Problem p02555 (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"
extern istream &mis;
extern ostream &mos;
#else
istream &mis = cin;
ostream &mos = cout;
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 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 A, class B, class C> struct tr {
  union {
    A a;
    A first;
    A x;
  };
  union {
    B b;
    B second;
    B y;
  };
  union {
    C c;
    C third;
    C z;
  };

  tr() : a(A()), b(B()), c(C()){};
  tr(A a_, B b_, C c_) : a(a_), b(b_), c(c_) {}
  tr(tr const &r) : a(r.a), b(r.b), c(r.c){};

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

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

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

  friend istream &operator>>(istream &is, tr &p) {
    is >> p.a >> p.b >> p.c;
    return is;
  }
  friend ostream &operator<<(ostream &os, tr const &p) {
    os << p.a << " " << p.b << " " << p.c;
    return os;
  }
};
using tint = tr<ll, ll, ll>;
using tints = arr<tint>;

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<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(h, vector<T>(w, 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(y, m_height) {
      REP(x, m_width) {
        if ((*this)(x, y) != r(x, y)) {
          return (*this)(x, y) < r(x, y);
        }
      }
    }
    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(h, vector<T>(w, 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][x]; }
  T const &operator()(int x, int y) const { return m_vec[y][x]; }

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

  T &operator[](pint p) { return m_vec[p.y][p.x]; }
  T const &operator[](pint p) const { return m_vec[p.y][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 / gcd(a, b) * b; }

//------------------------------------------------------------
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 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 &endl(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> void input(T &value) { mis >> value; }
void input(int &value, int add) {
  mis >> value;
  value += add;
}
template <class A, class B> void input(pr<A, B> &value) {
  mis >> value.a >> value.b;
}
template <class A, class B> void input(pr<A, B> &value, int addA, int addB) {
  mis >> value.a >> value.b;
  value.a += addA;
  value.b += addB;
}
template <class A, class B, class C> void input(tr<A, B, C> &value) {
  mis >> value.a >> value.b >> value.c;
}
template <class A, class B, class C>
void input(tr<A, B, C> &value, int addA, int addB, int addC) {
  mis >> value.a >> value.b >> value.c;
  value.a += addA;
  value.b += addB;
  value.c += addC;
}
template <class T, class... ARGS>
void input(arr<T> &value, int N, ARGS &&...args) {
  value.init(N);
  REP(i, N) { input(value[i], forward<ARGS>(args)...); }
}
template <class T, class... ARGS>
void input(arr2<T> &value, int H, int W, ARGS &&...args) {
  value.init(W, H);
  REP(y, H) {
    REP(x, W) { input(value(x, y), forward<ARGS>(args)...); }
  }
}
template <class K, class V, class... ARGS>
void input(dic<K, V> &value, int N, ARGS &&...args) {
  REP(i, N) {
    pair<K, V> pr;
    input(pr.first);
    input(pr.second, forward<ARGS>(args)...);
    value.insert(pr);
  }
}

template <class T> struct inputHolder {
  T value;
  template <class... ARGS> inputHolder(ARGS &&...args) {
    input(value, forward<ARGS>(args)...);
  }
  operator 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<inputHolder<int>>(param); }
  operator double() { return MakeFromTuple<inputHolder<double>>(param); }
  operator string() { return MakeFromTuple<inputHolder<string>>(param); }
  operator char() { return MakeFromTuple<inputHolder<char>>(param); }
  template <class A, class B> operator pr<A, B>() {
    return MakeFromTuple<inputHolder<pr<A, B>>>(param);
  }
  template <class A, class B, class C> operator tr<A, B, C>() {
    return MakeFromTuple<inputHolder<tr<A, B, C>>>(param);
  }
  template <class T> operator arr<T>() {
    return MakeFromTuple<inputHolder<arr<T>>>(param);
  }
  template <class A, class B> operator dic<A, B>() {
    return MakeFromTuple<inputHolder<dic<A, B>>>(param);
  }
  template <class T> operator arr2<T>() {
    return MakeFromTuple<inputHolder<arr2<T>>>(param);
  }
};
struct inputObject {
  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 A, class B, class C> operator tr<A, B, C>() {
    return inputWithParam<>();
  }
  template <class... ARGS> inputWithParam<ARGS...> operator()(ARGS &&...args) {
    inputWithParam<ARGS...> withParam(forward_as_tuple(args...));
    return withParam;
  }
} in;

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

struct MyMain {
  int S = in;

  void Run() {
    arr2<mint> dp(S + 1, S + 1);
    dp(0, S) = 1;
    int maxY = S;
    FOR(x, 1, (S / 3) + 3) {
      int newMaxY = 0;
      REP(by, maxY + 1) {
        FOR(cy, 3, by + 1) {
          mint count = dp(x - 1, by);
          int y = by - cy;
          if (y < 0) {
            break;
          }
          dp(x, y) += count;
          chmax(newMaxY, y);
        }
      }
      maxY = newMaxY;
    }

    mint ans = 0;
    FOR(x, 1, S + 1) { ans += dp(x, 0); }

    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"
extern istream &mis;
extern ostream &mos;
#else
istream &mis = cin;
ostream &mos = cout;
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 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 A, class B, class C> struct tr {
  union {
    A a;
    A first;
    A x;
  };
  union {
    B b;
    B second;
    B y;
  };
  union {
    C c;
    C third;
    C z;
  };

  tr() : a(A()), b(B()), c(C()){};
  tr(A a_, B b_, C c_) : a(a_), b(b_), c(c_) {}
  tr(tr const &r) : a(r.a), b(r.b), c(r.c){};

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

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

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

  friend istream &operator>>(istream &is, tr &p) {
    is >> p.a >> p.b >> p.c;
    return is;
  }
  friend ostream &operator<<(ostream &os, tr const &p) {
    os << p.a << " " << p.b << " " << p.c;
    return os;
  }
};
using tint = tr<ll, ll, ll>;
using tints = arr<tint>;

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<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(h, vector<T>(w, 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(y, m_height) {
      REP(x, m_width) {
        if ((*this)(x, y) != r(x, y)) {
          return (*this)(x, y) < r(x, y);
        }
      }
    }
    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(h, vector<T>(w, 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][x]; }
  T const &operator()(int x, int y) const { return m_vec[y][x]; }

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

  T &operator[](pint p) { return m_vec[p.y][p.x]; }
  T const &operator[](pint p) const { return m_vec[p.y][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 / gcd(a, b) * b; }

//------------------------------------------------------------
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 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 &endl(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> void input(T &value) { mis >> value; }
void input(int &value, int add) {
  mis >> value;
  value += add;
}
template <class A, class B> void input(pr<A, B> &value) {
  mis >> value.a >> value.b;
}
template <class A, class B> void input(pr<A, B> &value, int addA, int addB) {
  mis >> value.a >> value.b;
  value.a += addA;
  value.b += addB;
}
template <class A, class B, class C> void input(tr<A, B, C> &value) {
  mis >> value.a >> value.b >> value.c;
}
template <class A, class B, class C>
void input(tr<A, B, C> &value, int addA, int addB, int addC) {
  mis >> value.a >> value.b >> value.c;
  value.a += addA;
  value.b += addB;
  value.c += addC;
}
template <class T, class... ARGS>
void input(arr<T> &value, int N, ARGS &&...args) {
  value.init(N);
  REP(i, N) { input(value[i], forward<ARGS>(args)...); }
}
template <class T, class... ARGS>
void input(arr2<T> &value, int H, int W, ARGS &&...args) {
  value.init(W, H);
  REP(y, H) {
    REP(x, W) { input(value(x, y), forward<ARGS>(args)...); }
  }
}
template <class K, class V, class... ARGS>
void input(dic<K, V> &value, int N, ARGS &&...args) {
  REP(i, N) {
    pair<K, V> pr;
    input(pr.first);
    input(pr.second, forward<ARGS>(args)...);
    value.insert(pr);
  }
}

template <class T> struct inputHolder {
  T value;
  template <class... ARGS> inputHolder(ARGS &&...args) {
    input(value, forward<ARGS>(args)...);
  }
  operator 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<inputHolder<int>>(param); }
  operator double() { return MakeFromTuple<inputHolder<double>>(param); }
  operator string() { return MakeFromTuple<inputHolder<string>>(param); }
  operator char() { return MakeFromTuple<inputHolder<char>>(param); }
  template <class A, class B> operator pr<A, B>() {
    return MakeFromTuple<inputHolder<pr<A, B>>>(param);
  }
  template <class A, class B, class C> operator tr<A, B, C>() {
    return MakeFromTuple<inputHolder<tr<A, B, C>>>(param);
  }
  template <class T> operator arr<T>() {
    return MakeFromTuple<inputHolder<arr<T>>>(param);
  }
  template <class A, class B> operator dic<A, B>() {
    return MakeFromTuple<inputHolder<dic<A, B>>>(param);
  }
  template <class T> operator arr2<T>() {
    return MakeFromTuple<inputHolder<arr2<T>>>(param);
  }
};
struct inputObject {
  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 A, class B, class C> operator tr<A, B, C>() {
    return inputWithParam<>();
  }
  template <class... ARGS> inputWithParam<ARGS...> operator()(ARGS &&...args) {
    inputWithParam<ARGS...> withParam(forward_as_tuple(args...));
    return withParam;
  }
} in;

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

struct MyMain {
  int S = in;

  void Run() {
    arr2<mint> dp(S + 1, S + 1);
    dp(0, S) = 1;
    FOR(x, 1, (S / 3) + 3) {
      REP(by, S + 1) {
        FOR(cy, 3, S + 1) {
          mint count = dp(x - 1, by);
          int y = by - cy;
          if (y < 0) {
            continue;
          }
          dp(x, y) += count;
        }
      }
    }

    mint ans = 0;
    FOR(x, 1, S + 1) { ans += dp(x, 0); }

    out << ans;
  }
};