if (i >= sz()) {
      --i;
    } else if ((*this)[i] != v) {
      int p = i - 1;
      if (p >= 0) {
        int id = abs((*this)[i] - v);
        int pd = abs((*this)[p] - v);
        if (pd < id) {
          i = p;
        }
      }
    }
    return i;
  }

  // 見つからなければ-1
  int find(T const &v) {
    int i = this->lower_bound(v);
    if (i >= sz()) {
      return -1;
    }
    if ((*this)[i] != v) {
      return -1;
    }
    return i;
  }
};
using ints = arr<ll>;

template <class T> struct que : public queue<T> {
  ll sz() const { return (ll)this->size(); }
  T popfront() {
    T v = this->front();
    this->pop();
    return v;
  }
};

template <class A, class B> struct pr {
  union {
    A a;
    A key;
    A first;
    A x;
  };
  union {
    B b;
    B value;
    B second;
    B y;
  };

  pr() : a(A()), b(B()){};
  pr(A a_, B b_) : a(a_), b(b_) {}
  pr(pr const &r) : a(r.a), b(r.b){};
  pr(pair<A, B> const &r) : a(r.first), b(r.second){};

  bool operator==(pr const &r) const { return a == r.a && b == r.b; }
  bool operator!=(pr const &r) const { return !((*this) == r); }
  bool operator<(pr const &r) const {
    if (a == r.a) {
      return b < r.b;
    }
    return a < r.a;
  }

  pr operator+(pr v) const { return pr(x, y) += v; }
  pr operator-(pr v) const { return pr(x, y) -= v; }

  pr &operator+=(pr v) {
    x += v.x;
    y += v.y;
    return *this;
  }
  pr &operator-=(pr v) {
    x -= v.x;
    y -= v.y;
    return *this;
  }

  void flip() { swap(x, y); }

  friend istream &operator>>(istream &is, pr &p) {
    is >> p.a >> p.b;
    return is;
  }
  friend ostream &operator<<(ostream &os, pr const &p) {
    os << p.a << " " << p.b;
    return os;
  }
};
using pint = pr<ll, ll>;
using pints = arr<pint>;

template <class K, class V> struct dic : public map<K, V> {
  bool get(K const &k, V *v) {
    auto it = this->find(k);
    if (it != this->end()) {
      *v = it->second;
      return true;
    }
    return false;
  }
};

template <class T> struct arr2 {
  vector<T> m_vec;
  int m_width;
  int m_height;

  arr2() : m_width(0), m_height(0) {}
  arr2(int w, int h, T const &value = T()) : m_width(w), m_height(h) {
    m_vec.resize(w * h, value);
  }
  arr2(arr2 const &r) {
    m_vec = r.m_vec;
    m_width = r.m_width;
    m_height = r.m_height;
  }
  arr2(arr2 &&r) {
    m_vec = move(r.m_vec);
    m_width = r.m_width;
    m_height = r.m_height;
  }
  arr2 &operator=(arr2 const &r) {
    m_vec = r.m_vec;
    m_width = r.m_width;
    m_height = r.m_height;
    return *this;
  }
  arr2 &operator=(arr2 &&r) {
    m_vec = move(r.m_vec);
    m_width = r.m_width;
    m_height = r.m_height;
    return *this;
  }

  bool operator==(arr2 const &r) const { return m_vec = r.m_vec; }

  bool operator<(arr2 const &r) const {
    if (m_width != r.m_width) {
      return m_width < r.m_width;
    }
    if (m_height != r.m_height) {
      return m_height < r.m_height;
    }
    REP(i, m_vec.size()) {
      if (m_vec[i] != r.m_vec[i]) {
        return m_vec[i] < r.m_vec[i];
      }
    }
    return false;
  }

  pint size() const { return pint(m_width, m_height); }
  int width() const { return m_width; }
  int height() const { return m_height; }

  void init(int w, int h, T const &value = T()) {
    m_vec.clear();
    m_vec.resize(w * h, value);
    m_width = w;
    m_height = h;
  }
  void init(pint size, T const &value = T()) { init(size.x, size.y, value); }
  T &operator()(int x, int y) { return m_vec[y * m_width + x]; }
  T const &operator()(int x, int y) const { return m_vec[y * m_width + x]; }

  T &operator()(pint p) { return m_vec[p.y * m_width + p.x]; }
  T const &operator()(pint p) const { return m_vec[p.y * m_width + p.x]; }

  T &operator[](pint p) { return m_vec[p.y * m_width + p.x]; }
  T const &operator[](pint p) const { return m_vec[p.y * m_width + p.x]; }

  bool isIn(int x, int y) const {
    return x >= 0 && x < m_width && y >= 0 && y < m_height;
  }
  bool isIn(pint p) const { return isIn(p.x, p.y); }
  bool isOut(int x, int y) const {
    return x < 0 || x >= m_width || y < 0 || y >= m_height;
  }
  bool isOut(pint p) const { return isOut(p.x, p.y); }

  struct iterator {
  private:
    arr2<T> *owner;

  public:
    pint pt;

    iterator(arr2<T> *owner_, pint pt_) : owner(owner_), pt(pt_) {}

    bool operator==(iterator const &r) const { return pt == r.pt; }
    bool operator!=(iterator const &r) const { return !((*this) == r); }
    void operator++() {
      ++pt.x;
      if (pt.x >= owner->width()) {
        ++pt.y;
        pt.x = 0;
      }
    }
    T &operator*() { return (*owner)(pt); }
  };
  iterator begin() { return iterator(this, pint(0, 0)); }
  iterator end() { return iterator(this, pint(0, height())); }

  void disp(ostream &os) {
    REP(y, m_height) {
      REP(x, m_width) { os << setw(2) << (*this)(x, y) << " "; }
      os << endl;
    }
    os << endl;
  }
};

const pints around4 = {pint(-1, 0), pint(0, -1), pint(1, 0), pint(0, 1)};

//------------------------------------------------------------
template <class T> void chmin(T &a, T b) {
  if (b < a) {
    a = b;
  }
}
template <class T> void chmax(T &a, T b) {
  if (b > a) {
    a = b;
  }
}

constexpr int gcd(int a, int b) {
  if (a < 0) {
    a = -a;
  }
  if (b < 0) {
    b = -b;
  }
  if (a == 0) {
    return b;
  }
  if (b == 0) {
    return a;
  }

  while (int c = a % b) {
    a = b;
    b = c;
  }
  return b;
}

constexpr int lcm(int a, int b) { return a * b / gcd(a, b); }

//------------------------------------------------------------
struct bfs {
  ints froms;
  ints steps;

  bfs(int N, int start, function<ints(int)> getAround) {
    froms.init(N, -1);
    steps.init(N, -1);

    que<ll> queue;
    queue.push(start);
    froms[start] = start;
    steps[start] = 0;

    while (queue.empty() == false) {
      ll p = queue.popfront();

      for (ll n : getAround(p)) {
        if (steps[n] != -1) {
          continue;
        }

        froms[n] = p;
        steps[n] = steps[p] + 1;
        queue.push(n);
      }
    }
  }
};

struct BfsResult {
  arr2<pint> froms;
  arr2<int> steps;
};

template <class T>
BfsResult bfs2(arr2<T> const &field, pints const &starts,
               function<bool(T)> canMove) {
  BfsResult result;
  result.froms.init(field.size(), pint(-1, -1));
  result.steps.init(field.size(), -1);

  que<pint> queue;
  for (auto const &start : starts) {
    queue.push(start);
    result.froms(start) = start;
    result.steps(start) = 0;
  }

  while (queue.empty() == false) {
    auto p = queue.popfront();

    for (auto a : around4) {
      pint n = p + a;
      if (field.isOut(n)) {
        continue;
      }
      if (result.steps(n) != -1) {
        continue;
      }
      if (!canMove(field(n))) {
        continue;
      }

      result.froms(n) = p;
      result.steps(n) = result.steps(p) + 1;
      queue.push(n);
    }
  }

  return result;
}

//------------------------------------------------------------
template <int M> struct modint {
  int raw;

  modint() { raw = 0; }
  modint(int v) {
    if (v < 0) {
      raw = (v % M) + M;
    } else if (v >= M) {
      raw = v % M;
    } else {
      raw = v;
    }
  }
  modint operator+(modint v) const { return modint(raw) += v; }
  modint operator-(modint v) const { return modint(raw) -= v; }
  modint operator*(modint v) const { return modint(raw) *= v; }

  modint &operator+=(modint v) {
    raw += v.raw;
    if (raw >= M) {
      raw -= M;
    }
    return *this;
  }
  modint &operator-=(modint v) {
    raw -= v.raw;
    if (raw < 0) {
      raw += M;
    }
    return *this;
  }
  modint &operator*=(modint v) {
    raw = (raw * v.raw) % M;
    return *this;
  }
  modint pow(int n) const { return modint::pow(raw, n); }
  static modint pow(int a, int n) {
    if (n < 0) {
      // not support
      abort();
    }

    int r = 1;
    while (n) {
      if (n & 1) {
        r = (r * a) % M;
      }
      a = (a * a) % M;
      n >>= 1;
    }
    return modint(r);
  }

  modint inv() const {
    int a = raw;
    int b = M;
    int u = 1;
    int v = 0;
    while (b) {
      int t = a / b;
      a -= t * b;
      u -= t * v;
      swap(a, b);
      swap(u, v);
    }
    u %= M;
    if (u < 0) {
      u += M;
    }
    return u;
  }

  friend istream &operator>>(istream &is, modint &m) {
    int v;
    is >> v;
    m = modint(v);
    return is;
  }
  friend ostream &operator<<(ostream &os, modint const &m) {
    return os << m.raw;
  }
};

using mint = modint<MOD>;
using mints = arr<mint>;

//------------------------------------------------------------
struct UnionFind {
  struct Node {
    Node *parent = nullptr;
    int count = 1;

    Node *Root() {
      if (parent == nullptr) {
        return this;
      }
      return parent = parent->Root();
    }
  };
  vector<Node> nodes;

  UnionFind(int count) { nodes.resize(count); }

  void Join(int a, int b) {
    Node *rootA = nodes[a].Root();
    Node *rootB = nodes[b].Root();
    if (rootA == rootB) {
      return;
    }

    if (rootA->count > rootB->count) {
      swap(rootA, rootB);
    }

    rootB->count += rootA->count;
    rootA->parent = rootB;
    rootA->count = 0;
  }

  bool IsReachable(int a, int b) {
    Node *rootA = nodes[a].Root();
    Node *rootB = nodes[b].Root();
    return rootA == rootB;
  }

  int Count(int a) { return nodes[a].Root()->count; }
};

//------------------------------------------------------------
template <class T> struct SumsImpl {
private:
  int N;
  arr<T> S;

public:
  SumsImpl(int N_) : N(N_), S(N + 1, 0) {}
  void Set(int i, T const &value) { S(i + 1) = S(i) + value; }

  // l <= x < r
  T Get(int l, int r) const { return S(r) - S(l); }
};
using Sums = SumsImpl<int>;

template <class T> struct ImosImpl {
private:
  int N;
  arr<T> S;

public:
  ImosImpl() {}
  ImosImpl(int N_) : N(N_), S(N + 1, 0) {}

  void init(int N_) {
    N = N_;
    S.init(N + 1, 0);
  }

  void Add(int i, T const &value) { S(i + 1) += value; }

  void Calc() {
    REP(i, N) { S(i + 1) += S(i); }
  }

  // l <= x < r
  T Get(int l, int r) const { return S(r) - S(l); }

  T Get(int i) const { return S(i); }
};
using Imos = ImosImpl<int>;

template <class T> struct Sums2Impl {
private:
  arr2<T> sums;

public:
  Sums2Impl(int W, int H) : sums(W + 1, H + 1) {}

  void Set(int x, int y, T const &value) {
    T s = value;
    s += sums(x + 1, y);
    s += sums(x, y + 1);
    s -= sums(x, y);
    sums(x + 1, y + 1) = s;
  }

  // l <= x < r
  // t <= y < b
  T Get(int l, int t, int r, int b) const {
    int s = sums(r, b);
    s -= sums(r, t);
    s -= sums(l, b);
    s += sums(l, t);
    return s;
  }
};
using Sums2 = Sums2Impl<int>;

template <class T> struct Imos2Impl {
private:
  arr2<T> sums;

public:
  Imos2Impl(int W, int H) : sums(W + 1, H + 1) {}

  void Add(int x, int y, T const &value) { sums(x + 1, y + 1) += value; }

  void Calc() {
    REP(y, sums.height() - 1) {
      REP(x, sums.width() - 1) {
        T s = 0;
        s += sums(x + 1, y);
        s += sums(x, y + 1);
        s -= sums(x, y);
        sums(x + 1, y + 1) += s;
      }
    }
  }

  // l <= x < r
  // t <= y < b
  T Get(int l, int t, int r, int b) const {
    int s = sums(r, b);
    s -= sums(r, t);
    s -= sums(l, b);
    s += sums(l, t);
    return s;
  }
};
using Imos2 = Imos2Impl<int>;

//------------------------------------------------------------
struct CombiTbl {
  mints fac;
  mints ifac;

  // 重複組み合わせを使う場合は N*2 を指定しないといけない
  CombiTbl(int N) : fac(N), ifac(N) {
    fac[0] = 1;
    ifac[0] = 1;
    FOR(i, 1, N) {
      fac[i] = fac[i - 1] * i;
      ifac[i] = fac[i].inv();
    }
  }

  // a!
  mint Fac(int a) const { return fac(a); }

  // aPb
  mint Perm(int a, int b) const { return fac(a) * ifac(a - b); }

  // aCb
  mint Combi(int a, int b) const { return fac(a) * ifac(b) * ifac(a - b); }

  // aHb（重複組み合わせ）
  mint RepCombi(int a, int b) const { return Combi(a + b - 1, b); }
};

//------------------------------------------------------------
#if defined(TEST)
extern istream &mis;
extern ostream &mos;
#else
istream &mis = cin;
ostream &mos = cout;
#endif

//------------------------------------------------------------

struct OutputStream {
  template <class T>
  friend OutputStream &operator<<(OutputStream &s, T const &v) {
    mos << v << '\\n';
    return s;
  }
} out;

struct PrintStream {
  stringstream ss;

  template <class T> friend PrintStream &operator<<(PrintStream &s, T &&v) {
    s.ss << v << ' ';
    return s;
  }

  PrintStream &operator<<(PrintStream &(*manip)(PrintStream &)) {
    return (*manip)(*this);
  }
} prn;

PrintStream &en(PrintStream &s) {
  string str = s.ss.str();
  s.ss = stringstream();
  if (str.empty() == false) {
    str.pop_back();
  }
  mos << str << '\\n';
  return s;
}

//------------------------------------------------------------

template <class T> struct in_base {
  T value;
  in_base() { mis >> value; }
  operator T() { return value; }
};

struct in_int {
  int value;

  in_int() { mis >> value; }
  in_int(int add) {
    mis >> value;
    value += add;
  }
  operator int() { return value; }
};

template <class A, class B> struct in_pr {
  pr<A, B> value;

  in_pr() { mis >> value.a >> value.b; }
  in_pr(int addA, int addB) {
    mis >> value.a >> value.b;
    value.a += addA;
    value.b += addB;
  }
  in_pr(bool flip) { mis >> value.b >> value.a; }
  in_pr(int addA, int addB, bool flip) {
    mis >> value.b >> value.a;
    value.a += addB;
    value.b += addA;
  }
  operator pr<A, B>() { return value; }
};

template <class T> struct in_arr {
  arr<T> value;

  in_arr(int N) {
    value.init(N);
    REP(i, N) { mis >> value[i]; }
  }
  in_arr(int N, int add) {
    value.init(N);
    REP(i, N) {
      mis >> value[i];
      value[i] += add;
    }
  }
  operator arr<T>() { return value; }
};

template <> struct in_arr<pint> {
  arr<pint> value;

  in_arr(int N) {
    value.init(N);
    REP(i, N) { mis >> value[i]; }
  }
  in_arr(int N, int addA, int addB) {
    value.init(N);
    REP(i, N) {
      mis >> value[i].a >> value[i].b;
      value[i].a += addA;
      value[i].b += addB;
    }
  }
  in_arr(int N, bool flip) {
    value.init(N);
    REP(i, N) { mis >> value[i].b >> value[i].a; }
  }
  in_arr(int N, int addA, int addB, bool flip) {
    value.init(N);
    REP(i, N) {
      mis >> value[i].b >> value[i].a;
      value[i].a += addB;
      value[i].b += addA;
    }
  }
  operator arr<pint>() { return value; }
};

template <class A, class B> struct in_dic {
  dic<A, B> value;

  in_dic(int N) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.first >> pr.second;
      value.insert(pr);
    }
  }
  in_dic(int N, int addA, int addB) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.first >> pr.second;
      pr.first += addA;
      pr.second += addB;
      value.insert(pr);
    }
  }
  in_dic(int N, bool flip) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.second >> pr.first;
      value.insert(pr);
    }
  }
  in_dic(int N, int addA, int addB, bool flip) {
    REP(i, N) {
      pair<A, B> pr;
      mis >> pr.second >> pr.first;
      pr.first += addB;
      pr.second += addA;
      value.insert(pr);
    }
  }
  operator dic<A, B>() { return value; }
};

template <class T> struct in_arr2 {
  arr2<T> value;

  in_arr2(int H, int W) {
    value.init(W, H);
    REP(y, H) {
      REP(x, W) { mis >> value(x, y); }
    }
  }
  in_arr2(int H, int W, int add) {
    value.init(W, H);
    REP(y, H) {
      REP(x, W) {
        mis >> value(x, y);
        value(x, y) += add;
      }
    }
  }

  operator arr2<T>() { return value; }
};

template <class T, class Tuple, size_t... Index>
T MakeFromTupleImpl(Tuple &&t, index_sequence<Index...>) {
  return T(get<Index>(forward<Tuple>(t))...);
}

template <class T, class Tuple> T MakeFromTuple(Tuple &&t) {
  return MakeFromTupleImpl<T>(
      forward<Tuple>(t),
      make_index_sequence<tuple_size<remove_reference_t<Tuple>>::value>{});
}

template <class... ARGS> struct inputWithParam {
  tuple<ARGS...> param;
  inputWithParam() {}
  explicit inputWithParam(tuple<ARGS...> &&param_) : param(param_) {}

  operator int() { return MakeFromTuple<in_int>(param); }
  operator double() { return MakeFromTuple<in_base<double>>(param); }
  operator string() { return MakeFromTuple<in_base<string>>(param); }
  operator char() { return MakeFromTuple<in_base<char>>(param); }

  template <class A, class B> operator pr<A, B>() {
    return MakeFromTuple<in_pr<A, B>>(param);
  }

  template <class T> operator arr<T>() {
    return MakeFromTuple<in_arr<T>>(param);
  }

  template <class A, class B> operator dic<A, B>() {
    return MakeFromTuple<in_dic<A, B>>(param);
  }

  template <class T> operator arr2<T>() {
    return MakeFromTuple<in_arr2<T>>(param);
  }
};

struct input {
  operator int() { return inputWithParam<>(); }
  operator double() { return inputWithParam<>(); }
  operator string() { return inputWithParam<>(); }
  operator char() { return inputWithParam<>(); }

  template <class A, class B> operator pr<A, B>() { return inputWithParam<>(); }

  template <class... ARGS> inputWithParam<ARGS...> operator()(ARGS &&...args) {
    inputWithParam<ARGS...> withParam(forward_as_tuple(args...));
    return withParam;
  }
} in;

//------------------------------------------------------------
#endif

struct MyMain {
  int H = in;
  int W = in;
  int M = in;

  void Run() {
    ints xc(W);
    ints yc(H);
    set<pint> F;
    REP(i, M) {
      int y = in(-1);
      int x = in(-1);
      xc(x)++;
      yc(y)++;
      F.insert(pint(x, y));
    }

    int ans = 0;
    REP(y, H) {
      REP(x, W) {
        int r = xc(x) + yc(y);
        if (F.count(pint(x, y))) {
          r -= 1;
        }
        chmax(ans, r);
      }
    }

    out << ans;
  }
};