test/1_mytest/tutte.test.cpp

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• Last update: 2024-12-13 13:55:16+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• ds/unionfind/unionfind.hpp
• flow/bipartite.hpp
• graph/base.hpp
• graph/bipartite_vertex_coloring.hpp
• graph/maximum_matching_size.hpp
• graph/strongly_connected_component.hpp
• linalg/matrix_rank.hpp
• mod/modint61.hpp
• my_template.hpp
• random/base.hpp

Code

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

#include "graph/maximum_matching_size.hpp"
#include "flow/bipartite.hpp"

void test_bipartite() {
  FOR(N, 1, 50) {
    FOR(M, RNG(0, N * (N - 1) / 2 + 1)) {
      Graph<bool, 0> G(N);
      FOR(M) {
        int a = RNG(0, N);
        int b = RNG(0, N);
        if (a % 2 == b % 2) continue;
        G.add(a, b);
      }
      G.build();
      BipartiteMatching<decltype(G)> X(G);
      int a = len(X.matching());
      int b = maximum_matching_size(G);
      assert(a == b);
    }
  }
}

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

signed main() {
  test_bipartite();
  solve();

  return 0;
}

#line 1 "test/1_mytest/tutte.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_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 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/tutte.test.cpp"

#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 2 "mod/modint61.hpp"

struct modint61 {
  static constexpr u64 mod = (1ULL << 61) - 1;
  u64 val;
  constexpr modint61() : val(0ULL) {}
  constexpr modint61(u32 x) : val(x) {}
  constexpr modint61(u64 x) : val(x % mod) {}
  constexpr modint61(int x) : val((x < 0) ? (x + static_cast<ll>(mod)) : x) {}
  constexpr modint61(ll x) : val(((x %= static_cast<ll>(mod)) < 0) ? (x + static_cast<ll>(mod)) : x) {}
  static constexpr u64 get_mod() { return mod; }

  modint61 &operator+=(const modint61 &a) {
    val = ((val += a.val) >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 &operator-=(const modint61 &a) {
    val = ((val -= a.val) >= mod) ? (val + mod) : val;
    return *this;
  }
  modint61 &operator*=(const modint61 &a) {
    const unsigned __int128 y = static_cast<unsigned __int128>(val) * a.val;
    val = (y >> 61) + (y & mod);
    val = (val >= mod) ? (val - mod) : val;
    return *this;
  }
  modint61 operator-() const { return modint61(val ? mod - val : u64(0)); }
  modint61 &operator/=(const modint61 &a) { return (*this *= a.inverse()); }
  modint61 operator+(const modint61 &p) const { return modint61(*this) += p; }
  modint61 operator-(const modint61 &p) const { return modint61(*this) -= p; }
  modint61 operator*(const modint61 &p) const { return modint61(*this) *= p; }
  modint61 operator/(const modint61 &p) const { return modint61(*this) /= p; }
  bool operator<(const modint61 &other) const { return val < other.val; }
  bool operator==(const modint61 &p) const { return val == p.val; }
  bool operator!=(const modint61 &p) const { return val != p.val; }
  modint61 inverse() const {
    ll a = val, b = mod, u = 1, v = 0, t;
    while (b > 0) {
      t = a / b;
      swap(a -= t * b, b), swap(u -= t * v, v);
    }
    return modint61(u);
  }
  modint61 pow(ll n) const {
    assert(n >= 0);
    modint61 ret(1), mul(val);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul, n >>= 1;
    }
    return ret;
  }
};

#ifdef FASTIO
void rd(modint61 &x) {
  fastio::rd(x.val);
  assert(0 <= x.val && x.val < modint61::mod);
}

void wt(modint61 x) { fastio::wt(x.val); }
#endif
#line 1 "linalg/matrix_rank.hpp"
template <typename T>
int matrix_rank(vc<vc<T>> a, int n = -1, int m = -1) {
  if (n == 0) return 0;
  if (n == -1) { n = len(a), m = len(a[0]); }
  assert(n == len(a) && m == len(a[0]));
  int rk = 0;
  FOR(j, m) {
    if (rk == n) break;
    if (a[rk][j] == 0) {
      FOR(i, rk + 1, n) if (a[i][j] != T(0)) {
        swap(a[rk], a[i]);
        break;
      }
    }
    if (a[rk][j] == 0) continue;
    T c = T(1) / a[rk][j];
    FOR(k, j, m) a[rk][k] *= c;
    FOR(i, rk + 1, n) {
      T c = a[i][j];
      FOR3(k, j, m) { a[i][k] -= a[rk][k] * c; }
    }
    ++rk;
  }
  return rk;
}
#line 4 "graph/maximum_matching_size.hpp"

template <typename GT>
int maximum_matching_size(GT& G) {
  static_assert(!GT::is_directed);
  using mint = modint61;
  int N = G.N;
  vv(mint, tutte, N, N);
  for (auto&& e: G.edges) {
    mint x = RNG(mint::get_mod());
    int i = e.frm, j = e.to;
    tutte[i][j] += x;
    tutte[j][i] -= x;
  }
  return matrix_rank(tutte, N, N) / 2;
}
#line 2 "graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  // sum(deg(v)) の計算量になっていて、
  // 新しいグラフの n+m より大きい可能性があるので注意
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (len(used_e) <= e.id) used_e.resize(e.id + 1);
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

  Graph<T, true> to_directed_tree(int root = -1) {
    if (root == -1) root = 0;
    assert(!is_directed && prepared && M == N - 1);
    Graph<T, true> G1(N);
    vc<int> par(N, -1);
    auto dfs = [&](auto& dfs, int v) -> void {
      for (auto& e: (*this)[v]) {
        if (e.to == par[v]) continue;
        par[e.to] = v, dfs(dfs, e.to);
      }
    };
    dfs(dfs, root);
    for (auto& e: edges) {
      int a = e.frm, b = e.to;
      if (par[a] == b) swap(a, b);
      assert(par[b] == a);
      G1.add(a, b, e.cost);
    }
    G1.build();
    return G1;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 2 "graph/bipartite_vertex_coloring.hpp"

#line 2 "ds/unionfind/unionfind.hpp"

struct UnionFind {
  int n, n_comp;
  vc<int> dat; // par or (-size)
  UnionFind(int n = 0) { build(n); }

  void build(int m) {
    n = m, n_comp = m;
    dat.assign(n, -1);
  }

  void reset() { build(n); }

  int operator[](int x) {
    while (dat[x] >= 0) {
      int pp = dat[dat[x]];
      if (pp < 0) { return dat[x]; }
      x = dat[x] = pp;
    }
    return x;
  }

  ll size(int x) {
    x = (*this)[x];
    return -dat[x];
  }

  bool merge(int x, int y) {
    x = (*this)[x], y = (*this)[y];
    if (x == y) return false;
    if (-dat[x] < -dat[y]) swap(x, y);
    dat[x] += dat[y], dat[y] = x, n_comp--;
    return true;
  }

  vc<int> get_all() {
    vc<int> A(n);
    FOR(i, n) A[i] = (*this)[i];
    return A;
  }
};
#line 5 "graph/bipartite_vertex_coloring.hpp"

// 二部グラフでなかった場合には empty

template <typename GT>
vc<int> bipartite_vertex_coloring(GT& G) {
  assert(!GT::is_directed);
  assert(G.is_prepared());

  int n = G.N;
  UnionFind uf(2 * n);
  for (auto&& e: G.edges) {
    int u = e.frm, v = e.to;
    uf.merge(u + n, v), uf.merge(u, v + n);
  }

  vc<int> color(2 * n, -1);
  FOR(v, n) if (uf[v] == v && color[uf[v]] < 0) {
    color[uf[v]] = 0;
    color[uf[v + n]] = 1;
  }
  FOR(v, n) color[v] = color[uf[v]];
  color.resize(n);
  FOR(v, n) if (uf[v] == uf[v + n]) return {};
  return color;
}
#line 3 "graph/strongly_connected_component.hpp"

template <typename GT>
pair<int, vc<int>> strongly_connected_component(GT& G) {
  static_assert(GT::is_directed);
  assert(G.is_prepared());
  int N = G.N;
  int C = 0;
  vc<int> comp(N), low(N), ord(N, -1), path;
  int now = 0;

  auto dfs = [&](auto& dfs, int v) -> void {
    low[v] = ord[v] = now++;
    path.eb(v);
    for (auto&& [frm, to, cost, id]: G[v]) {
      if (ord[to] == -1) {
        dfs(dfs, to), chmin(low[v], low[to]);
      } else {
        chmin(low[v], ord[to]);
      }
    }
    if (low[v] == ord[v]) {
      while (1) {
        int u = POP(path);
        ord[u] = N, comp[u] = C;
        if (u == v) break;
      }
      ++C;
    }
  };
  FOR(v, N) {
    if (ord[v] == -1) dfs(dfs, v);
  }
  FOR(v, N) comp[v] = C - 1 - comp[v];
  return {C, comp};
}

template <typename GT>
Graph<int, 1> scc_dag(GT& G, int C, vc<int>& comp) {
  Graph<int, 1> DAG(C);
  vvc<int> edges(C);
  for (auto&& e: G.edges) {
    int x = comp[e.frm], y = comp[e.to];
    if (x == y) continue;
    edges[x].eb(y);
  }
  FOR(c, C) {
    UNIQUE(edges[c]);
    for (auto&& to: edges[c]) DAG.add(c, to);
  }
  DAG.build();
  return DAG;
}
#line 4 "flow/bipartite.hpp"

template <typename GT>
struct BipartiteMatching {
  int N;
  GT& G;
  vc<int> color;
  vc<int> dist, match;
  vc<int> vis;

  BipartiteMatching(GT& G) : N(G.N), G(G), dist(G.N, -1), match(G.N, -1) {
    color = bipartite_vertex_coloring(G);
    if (N > 0) assert(!color.empty());
    while (1) {
      bfs();
      vis.assign(N, false);
      int flow = 0;
      FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
      if (!flow) break;
    }
  }

  BipartiteMatching(GT& G, vc<int> color)
      : N(G.N), G(G), color(color), dist(G.N, -1), match(G.N, -1) {
    while (1) {
      bfs();
      vis.assign(N, false);
      int flow = 0;
      FOR(v, N) if (!color[v] && match[v] == -1 && dfs(v))++ flow;
      if (!flow) break;
    }
  }

  void bfs() {
    dist.assign(N, -1);
    queue<int> que;
    FOR(v, N) if (!color[v] && match[v] == -1) que.emplace(v), dist[v] = 0;
    while (!que.empty()) {
      int v = que.front();
      que.pop();
      for (auto&& e: G[v]) {
        dist[e.to] = 0;
        int w = match[e.to];
        if (w != -1 && dist[w] == -1) dist[w] = dist[v] + 1, que.emplace(w);
      }
    }
  }

  bool dfs(int v) {
    vis[v] = 1;
    for (auto&& e: G[v]) {
      int w = match[e.to];
      if (w == -1 || (!vis[w] && dist[w] == dist[v] + 1 && dfs(w))) {
        match[e.to] = v, match[v] = e.to;
        return true;
      }
    }
    return false;
  }

  vc<pair<int, int>> matching() {
    vc<pair<int, int>> res;
    FOR(v, N) if (v < match[v]) res.eb(v, match[v]);
    return res;
  }

  vc<int> vertex_cover() {
    vc<int> res;
    FOR(v, N) if (color[v] ^ (dist[v] == -1)) { res.eb(v); }
    return res;
  }

  vc<int> independent_set() {
    vc<int> res;
    FOR(v, N) if (!(color[v] ^ (dist[v] == -1))) { res.eb(v); }
    return res;
  }

  vc<int> edge_cover() {
    vc<bool> done(N);
    vc<int> res;
    for (auto&& e: G.edges) {
      if (done[e.frm] || done[e.to]) continue;
      if (match[e.frm] == e.to) {
        res.eb(e.id);
        done[e.frm] = done[e.to] = 1;
      }
    }
    for (auto&& e: G.edges) {
      if (!done[e.frm]) {
        res.eb(e.id);
        done[e.frm] = 1;
      }
      if (!done[e.to]) {
        res.eb(e.id);
        done[e.to] = 1;
      }
    }
    sort(all(res));
    return res;
  }

  /* Dulmage–Mendelsohn decomposition
  https://en.wikipedia.org/wiki/Dulmage%E2%80%93Mendelsohn_decomposition
  http://www.misojiro.t.u-tokyo.ac.jp/~murota/lect-ouyousurigaku/dm050410.pdf
  https://hitonanode.github.io/cplib-cpp/graph/dulmage_mendelsohn_decomposition.hpp.html
  - 最大マッチングとしてありうる iff 同じ W を持つ
  - 辺 uv が必ず使われる：同じ W を持つ辺が唯一
  - color=0 から 1 への辺：W[l] <= W[r]
  - color=0 の点が必ず使われる：W=1,2,...,K
  - color=1 の点が必ず使われる：W=0,1,...,K-1
  */
  pair<int, vc<int>> DM_decomposition() {
    // 非飽和点からの探索

    vc<int> W(N, -1);
    vc<int> que;
    auto add = [&](int v, int x) -> void {
      if (W[v] == -1) {
        W[v] = x;
        que.eb(v);
      }
    };
    FOR(v, N) if (match[v] == -1 && color[v] == 0) add(v, 0);
    FOR(v, N) if (match[v] == -1 && color[v] == 1) add(v, infty<int>);
    while (len(que)) {
      auto v = POP(que);
      if (match[v] != -1) add(match[v], W[v]);
      if (color[v] == 0 && W[v] == 0) {
        for (auto&& e: G[v]) { add(e.to, W[v]); }
      }
      if (color[v] == 1 && W[v] == infty<int>) {
        for (auto&& e: G[v]) { add(e.to, W[v]); }
      }
    }
    // 残った点からなるグラフを作って強連結成分分解

    vc<int> V;
    FOR(v, N) if (W[v] == -1) V.eb(v);
    int n = len(V);
    Graph<bool, 1> DG(n);
    FOR(i, n) {
      int v = V[i];
      if (match[v] != -1) {
        int j = LB(V, match[v]);
        DG.add(i, j);
      }
      if (color[v] == 0) {
        for (auto&& e: G[v]) {
          if (W[e.to] != -1 || e.to == match[v]) continue;
          int j = LB(V, e.to);
          DG.add(i, j);
        }
      }
    }
    DG.build();
    auto [K, comp] = strongly_connected_component(DG);
    K += 1;
    // 答

    FOR(i, n) { W[V[i]] = 1 + comp[i]; }
    FOR(v, N) if (W[v] == infty<int>) W[v] = K;
    return {K, W};
  }

#ifdef FASTIO
  void debug() {
    print("match", match);
    print("min vertex covor", vertex_cover());
    print("max indep set", independent_set());
    print("min edge cover", edge_cover());
  }
#endif
};
#line 6 "test/1_mytest/tutte.test.cpp"

void test_bipartite() {
  FOR(N, 1, 50) {
    FOR(M, RNG(0, N * (N - 1) / 2 + 1)) {
      Graph<bool, 0> G(N);
      FOR(M) {
        int a = RNG(0, N);
        int b = RNG(0, N);
        if (a % 2 == b % 2) continue;
        G.add(a, b);
      }
      G.build();
      BipartiteMatching<decltype(G)> X(G);
      int a = len(X.matching());
      int b = maximum_matching_size(G);
      assert(a == b);
    }
  }
}

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

signed main() {
  test_bipartite();
  solve();

  return 0;
}

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