test/library_checker/datastructure/add_remove_query.test.cpp

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• Last update: 2023-11-09 00:59:01+09:00
• Problem: https://judge.yosupo.jp/problem/dynamic_graph_vertex_add_component_sum

Depends on

• ds/offline_query/add_remove_query.hpp
• ds/rollback_array.hpp
• ds/unionfind/rollback_unionfind.hpp
• my_template.hpp
• other/io.hpp

Code

#define PROBLEM \
  "https://judge.yosupo.jp/problem/dynamic_graph_vertex_add_component_sum"
#include "my_template.hpp"
#include "other/io.hpp"
#include "ds/offline_query/add_remove_query.hpp"
#include "ds/rollback_array.hpp"
#include "ds/unionfind/rollback_unionfind.hpp"

void solve() {
  LL(N, Q);
  VEC(ll, A0, N);
  using P = pair<int, int>;

  vc<int> query;

  Add_Remove_Query<P, true> X;
  FOR(Q) {
    LL(t);
    if (t == 0) {
      LL(a, b);
      if (a > b) swap(a, b);
      P e = {a, b};
      X.add(len(query), e);
    }
    if (t == 1) {
      LL(a, b);
      if (a > b) swap(a, b);
      P e = {a, b};
      X.remove(len(query), e);
    }
    if (t == 2) {
      LL(v, x);
      P p = {~v, x};
      X.add(len(query), p);
    }
    if (t == 3) {
      LL(v);
      query.eb(v);
    }
  }

  auto upd = X.calc(len(query));
  Q = len(query);
  vi ANS(Q);
  vc<int> I(len(upd));
  iota(all(I), 0);

  Rollback_Array<ll> A(A0);
  Rollback_UnionFind uf(N);

  auto dfs = [&](auto& dfs, vc<int>& I, int begin, int end) -> void {
    int a_time = A.time();
    int uf_time = uf.time();

    vc<int> IL, IR;
    int mid = (begin + end) / 2;
    // 区間を完全に含む更新クエリを処理する。
    // 部分的に交わるクエリを J に入れる
    for (auto&& i: I) {
      auto [a, b, X] = upd[i];
      if (a <= begin && end <= b) {
        // update
        auto [u, v] = X;
        if (u < 0) {
          int i = uf[~u];
          A.set(i, A.get(i) + v);
        } else {
          u = uf[u], v = uf[v];
          if (u != v) {
            uf.merge(u, v);
            int r = uf[u];
            A.set(r, A.get(u) + A.get(v));
          }
        }
        continue;
      }
      if (a < mid) IL.eb(i);
      if (mid < b) IR.eb(i);
    }
    if (begin + 1 == end) {
      // 求値クエリ
      int v = query[begin];
      ANS[begin] = A.get(uf[v]);
    } else {
      dfs(dfs, IL, begin, mid);
      dfs(dfs, IR, mid, end);
    }
    A.rollback(a_time);
    uf.rollback(uf_time);
  };
  dfs(dfs, I, 0, Q);

  for (auto&& x: ANS) print(x);
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}

#line 1 "test/library_checker/datastructure/add_remove_query.test.cpp"
#define PROBLEM \
  "https://judge.yosupo.jp/problem/dynamic_graph_vertex_add_component_sum"
#line 1 "my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
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;
}
#endif
#line 1 "other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623

namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf

uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.

void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio

using fastio::read;
using fastio::print;
using fastio::flush;

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "ds/offline_query/add_remove_query.hpp"
/*
・時刻 t に x を追加する
・時刻 t に x を削除する
があるときに、
・時刻 [l, r) に x を追加する
に変換する。
クエリが時系列順に来ることが分かっているときは monotone = true の方が高速。
*/
template <typename X, bool monotone>
struct Add_Remove_Query {
  map<X, int> MP;
  vc<tuple<int, int, X>> dat;
  map<X, vc<int>> ADD;
  map<X, vc<int>> RM;

  void add(int time, X x) {
    if (monotone) return add_monotone(time, x);
    ADD[x].eb(time);
  }
  void remove(int time, X x) {
    if (monotone) return remove_monotone(time, x);
    RM[x].eb(time);
  }

  // すべてのクエリが終わった現在時刻を渡す
  vc<tuple<int, int, X>> calc(int time) {
    if (monotone) return calc_monotone(time);
    vc<tuple<int, int, X>> dat;
    for (auto&& [x, A]: ADD) {
      vc<int> B;
      if (RM.count(x)) {
        B = RM[x];
        RM.erase(x);
      }
      if (len(B) < len(A)) B.eb(time);
      assert(len(A) == len(B));

      sort(all(A));
      sort(all(B));
      FOR(i, len(A)) {
        assert(A[i] <= B[i]);
        if (A[i] < B[i]) dat.eb(A[i], B[i], x);
      }
    }
    assert(len(RM) == 0);
    return dat;
  }

private:
  void add_monotone(int time, X x) {
    assert(!MP.count(x));
    MP[x] = time;
  }
  void remove_monotone(int time, X x) {
    auto it = MP.find(x);
    assert(it != MP.end());
    int t = (*it).se;
    MP.erase(it);
    if (t == time) return;
    dat.eb(t, time, x);
  }
  vc<tuple<int, int, X>> calc_monotone(int time) {
    for (auto&& [x, t]: MP) {
      if (t == time) continue;
      dat.eb(t, time, x);
    }
    return dat;
  }
};
#line 2 "ds/rollback_array.hpp"

template <typename T>
struct Rollback_Array {
  int N;
  vc<T> dat;
  vc<pair<int, T>> history;

  Rollback_Array() {}
  Rollback_Array(vc<T> x) : N(len(x)), dat(x) {}
  Rollback_Array(int N) : N(N), dat(N) {}
  template <typename F>
  Rollback_Array(int N, F f) : N(N) {
    dat.reserve(N);
    FOR(i, N) dat.eb(f(i));
  }

  int time() { return len(history); }
  void rollback(int t) {
    FOR_R(i, t, time()) {
      auto& [idx, v] = history[i];
      dat[idx] = v;
    }
    history.resize(t);
  }
  T get(int idx) { return dat[idx]; }
  void set(int idx, T x) {
    history.eb(idx, dat[idx]);
    dat[idx] = x;
  }

  vc<T> get_all() {
    vc<T> res(N);
    FOR(i, N) res[i] = get(i);
    return res;
  }
};
#line 2 "ds/unionfind/rollback_unionfind.hpp"

struct Rollback_UnionFind {
  Rollback_Array<int> dat; // parent or size


  Rollback_UnionFind(int n) : dat(vc<int>(n, -1)) {}

  int operator[](int v) {
    while (dat.get(v) >= 0) v = dat.get(v);
    return v;
  }

  ll size(int v) { return -dat.get((*this)[v]); }
  int time() { return dat.time(); }
  void rollback(int t) { dat.rollback(t); }
  void reset() { rollback(0); }

  bool merge(int a, int b) {
    a = (*this)[a], b = (*this)[b];
    if (a == b) return false;
    if (dat.get(a) > dat.get(b)) swap(a, b);
    dat.set(a, dat.get(a) + dat.get(b));
    dat.set(b, a);
    return true;
  }
};
#line 8 "test/library_checker/datastructure/add_remove_query.test.cpp"

void solve() {
  LL(N, Q);
  VEC(ll, A0, N);
  using P = pair<int, int>;

  vc<int> query;

  Add_Remove_Query<P, true> X;
  FOR(Q) {
    LL(t);
    if (t == 0) {
      LL(a, b);
      if (a > b) swap(a, b);
      P e = {a, b};
      X.add(len(query), e);
    }
    if (t == 1) {
      LL(a, b);
      if (a > b) swap(a, b);
      P e = {a, b};
      X.remove(len(query), e);
    }
    if (t == 2) {
      LL(v, x);
      P p = {~v, x};
      X.add(len(query), p);
    }
    if (t == 3) {
      LL(v);
      query.eb(v);
    }
  }

  auto upd = X.calc(len(query));
  Q = len(query);
  vi ANS(Q);
  vc<int> I(len(upd));
  iota(all(I), 0);

  Rollback_Array<ll> A(A0);
  Rollback_UnionFind uf(N);

  auto dfs = [&](auto& dfs, vc<int>& I, int begin, int end) -> void {
    int a_time = A.time();
    int uf_time = uf.time();

    vc<int> IL, IR;
    int mid = (begin + end) / 2;
    // 区間を完全に含む更新クエリを処理する。
    // 部分的に交わるクエリを J に入れる
    for (auto&& i: I) {
      auto [a, b, X] = upd[i];
      if (a <= begin && end <= b) {
        // update
        auto [u, v] = X;
        if (u < 0) {
          int i = uf[~u];
          A.set(i, A.get(i) + v);
        } else {
          u = uf[u], v = uf[v];
          if (u != v) {
            uf.merge(u, v);
            int r = uf[u];
            A.set(r, A.get(u) + A.get(v));
          }
        }
        continue;
      }
      if (a < mid) IL.eb(i);
      if (mid < b) IR.eb(i);
    }
    if (begin + 1 == end) {
      // 求値クエリ
      int v = query[begin];
      ANS[begin] = A.get(uf[v]);
    } else {
      dfs(dfs, IL, begin, mid);
      dfs(dfs, IR, mid, end);
    }
    A.rollback(a_time);
    uf.rollback(uf_time);
  };
  dfs(dfs, I, 0, Q);

  for (auto&& x: ANS) print(x);
}

signed main() {
  cin.tie(nullptr);
  ios::sync_with_stdio(false);
  cout << setprecision(15);

  ll T = 1;
  // LL(T);
  FOR(T) solve();

  return 0;
}

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