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

Depends on

Code

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

#include "geo/base.hpp"
#include "geo/convex_hull.hpp"
#include "geo/convex_polygon.hpp"
#include "geo/incremental_convexhull.hpp"
#include "random/base.hpp"

using P = Point<ll>;

void test() {
  int N = RNG(3, 10);
  vc<P> point(N);
  FOR(i, N) point[i] = P(RNG(-5, 5), RNG(-5, 5));

  Incremental_ConvexHull<ll> Y;
  for (auto& p: point) Y.add(p);

  auto I = ConvexHull(point);
  point = rearrange(point, I);
  N = len(point);
  if (N <= 2) return;

  ConvexPolygon<ll> X(point);

  FOR(x, -10, 11) FOR(y, -10, 11) {
    P p(x, y);
    int ans = 1;
    [&]() -> int {
      FOR(i, N) {
        P A = point[i], B = point[(i + 1) % N];
        if ((B - A).det(p - A) <= 0) chmin(ans, 0);
        if ((B - A).det(p - A) < 0) chmin(ans, -1);
      }
      return ans;
    }();
    assert(ans == X.side(p));
    assert(ans == Y.side(p));
  }
}

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

signed main() {
  FOR(10000) test();
  solve();
  return 0;
}
#line 1 "test/1_mytest/convex_polygon_side.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
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #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 FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#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_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (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 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 3 "test/1_mytest/convex_polygon_side.test.cpp"

#line 2 "geo/base.hpp"
template <typename T>
struct Point {
  T x, y;

  Point() : x(0), y(0) {}

  template <typename A, typename B>
  Point(A x, B y) : x(x), y(y) {}

  template <typename A, typename B>
  Point(pair<A, B> p) : x(p.fi), y(p.se) {}

  Point operator+=(const Point p) {
    x += p.x, y += p.y;
    return *this;
  }
  Point operator-=(const Point p) {
    x -= p.x, y -= p.y;
    return *this;
  }
  Point operator+(Point p) const { return {x + p.x, y + p.y}; }
  Point operator-(Point p) const { return {x - p.x, y - p.y}; }
  bool operator==(Point p) const { return x == p.x && y == p.y; }
  bool operator!=(Point p) const { return x != p.x || y != p.y; }
  Point operator-() const { return {-x, -y}; }
  Point operator*(T t) const { return {x * t, y * t}; }
  Point operator/(T t) const { return {x / t, y / t}; }

  bool operator<(Point p) const {
    if (x != p.x) return x < p.x;
    return y < p.y;
  }
  T dot(const Point& other) const { return x * other.x + y * other.y; }
  T det(const Point& other) const { return x * other.y - y * other.x; }

  double norm() { return sqrtl(x * x + y * y); }
  double angle() { return atan2(y, x); }

  Point rotate(double theta) {
    static_assert(!is_integral<T>::value);
    double c = cos(theta), s = sin(theta);
    return Point{c * x - s * y, s * x + c * y};
  }
  Point rot90(bool ccw) { return (ccw ? Point{-y, x} : Point{y, -x}); }
};

#ifdef FASTIO
template <typename T>
void rd(Point<T>& p) {
  fastio::rd(p.x), fastio::rd(p.y);
}
template <typename T>
void wt(Point<T>& p) {
  fastio::wt(p.x);
  fastio::wt(' ');
  fastio::wt(p.y);
}
#endif

// A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1
template <typename T>
int ccw(Point<T> A, Point<T> B, Point<T> C) {
  T x = (B - A).det(C - A);
  if (x > 0) return 1;
  if (x < 0) return -1;
  return 0;
}

template <typename REAL, typename T, typename U>
REAL dist(Point<T> A, Point<U> B) {
  REAL dx = REAL(A.x) - REAL(B.x);
  REAL dy = REAL(A.y) - REAL(B.y);
  return sqrt(dx * dx + dy * dy);
}

// ax+by+c
template <typename T>
struct Line {
  T a, b, c;

  Line(T a, T b, T c) : a(a), b(b), c(c) {}
  Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; }
  Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {}

  template <typename U>
  U eval(Point<U> P) {
    return a * P.x + b * P.y + c;
  }

  template <typename U>
  T eval(U x, U y) {
    return a * x + b * y + c;
  }

  // 同じ直線が同じ a,b,c で表現されるようにする
  void normalize() {
    static_assert(is_same_v<T, int> || is_same_v<T, long long>);
    T g = gcd(gcd(abs(a), abs(b)), abs(c));
    a /= g, b /= g, c /= g;
    if (b < 0) { a = -a, b = -b, c = -c; }
    if (b == 0 && a < 0) { a = -a, b = -b, c = -c; }
  }

  bool is_parallel(Line other) { return a * other.b - b * other.a == 0; }
  bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; }
};

template <typename T>
struct Segment {
  Point<T> A, B;

  Segment(Point<T> A, Point<T> B) : A(A), B(B) {}
  Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {}

  bool contain(Point<T> C) {
    T det = (C - A).det(B - A);
    if (det != 0) return 0;
    return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0;
  }

  Line<T> to_Line() { return Line(A, B); }
};

template <typename REAL>
struct Circle {
  Point<REAL> O;
  REAL r;
  Circle(Point<REAL> O, REAL r) : O(O), r(r) {}
  Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {}
  template <typename T>
  bool contain(Point<T> p) {
    REAL dx = p.x - O.x, dy = p.y - O.y;
    return dx * dx + dy * dy <= r * r;
  }
};
#line 2 "geo/convex_hull.hpp"

#line 4 "geo/convex_hull.hpp"

// allow_180=true で同一座標点があるとこわれる
// full なら I[0] が sorted で min になる
template <typename T, bool allow_180 = false>
vector<int> ConvexHull(vector<Point<T>>& XY, string mode = "full", bool sorted = false) {
  assert(mode == "full" || mode == "lower" || mode == "upper");
  ll N = XY.size();
  if (N == 1) return {0};
  if (N == 2) {
    if (XY[0] < XY[1]) return {0, 1};
    if (XY[1] < XY[0]) return {1, 0};
    return {0};
  }
  vc<int> I(N);
  if (sorted) {
    FOR(i, N) I[i] = i;
  } else {
    I = argsort(XY);
  }
  if constexpr (allow_180) { FOR(i, N - 1) assert(XY[i] != XY[i + 1]); }

  auto check = [&](ll i, ll j, ll k) -> bool {
    T det = (XY[j] - XY[i]).det(XY[k] - XY[i]);
    if constexpr (allow_180) return det >= 0;
    return det > T(0);
  };

  auto calc = [&]() {
    vector<int> P;
    for (auto&& k: I) {
      while (P.size() > 1) {
        auto i = P[P.size() - 2];
        auto j = P[P.size() - 1];
        if (check(i, j, k)) break;
        P.pop_back();
      }
      P.eb(k);
    }
    return P;
  };

  vc<int> P;
  if (mode == "full" || mode == "lower") {
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "full" || mode == "upper") {
    if (!P.empty()) P.pop_back();
    reverse(all(I));
    vc<int> Q = calc();
    P.insert(P.end(), all(Q));
  }
  if (mode == "upper") reverse(all(P));
  while (len(P) >= 2 && XY[P[0]] == XY[P.back()]) P.pop_back();
  return P;
}
#line 2 "geo/convex_polygon.hpp"

#line 5 "geo/convex_polygon.hpp"

// n=2 は現状サポートしていない
template <typename T>
struct ConvexPolygon {
  using P = Point<T>;
  int n;
  vc<P> point;

  ConvexPolygon(vc<P> point_) : n(len(point_)), point(point_) {
    assert(n >= 3);
    FOR(i, n) {
      int j = nxt_idx(i), k = nxt_idx(j);
      assert((point[j] - point[i]).det(point[k] - point[i]) >= 0);
    }
  }

  // 比較関数 comp(i,j)
  template <typename F>
  int periodic_min_comp(F comp) {
    int L = 0, M = n, R = n + n;
    while (1) {
      if (R - L == 2) break;
      int L1 = (L + M) / 2, R1 = (M + R + 1) / 2;
      if (comp(L1 % n, M % n)) { R = M, M = L1; }
      elif (comp(R1 % n, M % n)) { L = M, M = R1; }
      else {
        L = L1, R = R1;
      }
    }
    return M % n;
  }

  int nxt_idx(int i) { return (i + 1 == n ? 0 : i + 1); }
  int prev_idx(int i) { return (i == 0 ? n - 1 : i - 1); }

  // 中：1, 境界：0, 外：-1. test した.
  int side(P p) {
    int L = 1, R = n - 1;
    T a = (point[L] - point[0]).det(p - point[0]);
    T b = (point[R] - point[0]).det(p - point[0]);
    if (a < 0 || b > 0) return -1;
    // p は 0 から見て [L,R] 方向
    while (R - L >= 2) {
      int M = (L + R) / 2;
      T c = (point[M] - point[0]).det(p - point[0]);
      if (c < 0)
        R = M, b = c;
      else
        L = M, a = c;
    }
    T c = (point[R] - point[L]).det(p - point[L]);
    T x = min({a, -b, c});
    if (x < 0) return -1;
    if (x > 0) return 1;
    // on triangle p[0]p[L]p[R]
    if (p == point[0]) return 0;
    if (c != 0 && a == 0 && L != 1) return 1;
    if (c != 0 && b == 0 && R != n - 1) return 1;
    return 0;
  }

  // return {min, idx}. test した.
  pair<T, int> min_dot(P p) {
    int idx = periodic_min_comp([&](int i, int j) -> bool { return point[i].dot(p) < point[j].dot(p); });
    return {point[idx].dot(p), idx};
  }

  // return {max, idx}. test した.
  pair<T, int> max_dot(P p) {
    int idx = periodic_min_comp([&](int i, int j) -> bool { return point[i].dot(p) > point[j].dot(p); });
    return {point[idx].dot(p), idx};
  }

  // p から見える範囲. p 辺に沿って見えるところも見えるとする. test した.
  // 多角形からの反時計順は [l,r] だが p から見た偏角順は [r,l] なので注意
  pair<int, int> visible_range(P p) {
    int a = periodic_min_comp([&](int i, int j) -> bool { return ((point[i] - p).det(point[j] - p) < 0); });
    int b = periodic_min_comp([&](int i, int j) -> bool { return ((point[i] - p).det(point[j] - p) > 0); });
    if ((p - point[a]).det(p - point[prev_idx(a)]) == T(0)) a = prev_idx(a);
    if ((p - point[b]).det(p - point[nxt_idx(b)]) == T(0)) b = nxt_idx(b);
    return {a, b};
  }

  // 線分が「内部と」交わるか
  // https://codeforces.com/contest/1906/problem/D
  bool check_cross(P A, P B) {
    FOR(2) {
      swap(A, B);
      auto [a, b] = visible_range(A);
      if ((point[a] - A).det(B - A) >= 0) return 0;
      if ((point[b] - A).det(B - A) <= 0) return 0;
    }
    return 1;
  }

  vc<T> AREA;

  // point[i,...,j] (inclusive) の面積
  T area_between(int i, int j) {
    assert(0 <= i && i < n);
    assert((0 <= j && j < n) || (i <= j && j < i + n));
    if (i > j) j += n;
    if (AREA.empty()) build_AREA();
    return AREA[j] - AREA[i] + (point[j % n].det(point[i]));
  }

  void build_AREA() {
    AREA.resize(2 * n);
    FOR(i, n) AREA[n + i] = AREA[i] = point[i].det(point[nxt_idx(i)]);
    AREA = cumsum<T>(AREA);
  }
};
#line 2 "geo/incremental_convexhull.hpp"

// 下側凸包
template <typename T, bool strict = true>
struct IncrementalConvexHull_Lower {
  using P = Point<T>;
  set<P> S;

  IncrementalConvexHull_Lower() {}

  int size() { return len(S); }

  template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E>
  void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) {
    int s = side(p);
    if (strict && s >= 0) return;
    if (!strict && s > 0) return;

    // 点追加
    add_v(p);
    S.insert(p);

    vc<P> left;
    {
      auto it = S.find(p);
      while (it != S.begin()) {
        --it;
        if (left.empty()) {
          left.eb(*it);
          continue;
        }
        auto a = *it;
        auto b = left.back();
        T det = (b - a).det(p - a);
        if (strict && det > 0) break;
        if (!strict && det >= 0) break;
        left.eb(a);
      }
    }

    vc<P> right;
    {
      auto it = S.find(p);
      while (1) {
        ++it;
        if (it == S.end()) break;
        if (right.empty()) {
          right.eb(*it);
          continue;
        }
        auto a = right.back();
        auto b = *it;
        T det = (a - p).det(b - p);
        if (strict && det > 0) break;
        if (!strict && det >= 0) break;
        right.eb(b);
      }
    }

    // 点削除
    if (len(left) > 1) { S.erase(next(S.find(left.back())), S.find(p)); }
    if (len(right) > 1) { S.erase(next(S.find(p)), S.find(right.back())); }
    FOR(i, len(left) - 1) rm_v(left[i]);
    FOR(i, len(right) - 1) rm_v(right[i]);

    // 辺削除
    if (len(left) && len(right)) {
      auto a = left[0], b = right[0];
      rm_e(a, b);
    }
    FOR(i, len(left) - 1) {
      auto a = left[i + 1], b = left[i];
      rm_e(a, b);
    }
    FOR(i, len(right) - 1) {
      auto a = right[i], b = right[i + 1];
      rm_e(a, b);
    }
    // 辺追加
    if (len(left)) { add_e(left.back(), p); }
    if (len(right)) { add_e(p, right.back()); }
  }

  // 中：1, 境界：0, 外：-1
  int side(Point<T> p) {
    auto r = S.lower_bound(p);
    if (r == S.begin()) {
      // 全部 p 以上
      if (len(S) && (*r) == p) return 0;
      return -1;
    }
    if (r == S.end()) {
      // p は max より大きい
      return -1;
    }
    auto l = prev(r);
    auto p1 = *l, p2 = *r;
    T det = (p - p1).det(p2 - p1);
    if (det == 0) return 0;
    return (det > 0 ? -1 : 1);
  }
};

template <typename T, bool strict = true>
struct Incremental_ConvexHull {
  using P = Point<T>;
  IncrementalConvexHull_Lower<T, strict> LOWER, UPPER;
  int cnt_E;
  T det_sum;
  bool is_empty;

  Incremental_ConvexHull() : cnt_E(0), det_sum(0), is_empty(1) {}

  int size() { return cnt_E; }

  bool empty() { return is_empty; }

  template <typename REAL>
  REAL area() {
    return det_sum * 0.5;
  }
  T area_2() { return det_sum; }

  template <typename ADD_V, typename RM_V, typename ADD_E, typename RM_E>
  void add(Point<T> p, ADD_V add_v, RM_V rm_v, ADD_E add_e, RM_E rm_e) {
    is_empty = 0;
    LOWER.add(
        p, add_v, rm_v,
        [&](Point<T> a, Point<T> b) {
          add_e(a, b);
          ++cnt_E;
          det_sum += a.det(b);
        },
        [&](Point<T> a, Point<T> b) {
          rm_e(a, b);
          --cnt_E;
          det_sum -= a.det(b);
        });
    UPPER.add(
        -p, [&](Point<T> p) { add_v(-p); }, [&](Point<T> p) { rm_v(-p); },
        [&](Point<T> a, Point<T> b) {
          add_e(-a, -b);
          ++cnt_E;
          det_sum += a.det(b);
        },
        [&](Point<T> a, Point<T> b) {
          rm_e(-a, -b);
          --cnt_E;
          det_sum -= a.det(b);
        });
  }
  void add(Point<T> p) {
    add(
        p, [](Point<T> p) {}, [](Point<T> p) {}, [](Point<T> s, Point<T> t) {},
        [](Point<T> s, Point<T> t) {});
  }

  // 中：1、境界：0、外：-1
  int side(Point<T> p) {
    int a = LOWER.side(p);
    int b = UPPER.side(-p);
    if (a == 0 || b == 0) return 0;
    return min(a, b);
  }
};
#line 2 "random/base.hpp"

u64 RNG_64() {
  static u64 x_ = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL;
  x_ ^= x_ << 7;
  return x_ ^= x_ >> 9;
}

u64 RNG(u64 lim) { return RNG_64() % lim; }

ll RNG(ll l, ll r) { return l + RNG_64() % (r - l); }
#line 9 "test/1_mytest/convex_polygon_side.test.cpp"

using P = Point<ll>;

void test() {
  int N = RNG(3, 10);
  vc<P> point(N);
  FOR(i, N) point[i] = P(RNG(-5, 5), RNG(-5, 5));

  Incremental_ConvexHull<ll> Y;
  for (auto& p: point) Y.add(p);

  auto I = ConvexHull(point);
  point = rearrange(point, I);
  N = len(point);
  if (N <= 2) return;

  ConvexPolygon<ll> X(point);

  FOR(x, -10, 11) FOR(y, -10, 11) {
    P p(x, y);
    int ans = 1;
    [&]() -> int {
      FOR(i, N) {
        P A = point[i], B = point[(i + 1) % N];
        if ((B - A).det(p - A) <= 0) chmin(ans, 0);
        if ((B - A).det(p - A) < 0) chmin(ans, -1);
      }
      return ans;
    }();
    assert(ans == X.side(p));
    assert(ans == Y.side(p));
  }
}

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

signed main() {
  FOR(10000) test();
  solve();
  return 0;
}
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