Problem p02561 (C++) — buggy submission, verdict: Memory Limit Exceeded

/* #region Head */

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  os << "{";
  REPI(itr, map_var) {
    auto [key, value] = *itr;
    os << "(" << key << ", " << value << ")";
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) {
  return is >> rhs;
}
template <typename T> ostream &operator,(ostream &os, const T &rhs) {
  return os << ' ' << rhs;
}

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region Graph */

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t = int, class flow_t = int> struct Edge {
  ll src;          // エッジ始点となる頂点
  ll dst;          // エッジ終点となる頂点
  weight_t weight; // 重み
  flow_t cap;
  Edge() : src(0), dst(0), weight(0) {}
  Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
  Edge(ll src, ll dst, weight_t weight, flow_t cap)
      : src(src), dst(dst), weight(weight), cap(cap) {}
  // Edge 標準出力
  friend ostream &operator<<(ostream &os, Edge &edge) {
    os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
    return os;
  }
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t = int, class flow_t = int>
class Node : public vc<Edge<weight_t, flow_t>> {
public:
  ll idx;
  Node() : vc<Edge<weight_t, flow_t>>() {}
  // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b,
  // w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t = int, class flow_t = int>
class Graph : public vc<Node<weight_t, flow_t>> {
public:
  Graph() : vc<Node<weight_t, flow_t>>() {}
  Graph(int n) : vc<Node<weight_t, flow_t>>(n) {
    REP(i, 0, n)(*this)[i].idx = i;
  }
  // 単方向
  void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) {
    (*this)[a].emplace_back(a, b, w, cap);
  }
  // 双方向
  void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) {
    add_arc(a, b, w, cap), add_arc(b, a, w, cap);
  }
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;

/* #endregion */

/* #region Dinic */

// 最大流 (Dinic) | libalgo https://tubo28.me/compprog/algorithm/dinic/
template <class weight_t, class flow_t> struct dinic {
  int n, s, t;
  vc<int> level, prog, que;
  vc<vc<flow_t>> cap, flow;
  vc<vc<int>> g;
  flow_t inf;

  dinic(const int n)
      : n(n), cap(n, vc<flow_t>(n)), flow(n, vc<flow_t>(n)), g(n, vc<int>()),
        inf(std::numeric_limits<flow_t>::max() / 8) {}
  dinic(const Graph<weight_t, flow_t> &graph)
      : n(graph.size()), cap(n, vc<flow_t>(n)), flow(n, vc<flow_t>(n)),
        g(n, vc<int>()), inf(std::numeric_limits<flow_t>::max() / 8) {
    build(graph);
  }
  void build(const Graph<weight_t, flow_t> &graph) {
    for (int i = 0; i < n; i++) {
      for (auto &e : graph[i]) {
        int u = e.src, v = e.dst;
        flow_t c = e.cap;
        cap[u][v] += c;
        cap[v][u] += c;
        flow[v][u] += c;
        g[u].push_back(v);
        g[v].push_back(u);
      }
    }
  }
  inline flow_t residue(int u, int v) { return cap[u][v] - flow[u][v]; }
  flow_t solve(int s_, int t_) {
    this->t = t_, this->s = s_;
    que.resize(n + 1);
    flow_t res = 0;
    while (levelize()) {
      prog.assign(n, 0);
      res += augment(s, inf);
    }
    return res;
  }
  bool levelize() {
    int l = 0, r = 0;
    level.assign(n, -1);
    level[s] = 0;
    que[r++] = s;
    while (l != r) {
      int v = que[l++];
      if (v == t)
        break;
      for (const int &d : g[v])
        if (level[d] == -1 && residue(v, d) != 0) {
          level[d] = level[v] + 1;
          que[r++] = d;
        }
    }
    return level[t] != -1;
  }
  flow_t augment(int v, flow_t lim) {
    flow_t res = 0;
    if (v == t)
      return lim;
    for (int &i = prog[v]; i < (int)g[v].size(); i++) {
      const int &d = g[v][i];
      if (residue(v, d) == 0 || level[v] >= level[d])
        continue;
      const flow_t aug = augment(d, std::min(lim, residue(v, d)));
      flow[v][d] += aug;
      flow[d][v] -= aug;
      res += aug;
      lim -= aug;
      if (lim == 0)
        break;
    }
    return res;
  }
};

/* #endregion */

// Problem
void solve() {
  VAR(ll, n, m); //
  vc<string> s(n);
  cin >> s;

  using Flow = int;
  Graph<int, Flow> g(n * m + 2);
  int S = n * m, T = n * m + 1;

  // s -> even / odd -> t
  REP(i, 0, n) REP(j, 0, m) {
    if (s[i][j] == '#')
      continue;
    int v = i * m + j;
    if ((i + j) % 2 == 0) {
      g.add_arc(S, v, 0, 1);
    } else {
      g.add_arc(v, T, 0, 1);
    }
  }

  // even -> odd
  REP(i, 0, n) REP(j, 0, m) {
    if ((i + j) % 2 == 1 || s[i][j] == '#')
      continue;
    int v0 = i * m + j;
    if (i && s[i - 1][j] == '.') {
      int v1 = (i - 1) * m + j;
      g.add_arc(v0, v1, 0, 1);
    }
    if (j && s[i][j - 1] == '.') {
      int v1 = i * m + (j - 1);
      g.add_arc(v0, v1, 0, 1);
    }
    if (i + 1 < n && s[i + 1][j] == '.') {
      int v1 = (i + 1) * m + j;
      g.add_arc(v0, v1, 0, 1);
    }
    if (j + 1 < m && s[i][j + 1] == '.') {
      int v1 = i * m + (j + 1);
      g.add_arc(v0, v1, 0, 1);
    }
  }

  dinic<int, int> dn(g);
  int f = dn.solve(S, T);
  cout << f << endl;

  vc<string> ans = s;
  REP(i, 0, n) REP(j, 0, m) {
    if ((i + j) % 2 == 1 || s[i][j] == '#')
      continue;
    int v0 = i * m + j;
    if (i && s[i - 1][j] == '.') { // 上へ
      int v1 = (i - 1) * m + j;
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '^', ans[i - 1][j] = 'v';
      }
    }
    if (j && s[i][j - 1] == '.') { // 左へ
      int v1 = i * m + (j - 1);
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '<', ans[i][j - 1] = '>';
      }
    }
    if (i + 1 < n && s[i + 1][j] == '.') { // 下へ
      int v1 = (i + 1) * m + j;
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = 'v', ans[i + 1][j] = '^';
      }
    }
    if (j + 1 < m && s[i][j + 1] == '.') { // 右へ
      int v1 = i * m + (j + 1);
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '>', ans[i][j + 1] = '<';
      }
    }
  }
  // dump(s, ans);
  REP(i, 0, n) cout << ans[i] << endl;
}

// entry point
int main() {
  solve();
  return 0;
}


Error: MLE

Fixed submission:

/* #region Head */

// #define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;

#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d)                                                       \\
  for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d)                                                      \\
  for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c)                                                                \\
  sort(ALL(c));                                                                \\
  for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());

#define endl '\\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;

template <typename T>
istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
  for (T &x : vec)
    is >> x;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
  os << "{";
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
  os << "}";
  return os;
}
template <typename T>
ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
  REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\\n" : " ");
  return os;
}

template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
  is >> pair_var.first >> pair_var.second;
  return is;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
  os << "(" << pair_var.first << ", " << pair_var.second << ")";
  return os;
}

// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
  os << "{";
  REPI(itr, map_var) {
    os << *itr;
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  return os << "}";
}
template <typename T, typename U>
ostream &operator<<(ostream &os, map<T, U> &map_var) {
  return out_iter(os, map_var);
}
template <typename T, typename U>
ostream &operator<<(ostream &os, um<T, U> &map_var) {
  os << "{";
  REPI(itr, map_var) {
    auto [key, value] = *itr;
    os << "(" << key << ", " << value << ")";
    auto itrcp = itr;
    if (++itrcp != map_var.end())
      os << ", ";
  }
  os << "}";
  return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) {
  return out_iter(os, set_var);
}
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
  pq<T> pq_cp(pq_var);
  os << "{";
  if (!pq_cp.empty()) {
    os << pq_cp.top(), pq_cp.pop();
    while (!pq_cp.empty())
      os << ", " << pq_cp.top(), pq_cp.pop();
  }
  return os << "}";
}

// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail>
void dump_func(Head &&head, Tail &&...tail) {
  DUMPOUT << head;
  if (sizeof...(Tail) > 0)
    DUMPOUT << ", ";
  dump_func(move(tail)...);
}

// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmax(T &xmax, const U &x, Comp comp = {}) {
  if (comp(xmax, x)) {
    xmax = x;
    return true;
  }
  return false;
}

// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>>
bool chmin(T &xmin, const U &x, Comp comp = {}) {
  if (comp(x, xmin)) {
    xmin = x;
    return true;
  }
  return false;
}

// ローカル用
#define DEBUG_

#ifdef DEBUG_
#define DEB
#define dump(...)                                                              \\
  DUMPOUT << "  " << string(#__VA_ARGS__) << ": "                              \\
          << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl  \\
          << "    ",                                                           \\
      dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif

#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) {
  return is >> rhs;
}
template <typename T> ostream &operator,(ostream &os, const T &rhs) {
  return os << ' ' << rhs;
}

struct AtCoderInitialize {
  static constexpr int IOS_PREC = 15;
  static constexpr bool AUTOFLUSH = false;
  AtCoderInitialize() {
    ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
    cout << fixed << setprecision(IOS_PREC);
    if (AUTOFLUSH)
      cout << unitbuf;
  }
} ATCODER_INITIALIZE;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

/* #region Graph */

// エッジ（本来エッジは双方向だが，ここでは単方向で管理）
template <class weight_t = int, class flow_t = int> struct Edge {
  ll src;          // エッジ始点となる頂点
  ll dst;          // エッジ終点となる頂点
  weight_t weight; // 重み
  flow_t cap;
  Edge() : src(0), dst(0), weight(0) {}
  Edge(ll src, ll dst, weight_t weight) : src(src), dst(dst), weight(weight) {}
  Edge(ll src, ll dst, weight_t weight, flow_t cap)
      : src(src), dst(dst), weight(weight), cap(cap) {}
  // Edge 標準出力
  friend ostream &operator<<(ostream &os, Edge &edge) {
    os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";
    return os;
  }
};
// 同じ頂点を始点とするエッジ集合
template <class weight_t = int, class flow_t = int>
class Node : public vc<Edge<weight_t, flow_t>> {
public:
  ll idx;
  Node() : vc<Edge<weight_t, flow_t>>() {}
  // void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b,
  // w, cap); };
};
// graph[i] := 頂点 i を始点とするエッジ集合
template <class weight_t = int, class flow_t = int>
class Graph : public vc<Node<weight_t, flow_t>> {
public:
  Graph() : vc<Node<weight_t, flow_t>>() {}
  Graph(int n) : vc<Node<weight_t, flow_t>>(n) {
    REP(i, 0, n)(*this)[i].idx = i;
  }
  // 単方向
  void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) {
    (*this)[a].emplace_back(a, b, w, cap);
  }
  // 双方向
  void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) {
    add_arc(a, b, w, cap), add_arc(b, a, w, cap);
  }
};
// using Array = vc<Weight>;
// using Matrix = vc<Array>;

/* #endregion */

/* #region Dinic */

// 最大流 (Dinic) | libalgo https://tubo28.me/compprog/algorithm/dinic/
template <class weight_t, class flow_t> struct dinic {
  int n, s, t;
  vc<int> level, prog, que;
  vc<vc<flow_t>> cap, flow;
  vc<vc<int>> g;
  flow_t inf;

  dinic(const int n)
      : n(n), cap(n, vc<flow_t>(n)), flow(n, vc<flow_t>(n)), g(n, vc<int>()),
        inf(std::numeric_limits<flow_t>::max() / 8) {}
  dinic(const Graph<weight_t, flow_t> &graph)
      : n(graph.size()), cap(n, vc<flow_t>(n)), flow(n, vc<flow_t>(n)),
        g(n, vc<int>()), inf(std::numeric_limits<flow_t>::max() / 8) {
    build(graph);
  }
  void build(const Graph<weight_t, flow_t> &graph) {
    for (int i = 0; i < n; i++) {
      for (auto &e : graph[i]) {
        int u = e.src, v = e.dst;
        flow_t c = e.cap;
        cap[u][v] += c;
        cap[v][u] += c;
        flow[v][u] += c;
        g[u].push_back(v);
        g[v].push_back(u);
      }
    }
  }
  inline flow_t residue(int u, int v) { return cap[u][v] - flow[u][v]; }
  flow_t solve(int s_, int t_) {
    this->t = t_, this->s = s_;
    que.resize(n + 1);
    flow_t res = 0;
    while (levelize()) {
      prog.assign(n, 0);
      res += augment(s, inf);
    }
    return res;
  }
  bool levelize() {
    int l = 0, r = 0;
    level.assign(n, -1);
    level[s] = 0;
    que[r++] = s;
    while (l != r) {
      int v = que[l++];
      if (v == t)
        break;
      for (const int &d : g[v])
        if (level[d] == -1 && residue(v, d) != 0) {
          level[d] = level[v] + 1;
          que[r++] = d;
        }
    }
    return level[t] != -1;
  }
  flow_t augment(int v, flow_t lim) {
    flow_t res = 0;
    if (v == t)
      return lim;
    for (int &i = prog[v]; i < (int)g[v].size(); i++) {
      const int &d = g[v][i];
      if (residue(v, d) == 0 || level[v] >= level[d])
        continue;
      const flow_t aug = augment(d, std::min(lim, residue(v, d)));
      flow[v][d] += aug;
      flow[d][v] -= aug;
      res += aug;
      lim -= aug;
      if (lim == 0)
        break;
    }
    return res;
  }
};

/* #endregion */

// Problem
void solve() {
  VAR(ll, n, m); //
  vc<string> s(n);
  cin >> s;

  using Flow = ll;
  Graph<ll, Flow> g(n * m + 2);
  int S = n * m, T = n * m + 1;

  // s -> even / odd -> t
  REP(i, 0, n) REP(j, 0, m) {
    if (s[i][j] == '#')
      continue;
    int v = i * m + j;
    if ((i + j) % 2 == 0) {
      g.add_arc(S, v, 0, 1);
    } else {
      g.add_arc(v, T, 0, 1);
    }
  }

  // even -> odd
  REP(i, 0, n) REP(j, 0, m) {
    if ((i + j) % 2 == 1 || s[i][j] == '#')
      continue;
    int v0 = i * m + j;
    if (i && s[i - 1][j] == '.') {
      int v1 = (i - 1) * m + j;
      g.add_arc(v0, v1, 0, 1);
    }
    if (j && s[i][j - 1] == '.') {
      int v1 = i * m + (j - 1);
      g.add_arc(v0, v1, 0, 1);
    }
    if (i + 1 < n && s[i + 1][j] == '.') {
      int v1 = (i + 1) * m + j;
      g.add_arc(v0, v1, 0, 1);
    }
    if (j + 1 < m && s[i][j + 1] == '.') {
      int v1 = i * m + (j + 1);
      g.add_arc(v0, v1, 0, 1);
    }
  }

  dinic<ll, Flow> dn(g);
  ll f = dn.solve(S, T);
  cout << f << endl;

  vc<string> ans = s;
  REP(i, 0, n) REP(j, 0, m) {
    if ((i + j) % 2 == 1 || s[i][j] == '#')
      continue;
    int v0 = i * m + j;
    if (i && s[i - 1][j] == '.') { // 上へ
      int v1 = (i - 1) * m + j;
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '^', ans[i - 1][j] = 'v';
      }
    }
    if (j && s[i][j - 1] == '.') { // 左へ
      int v1 = i * m + (j - 1);
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '<', ans[i][j - 1] = '>';
      }
    }
    if (i + 1 < n && s[i + 1][j] == '.') { // 下へ
      int v1 = (i + 1) * m + j;
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = 'v', ans[i + 1][j] = '^';
      }
    }
    if (j + 1 < m && s[i][j + 1] == '.') { // 右へ
      int v1 = i * m + (j + 1);
      if (dn.flow[v0][v1] > 0) {
        ans[i][j] = '>', ans[i][j + 1] = '<';
      }
    }
  }
  // dump(s, ans);
  REP(i, 0, n) cout << ans[i] << endl;
}

// entry point
int main() {
  solve();
  return 0;
}