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:heavy_check_mark: test/1_mytest/partizan.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "my_template.hpp"

#include "game/solve_partizan_game.hpp"

void test_push() {
  // LESSONS IN PLAY p.113
  vc<string> states = {"LR", ".RL", ".R", "RRL"};
  auto get_options = [&](string s) -> pair<vc<string>, vc<string>> {
    vc<string> left_ops, right_ops;
    FOR(i, len(s)) {
      if (s[i] == '.') continue;
      string t = s;
      char x = '.';
      int p = i;
      while (p >= 0) {
        swap(x, t[p--]);
        if (x == '.') break;
      }
      if (s[i] == 'L') left_ops.eb(t);
      if (s[i] == 'R') right_ops.eb(t);
    }
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<string>(states, get_options);
  assert(MP["LR"].to_string() == "-3/2 + *0");
  assert(MP[".RL"].to_string() == "7/4 + *0");
  assert(MP[".R"].to_string() == "-2/1 + *0");
  assert(MP["RRL"].to_string() == "13/8 + *0");
}

void test_problem_5_2() {
  // switch になるので解けない
  int LIM = 10;
  vc<int> states(LIM);
  iota(all(states), 0);

  auto get_options = [&](int s) -> pair<vc<int>, vc<int>> {
    vc<int> left_ops, right_ops;
    if (s % 3 == 0 && s >= 1) left_ops.eb(s - 1), right_ops.eb(s - 1);
    if (s % 3 == 0 && s >= 2) left_ops.eb(s - 2), right_ops.eb(s - 2);
    if (s % 3 == 1 && s >= 1) left_ops.eb(s - 1);
    if (s % 3 == 1 && s >= 2) left_ops.eb(s - 2);
    if (s % 3 == 2 && s >= 1) right_ops.eb(s - 1);
    if (s % 3 == 2 && s >= 2) right_ops.eb(s - 2);
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<int>(states, get_options);
  assert(MP.empty());
}

void test_problem_5_3() {
  int LIM = 10;
  vc<int> states(LIM);
  iota(all(states), 0);

  auto get_options = [&](int s) -> pair<vc<int>, vc<int>> {
    vc<int> left_ops, right_ops;
    if (s % 2 == 0 && s >= 2) left_ops.eb(s - 2);
    if (s % 2 == 0 && s >= 1) right_ops.eb(s - 1);
    if (s % 2 == 1 && s >= 1) left_ops.eb(s - 1);
    if (s % 2 == 1 && s >= 2) right_ops.eb(s - 2);
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<int>(states, get_options);
  assert(MP[0].to_string() == "0/1 + *0");
  assert(MP[1].to_string() == "1/1 + *0");
  assert(MP[2].to_string() == "1/2 + *0");
  assert(MP[3].to_string() == "3/4 + *0");
  assert(MP[4].to_string() == "5/8 + *0");
  assert(MP[5].to_string() == "11/16 + *0");
}

int solve_cherries(string s) {
  // LR cherries を O(N) で解く
  auto eval = [&](char c) -> int {
    if (c == 'L') return 1;
    if (c == 'R') return -1;
    return 0;
  };

  int n = len(s);
  if (n == 0) return 0;
  int res = 0;

  FOR(2) {
    reverse(all(s));
    while (n >= 2 && s[n - 1] == s[n - 2]) {
      res += eval(s[n - 1]);
      s.pop_back();
      n = len(s);
    }
  }

  char a = '.', b = '.';
  FOR_R(i, n - 1) if (s[i] == s[i + 1]) a = s[i];
  FOR(i, n - 1) if (s[i] == s[i + 1]) b = s[i];
  int x = eval(s[0]) + eval(a) + eval(b) + eval(s[n - 1]);
  return res + x / 2;
};

void test_cherries() {
  int MAX_LEN = 20;
  vc<string> states;
  states.eb("");
  int p = 0, q = 1;
  FOR(MAX_LEN) {
    FOR(i, p, q) {
      states.eb(states[i] + "L");
      states.eb(states[i] + "R");
    }
    p = q;
    q = len(states);
  }

  auto get_options = [&](string s) -> pair<vc<string>, vc<string>> {
    vc<string> left, right;
    int n = len(s);

    if (n && s[0] == 'L') left.eb(s.substr(1, n - 1));
    if (n && s[0] == 'R') right.eb(s.substr(1, n - 1));
    if (n && s[n - 1] == 'L') left.eb(s.substr(0, n - 1));
    if (n && s[n - 1] == 'R') right.eb(s.substr(0, n - 1));
    return {left, right};
  };

  auto MP = solve_partizan_game<string>(states, get_options);

  for (auto&& [s, x]: MP) {
    int my_ans = solve_cherries(s);
    assert(x.a == Dyadic_Rational<ll>(my_ans, 1));
  }
}

void test() {
  test_push();
  test_problem_5_2();
  test_problem_5_3();
  test_cherries();
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
#line 1 "test/1_mytest/partizan.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
// https://codeforces.com/blog/entry/126772?#comment-1154880
#include <bits/allocator.h>
#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2,popcnt")
#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(unsigned(x)) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parityll(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename UINT>
struct all_bit {
  struct iter {
    UINT s;
    iter(UINT s) : s(s) {}
    int operator*() const { return lowbit(s); }
    iter &operator++() {
      s &= s - 1;
      return *this;
    }
    bool operator!=(const iter) const { return s != 0; }
  };
  UINT s;
  all_bit(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename UINT>
struct all_subset {
  static_assert(is_unsigned<UINT>::value);
  struct iter {
    UINT s, t;
    bool ed;
    iter(UINT s) : s(s), t(s), ed(0) {}
    int operator*() const { return s ^ t; }
    iter &operator++() {
      (t == 0 ? ed = 1 : t = (t - 1) & s);
      return *this;
    }
    bool operator!=(const iter) const { return !ed; }
  };
  UINT s;
  all_subset(UINT s) : s(s) {}
  iter begin() const { return iter(s); }
  iter end() const { return iter(0); }
};

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 4 "test/1_mytest/partizan.test.cpp"

#line 1 "game/solve_partizan_game.hpp"

#line 1 "game/dyadic_rational.hpp"
// a+b/2^M の形で持つ
template <typename INTEGER>
struct Dyadic_Rational {
  using X = Dyadic_Rational;
  INTEGER a, b;
  static constexpr int M = std::numeric_limits<INTEGER>::digits - 2;

  Dyadic_Rational(INTEGER a = 0) : a(a), b(0) {}

  // x + y / z
  Dyadic_Rational(INTEGER x, INTEGER y, INTEGER z) : a(x), b(y) {
    auto [q, r] = divmod(b, z);
    a += q;
    b = r;
    b *= (INTEGER(1) << M) / z;
  }

  // x/y
  Dyadic_Rational(INTEGER x, INTEGER y) : Dyadic_Rational(0, x, y) {}

  static X from_ab(INTEGER a, INTEGER b) {
    X x(a);
    x.b = b;
    return x;
  }

  // 比較
  bool operator==(X const& rhs) const { return (a == rhs.a && b == rhs.b); }
  bool operator!=(X const& rhs) const { return !(*this == rhs); }
  bool operator<(X const& rhs) const { return (a < rhs.a) || (a == rhs.a && b < rhs.b); }
  bool operator<=(X const& rhs) const { return (a < rhs.a) || (a == rhs.a && b <= rhs.b); }
  bool operator>(X const& rhs) const { return (a > rhs.a) || (a == rhs.a && b > rhs.b); }
  bool operator>=(X const& rhs) const { return (a > rhs.a) || (a == rhs.a && b >= rhs.b); }

  // 加法
  friend X operator+(const X& x, const X& y) {
    INTEGER a = x.a + y.a, b = x.b + y.b;
    while (b >= INTEGER(1) << M) {
      ++a;
      b -= INTEGER(1) << M;
    }
    return from_ab(a, b);
  }
  friend X operator-(const X& x, const X& y) {
    INTEGER a = x.a - y.a, b = x.b - y.b;
    while (b < 0) {
      --a;
      b += INTEGER(1) << M;
    }
    return from_ab(a, b);
  }
  friend X operator-(const X& x) {
    INTEGER a = -x.a, b = -x.b;
    while (b < 0) {
      --a;
      b += INTEGER(1) << M;
    }
    return from_ab(a, b);
  }
  X& operator+=(const X& x) { return (*this) = (*this) + x; }
  X& operator-=(const X& x) { return (*this) = (*this) - x; }

  static X simplest(X x, X y, bool include_x = false, bool include_y = false) {
    if (include_x && x != -infinity()) {
      // eps を引く, あとでもっと小さい eps を使っている !
      x = x - from_ab(0, 2);
    }
    if (include_y && y != infinity()) {
      // eps を足す
      y = y + from_ab(0, 2);
    }
    assert(x < y);
    if (y.a < 0) return -simplest(-y, -x);
    {
      INTEGER l = x.a + 1;
      INTEGER r = (y.b == 0 ? y.a - 1 : y.a);
      if (l <= 0 && 0 <= r) return X(0);
      if (l <= r && 0 <= l) return X(l);
      if (l <= r && r <= 0) return X(r);
    }

    INTEGER l = x.b + 1;
    INTEGER r = (y.b == 0 ? (INTEGER(1) << M) - 1 : y.b - 1);
    if (l == r) return from_ab(x.a, l);
    int k = topbit(l ^ r);
    r &= ~((INTEGER(1) << k) - 1);
    return from_ab(x.a, r);
  }

  static constexpr X infinity() { return from_ab(INTEGER(1) << M, 0); }

  string to_string() {
    ll x = a, y = b, z = INTEGER(1) << M;
    while (y % 2 == 0 && z % 2 == 0) { y /= 2, z /= 2; }
    y += x * z;
    return std::to_string(y) + "/" + std::to_string(z);
  }
};
#line 1 "other/mex.hpp"
int mex(const vc<int>& A) {
  int n = len(A);
  vc<bool> aru(n + 1);
  for (auto& x: A)
    if (x < n) aru[x] = 1;
  int mex = 0;
  while (aru[mex]) ++mex;
  return mex;
}
#line 3 "game/number_and_star.hpp"

struct Number_And_Star {
  using A = Dyadic_Rational<ll>;
  // a + *b
  A a;
  int b;
  using T = Number_And_Star;

  Number_And_Star(A a = 0, ll b = 0) : a(a), b(b) {}
  T& operator+=(const T& p) {
    a += p.a, b ^= p.b;
    return *this;
  }
  T& operator-=(const T& p) {
    a -= p.a, b ^= p.b;
    return *this;
  }
  T operator-() const { return T(-a, b); }
  bool operator==(const T& p) const { return (a == p.a && b == p.b); }

  // {計算できたか, 値}
  static pair<bool, T> from_options(vc<T> left_ops, vc<T> right_ops) {
    A xl = -A::infinity(), xr = A::infinity();
    vc<int> Lb, Rb;
    for (auto&& t: left_ops) {
      if (chmax(xl, t.a)) Lb.clear();
      if (xl == t.a) Lb.eb(t.b);
    }
    for (auto&& t: right_ops) {
      if (chmin(xr, t.a)) Rb.clear();
      if (xr == t.a) Rb.eb(t.b);
    }
    int Lm = mex(Lb), Rm = mex(Rb);
    if (xl < xr) {
      A a = A::simplest(xl, xr, Lm == 0, Rm == 0);
      return {true, T(a, 0)};
    }
    if (xl == xr) {
      if (Lm == Rm) return {true, T(xl, Lm)};
    }
    return {false, T(0, 0)};
  }

  string to_string() {
    string x = a.to_string();
    x += " + *";
    x += ::to_string(b);
    return x;
  }

  // L, R はそれぞれ自分手番のときに勝てるか？
  pair<bool, bool> outcome() {
    if (a > 0) return {1, 0};
    if (a < 0) return {0, 1};
    if (b == 0) return {0, 0};
    return {1, 1};
  }
};
#line 3 "game/solve_partizan_game.hpp"

// number, star でいい感じに計算できたときだけ成功
// 失敗したときは、empty map が返る
// ・states：興味のある state 全体
// ・get_options：pair<vc<STATE>, vc<STATE>>(STATE), left ops / right ops
// https://qoj.ac/contest/1828/problem/9567
template <typename STATE, typename F>
map<STATE, Number_And_Star> solve_partizan_game(const vector<STATE>& states, F get_options) {
  using X = Number_And_Star;
  map<STATE, X> MP;

  bool success = 1;

  auto dfs = [&](auto& dfs, const STATE& s) -> X {
    if (!success) return X();
    if (MP.count(s)) return MP[s];
    vc<X> left, right;
    auto [lop, rop] = get_options(s);
    for (auto&& t: lop) left.eb(dfs(dfs, t));
    for (auto&& t: rop) right.eb(dfs(dfs, t));
    auto [ok, t] = X::from_options(left, right);
    if (!success) return X{};
    if (!ok) {
      // print("FAILED");
      // print(s);
      // print("LEFT");
      // for (auto& t: lop) {
      //   X x = dfs(dfs, t);
      //   print(t, x.to_string());
      // }
      // print("RIGHT");
      // for (auto& t: rop) {
      //   X x = dfs(dfs, t);
      //   print(t, x.to_string());
      // }
      success = 0;
      return X();
    }
    MP[s] = t;
    return MP[s] = t;
  };

  for (auto&& s: states) dfs(dfs, s);
  if (!success) MP.clear();
  return MP;
}
#line 6 "test/1_mytest/partizan.test.cpp"

void test_push() {
  // LESSONS IN PLAY p.113
  vc<string> states = {"LR", ".RL", ".R", "RRL"};
  auto get_options = [&](string s) -> pair<vc<string>, vc<string>> {
    vc<string> left_ops, right_ops;
    FOR(i, len(s)) {
      if (s[i] == '.') continue;
      string t = s;
      char x = '.';
      int p = i;
      while (p >= 0) {
        swap(x, t[p--]);
        if (x == '.') break;
      }
      if (s[i] == 'L') left_ops.eb(t);
      if (s[i] == 'R') right_ops.eb(t);
    }
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<string>(states, get_options);
  assert(MP["LR"].to_string() == "-3/2 + *0");
  assert(MP[".RL"].to_string() == "7/4 + *0");
  assert(MP[".R"].to_string() == "-2/1 + *0");
  assert(MP["RRL"].to_string() == "13/8 + *0");
}

void test_problem_5_2() {
  // switch になるので解けない
  int LIM = 10;
  vc<int> states(LIM);
  iota(all(states), 0);

  auto get_options = [&](int s) -> pair<vc<int>, vc<int>> {
    vc<int> left_ops, right_ops;
    if (s % 3 == 0 && s >= 1) left_ops.eb(s - 1), right_ops.eb(s - 1);
    if (s % 3 == 0 && s >= 2) left_ops.eb(s - 2), right_ops.eb(s - 2);
    if (s % 3 == 1 && s >= 1) left_ops.eb(s - 1);
    if (s % 3 == 1 && s >= 2) left_ops.eb(s - 2);
    if (s % 3 == 2 && s >= 1) right_ops.eb(s - 1);
    if (s % 3 == 2 && s >= 2) right_ops.eb(s - 2);
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<int>(states, get_options);
  assert(MP.empty());
}

void test_problem_5_3() {
  int LIM = 10;
  vc<int> states(LIM);
  iota(all(states), 0);

  auto get_options = [&](int s) -> pair<vc<int>, vc<int>> {
    vc<int> left_ops, right_ops;
    if (s % 2 == 0 && s >= 2) left_ops.eb(s - 2);
    if (s % 2 == 0 && s >= 1) right_ops.eb(s - 1);
    if (s % 2 == 1 && s >= 1) left_ops.eb(s - 1);
    if (s % 2 == 1 && s >= 2) right_ops.eb(s - 2);
    return {left_ops, right_ops};
  };

  auto MP = solve_partizan_game<int>(states, get_options);
  assert(MP[0].to_string() == "0/1 + *0");
  assert(MP[1].to_string() == "1/1 + *0");
  assert(MP[2].to_string() == "1/2 + *0");
  assert(MP[3].to_string() == "3/4 + *0");
  assert(MP[4].to_string() == "5/8 + *0");
  assert(MP[5].to_string() == "11/16 + *0");
}

int solve_cherries(string s) {
  // LR cherries を O(N) で解く
  auto eval = [&](char c) -> int {
    if (c == 'L') return 1;
    if (c == 'R') return -1;
    return 0;
  };

  int n = len(s);
  if (n == 0) return 0;
  int res = 0;

  FOR(2) {
    reverse(all(s));
    while (n >= 2 && s[n - 1] == s[n - 2]) {
      res += eval(s[n - 1]);
      s.pop_back();
      n = len(s);
    }
  }

  char a = '.', b = '.';
  FOR_R(i, n - 1) if (s[i] == s[i + 1]) a = s[i];
  FOR(i, n - 1) if (s[i] == s[i + 1]) b = s[i];
  int x = eval(s[0]) + eval(a) + eval(b) + eval(s[n - 1]);
  return res + x / 2;
};

void test_cherries() {
  int MAX_LEN = 20;
  vc<string> states;
  states.eb("");
  int p = 0, q = 1;
  FOR(MAX_LEN) {
    FOR(i, p, q) {
      states.eb(states[i] + "L");
      states.eb(states[i] + "R");
    }
    p = q;
    q = len(states);
  }

  auto get_options = [&](string s) -> pair<vc<string>, vc<string>> {
    vc<string> left, right;
    int n = len(s);

    if (n && s[0] == 'L') left.eb(s.substr(1, n - 1));
    if (n && s[0] == 'R') right.eb(s.substr(1, n - 1));
    if (n && s[n - 1] == 'L') left.eb(s.substr(0, n - 1));
    if (n && s[n - 1] == 'R') right.eb(s.substr(0, n - 1));
    return {left, right};
  };

  auto MP = solve_partizan_game<string>(states, get_options);

  for (auto&& [s, x]: MP) {
    int my_ans = solve_cherries(s);
    assert(x.a == Dyadic_Rational<ll>(my_ans, 1));
  }
}

void test() {
  test_push();
  test_problem_5_2();
  test_problem_5_3();
  test_cherries();
}

void solve() {
  int a, b;
  cin >> a >> b;
  cout << a + b << "\n";
}

signed main() {
  test();
  solve();
  return 0;
}
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