Problem p02604 (C++) — buggy submission, verdict: Time Limit Exceeded

//
//                               S i r o t a n   w a t c h e s   o v e r   y o u
//                               .
//
//                                          ...Jggg+J+JJJg@NQmgJa.....,
//                                 ....gH@@@@HHB""""7"YYYYHMMMMMMM@@@@@@@Hma,.
//                            ...JH@@MMHY"!                        ?
//                            __""YH@@@@N&...
//                        ..JH@@HY"~ _TW@@@Mme.
//                     .Jg@@#"= _TTM@@N..
//                  .Jg@@MY! ?T@@@h,.
//                .-@@@B! (TM@@@L
//              .(H@MY ?W@@@+
//             .W@@@ .T@@@[
//           .d@@M! .T@@N,
//          .d@M@' -W@@o.
//         (@@M\\ ?M@N,
//        -d@M%                    ..,                                      ..,
//        j@@b
//       d@@M=                     TM9                                      ?MD
//       W@@[
//      .H@M: .W@H, H@Ht ,@@#
//     (@@M~ .@@h.
//    .@@M%                        ..gmHHJ.                             .JdHga.
//    .H@@e
//    j@@#_                       .@@@@@@@b J@@@@@@@h. .H@@\\  d@@@ .4@@@@@@MF
//    (@@@@@@@@                        H@@b d@@[                         ?"BMY"=
//    .d@@@@H,          ?TWHHY"!                        d@@e J@@b .JJJ-..,
//    ,@@@@@@M%                       .........         -@@@M.
//    ?@@M\\         ?YHHM@@@@b                ..      .W@@HP X@@HMWY"= d@@@#
//    ,@@@L.                                 ?H@Ng&+gd@@#H@@NHaJ+gH@[ J@@@]
//     X@@@[            ......                 ?"YYYYY""   ?"YHHHB"^ ..... (@@@#
//      WH@N+.      .W@@@@MHB= .TWH@M@Hmc       .H@@M~
//     .H@@@@N,      _!~ .d@@@N,
//   .J@@#T@@@N, .d@@@@@@@b.
//  (@@@@! .T@@@n, .(H@@@H>.W@@@x
// (@@@F      4@@@@MaJ. .d@@@@Y77   4@@@r
//.H@@P         ?TM@@@@N... .-JH@HMY=        d@@N,
//(@@@F             ?"WM@@@MQa-,. .(J(JN@@M#"             Z@@@L
// d@@H,                 (M@@@@@@@Ng&maJ....                           ..
// ...J.J+W@@@@@@HY!               .dH@b ?M@@@N&.
// ..(JW@@@MM"?7""TYHMH@@HH@@@@@HHHgkHagHa(mggdmmagH@H@@Q@@HMMMHY"7!TMM@@@HaJ,.
// ..H@@@M^
//   ?"W@@@@MN@@@@@H@@MMY"                  _???!"= ?WMMBYYTMH=7""Y@""?"~^
//   _"YM@@@@@@@@MH@@@@@#"^
//       ?77WMMMYB""! _7"WWMMMY"7=

// need
#include <algorithm>
#include <iostream>
// data structure
#include <bitset>
#include <complex>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <deque>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <valarray>
// etc
#include <cassert>
#include <chrono>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <numeric>
#include <random>

auto &scan_in = std::cin;

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { scan_in >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  scan_in >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int w_ = 0; w_ < n; ++w_) {                                             \\
    MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);                                       \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { scan_in >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  scan_in >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    scan_in >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &R : c)                                                            \\
    for (auto &w : R)                                                          \\
      scan_in >> w;
// output
template <typename T> void MACRO_OUT(const T t) { std::cout << t; }
template <typename First, typename... Rest>
void MACRO_OUT(const First first, const Rest... rest) {
  std::cout << first << " ";
  MACRO_OUT(rest...);
}
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout << std::fixed << std::setprecision(n) << (dist);
#define SOUT(n, c, dist) std::cout << std::setw(n) << std::setfill(c) << (dist);
#define VOUT(v)                                                                \\
  for (size_t i = 0; i < v.size(); ++i) {                                      \\
    OUT(v[i]);                                                                 \\
    if (i + 1 < v.size()) {                                                    \\
      SP                                                                       \\
    }                                                                          \\
  }
#define EOUT(...)                                                              \\
  do {                                                                         \\
    OUT(__VA_ARGS__) BR;                                                       \\
    exit(0);                                                                   \\
  } while (0);
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(w, n) std::cout << (w + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(dist)                                                             \\
  { std::cerr << #dist << "\\t: " << (dist) << "\\n"; }
// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(w, a, n) for (int w = (a); w < (n); ++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for (int w = (n)-1; w >= (a); --w)
#define RREP(w, n) RFOR(w, 0, n)
template <class S, class T, class U> bool IN(S a, T x, U b) {
  return a <= x && x < b;
}
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
// test
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;

template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::pair<S, T> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  os << "{";
  for (size_t i = 0; i < v.size(); ++i)
    os << v[i] << ((i + 1 < v.size()) ? ", " : "");
  os << "}";
  return os;
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::map<S, T> &m) {
  os << "{";
  for (auto it = m.cbegin(); it != m.cend();) {
    os << it->first << ":" << it->second;
    ++it;
    os << (it == m.cend() ? "" : ", ");
  }
  os << "}";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> q) {
  os << "<";
  while (!q.empty()) {
    os << q.front();
    q.pop();
    os << (q.empty() ? "<" : ", ");
  }
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::stack<T> q) {
  os << ">";
  while (!q.empty()) {
    os << q.top();
    q.pop();
    os << (q.empty() ? "]" : ", ");
  }
  return os;
}
namespace std {
template <typename S, typename T> class numeric_limits<pair<S, T>> {
public:
  static constexpr pair<S, T> max() noexcept {
    return {numeric_limits<S>::max(), numeric_limits<T>::max()};
  }
  static constexpr pair<S, T> lowest() noexcept {
    return {numeric_limits<S>::lowest(), numeric_limits<T>::lowest()};
  }
};
} // namespace std

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<i64, i64>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                   // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N> void FILL(T (&a)[N], const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
template <class T> void FILL(std::vector<T> &a, const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>> &a, const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
// ------------>8---------

unsigned long long popCount(unsigned long long x) {
  x = ((x & 0xaaaaaaaaaaaaaaaaUL) >> 1) + (x & 0x5555555555555555UL);
  x = ((x & 0xccccccccccccccccUL) >> 2) + (x & 0x3333333333333333UL);
  x = ((x & 0xf0f0f0f0f0f0f0f0UL) >> 4) + (x & 0x0f0f0f0f0f0f0f0fUL);
  x = ((x & 0xff00ff00ff00ff00UL) >> 8) + (x & 0x00ff00ff00ff00ffUL);
  x = ((x & 0xffff0000ffff0000UL) >> 16) + (x & 0x0000ffff0000ffffUL);
  return x;
}

int n;
int x[20], y[20], P[20];
i64 ans[20];
std::map<int, int> X, Y;

void rec(int p, int bit) {
  if (p == n) {
    i64 sum = 0;
    REP(i, n) {
      if (bit & 1 << i)
        continue;
      int mi = INFINT;
      {
        auto it = X.lower_bound(x[i]);
        CHMIN(mi, it->first - x[i]);
        if (mi == 0)
          continue;
        --it;
        CHMIN(mi, x[i] - it->first);
      }
      {
        auto it = Y.lower_bound(y[i]);
        CHMIN(mi, it->first - y[i]);
        if (mi == 0)
          continue;
        --it;
        CHMIN(mi, y[i] - it->first);
      }
      sum += (i64)mi * P[i];
    }
    CHMIN(ans[popCount(bit)], sum);
  } else {
    rec(p + 1, bit);

    ++X[x[p]];
    rec(p + 1, bit | 1 << p);
    if (--X[x[p]] == 0)
      X.erase(x[p]);

    ++Y[y[p]];
    rec(p + 1, bit | 1 << p);
    if (--Y[y[p]] == 0)
      Y.erase(y[p]);
  }
}

signed main() {
  INIT;

  std::cin >> n;
  REP(i, n) std::cin >> x[i] >> y[i] >> P[i];

  REP(i, n + 1) ans[i] = INFLL;
  ++X[-30000];
  ++X[0];
  ++X[30000];
  ++Y[-30000];
  ++Y[0];
  ++Y[30000];

  rec(0, 0);
  REP(i, n + 1) { OUT(ans[i]) BR; }

  return 0;
}

Error: TLE

Fixed submission:

//
//                               S i r o t a n   w a t c h e s   o v e r   y o u
//                               .
//
//                                          ...Jggg+J+JJJg@NQmgJa.....,
//                                 ....gH@@@@HHB""""7"YYYYHMMMMMMM@@@@@@@Hma,.
//                            ...JH@@MMHY"!                        ?
//                            __""YH@@@@N&...
//                        ..JH@@HY"~ _TW@@@Mme.
//                     .Jg@@#"= _TTM@@N..
//                  .Jg@@MY! ?T@@@h,.
//                .-@@@B! (TM@@@L
//              .(H@MY ?W@@@+
//             .W@@@ .T@@@[
//           .d@@M! .T@@N,
//          .d@M@' -W@@o.
//         (@@M\\ ?M@N,
//        -d@M%                    ..,                                      ..,
//        j@@b
//       d@@M=                     TM9                                      ?MD
//       W@@[
//      .H@M: .W@H, H@Ht ,@@#
//     (@@M~ .@@h.
//    .@@M%                        ..gmHHJ.                             .JdHga.
//    .H@@e
//    j@@#_                       .@@@@@@@b J@@@@@@@h. .H@@\\  d@@@ .4@@@@@@MF
//    (@@@@@@@@                        H@@b d@@[                         ?"BMY"=
//    .d@@@@H,          ?TWHHY"!                        d@@e J@@b .JJJ-..,
//    ,@@@@@@M%                       .........         -@@@M.
//    ?@@M\\         ?YHHM@@@@b                ..      .W@@HP X@@HMWY"= d@@@#
//    ,@@@L.                                 ?H@Ng&+gd@@#H@@NHaJ+gH@[ J@@@]
//     X@@@[            ......                 ?"YYYYY""   ?"YHHHB"^ ..... (@@@#
//      WH@N+.      .W@@@@MHB= .TWH@M@Hmc       .H@@M~
//     .H@@@@N,      _!~ .d@@@N,
//   .J@@#T@@@N, .d@@@@@@@b.
//  (@@@@! .T@@@n, .(H@@@H>.W@@@x
// (@@@F      4@@@@MaJ. .d@@@@Y77   4@@@r
//.H@@P         ?TM@@@@N... .-JH@HMY=        d@@N,
//(@@@F             ?"WM@@@MQa-,. .(J(JN@@M#"             Z@@@L
// d@@H,                 (M@@@@@@@Ng&maJ....                           ..
// ...J.J+W@@@@@@HY!               .dH@b ?M@@@N&.
// ..(JW@@@MM"?7""TYHMH@@HH@@@@@HHHgkHagHa(mggdmmagH@H@@Q@@HMMMHY"7!TMM@@@HaJ,.
// ..H@@@M^
//   ?"W@@@@MN@@@@@H@@MMY"                  _???!"= ?WMMBYYTMH=7""Y@""?"~^
//   _"YM@@@@@@@@MH@@@@@#"^
//       ?77WMMMYB""! _7"WWMMMY"7=

// need
#include <algorithm>
#include <iostream>
// data structure
#include <bitset>
#include <complex>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
// #include <deque>
#include <array>
#include <unordered_map>
#include <unordered_set>
#include <valarray>
// etc
#include <cassert>
#include <chrono>
#include <cmath>
#include <fstream>
#include <functional>
#include <iomanip>
#include <numeric>
#include <random>

auto &scan_in = std::cin;

// input
#define INIT                                                                   \\
  std::ios::sync_with_stdio(false);                                            \\
  std::cin.tie(0);
#define VAR(type, ...)                                                         \\
  type __VA_ARGS__;                                                            \\
  MACRO_VAR_Scan(__VA_ARGS__);
template <typename T> void MACRO_VAR_Scan(T &t) { scan_in >> t; }
template <typename First, typename... Rest>
void MACRO_VAR_Scan(First &first, Rest &...rest) {
  scan_in >> first;
  MACRO_VAR_Scan(rest...);
}
#define VEC_ROW(type, n, ...)                                                  \\
  std::vector<type> __VA_ARGS__;                                               \\
  MACRO_VEC_ROW_Init(n, __VA_ARGS__);                                          \\
  for (int w_ = 0; w_ < n; ++w_) {                                             \\
    MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);                                       \\
  }
template <typename T> void MACRO_VEC_ROW_Init(int n, T &t) { t.resize(n); }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Init(int n, First &first, Rest &...rest) {
  first.resize(n);
  MACRO_VEC_ROW_Init(n, rest...);
}
template <typename T> void MACRO_VEC_ROW_Scan(int p, T &t) { scan_in >> t[p]; }
template <typename First, typename... Rest>
void MACRO_VEC_ROW_Scan(int p, First &first, Rest &...rest) {
  scan_in >> first[p];
  MACRO_VEC_ROW_Scan(p, rest...);
}
#define VEC(type, c, n)                                                        \\
  std::vector<type> c(n);                                                      \\
  for (auto &i : c)                                                            \\
    scan_in >> i;
#define MAT(type, c, m, n)                                                     \\
  std::vector<std::vector<type>> c(m, std::vector<type>(n));                   \\
  for (auto &R : c)                                                            \\
    for (auto &w : R)                                                          \\
      scan_in >> w;
// output
template <typename T> void MACRO_OUT(const T t) { std::cout << t; }
template <typename First, typename... Rest>
void MACRO_OUT(const First first, const Rest... rest) {
  std::cout << first << " ";
  MACRO_OUT(rest...);
}
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout << std::fixed << std::setprecision(n) << (dist);
#define SOUT(n, c, dist) std::cout << std::setw(n) << std::setfill(c) << (dist);
#define VOUT(v)                                                                \\
  for (size_t i = 0; i < v.size(); ++i) {                                      \\
    OUT(v[i]);                                                                 \\
    if (i + 1 < v.size()) {                                                    \\
      SP                                                                       \\
    }                                                                          \\
  }
#define EOUT(...)                                                              \\
  do {                                                                         \\
    OUT(__VA_ARGS__) BR;                                                       \\
    exit(0);                                                                   \\
  } while (0);
#define SP std::cout << " ";
#define TAB std::cout << "\\t";
#define BR std::cout << "\\n";
#define SPBR(w, n) std::cout << (w + 1 == n ? '\\n' : ' ');
#define ENDL std::cout << std::endl;
#define FLUSH std::cout << std::flush;
#define SHOW(dist)                                                             \\
  { std::cerr << #dist << "\\t: " << (dist) << "\\n"; }
// utility
#define ALL(a) (a).begin(), (a).end()
#define FOR(w, a, n) for (int w = (a); w < (n); ++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for (int w = (n)-1; w >= (a); --w)
#define RREP(w, n) RFOR(w, 0, n)
template <class S, class T, class U> bool IN(S a, T x, U b) {
  return a <= x && x < b;
}
template <class T> inline T CHMAX(T &a, const T b) {
  return a = (a < b) ? b : a;
}
template <class T> inline T CHMIN(T &a, const T b) {
  return a = (a > b) ? b : a;
}
// test
template <class T> using V = std::vector<T>;
template <class T> using VV = V<V<T>>;

template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::pair<S, T> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
  os << "{";
  for (size_t i = 0; i < v.size(); ++i)
    os << v[i] << ((i + 1 < v.size()) ? ", " : "");
  os << "}";
  return os;
}
template <typename S, typename T>
std::ostream &operator<<(std::ostream &os, const std::map<S, T> &m) {
  os << "{";
  for (auto it = m.cbegin(); it != m.cend();) {
    os << it->first << ":" << it->second;
    ++it;
    os << (it == m.cend() ? "" : ", ");
  }
  os << "}";
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> q) {
  os << "<";
  while (!q.empty()) {
    os << q.front();
    q.pop();
    os << (q.empty() ? "<" : ", ");
  }
  return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::stack<T> q) {
  os << ">";
  while (!q.empty()) {
    os << q.top();
    q.pop();
    os << (q.empty() ? "]" : ", ");
  }
  return os;
}
namespace std {
template <typename S, typename T> class numeric_limits<pair<S, T>> {
public:
  static constexpr pair<S, T> max() noexcept {
    return {numeric_limits<S>::max(), numeric_limits<T>::max()};
  }
  static constexpr pair<S, T> lowest() noexcept {
    return {numeric_limits<S>::lowest(), numeric_limits<T>::lowest()};
  }
};
} // namespace std

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<i64, i64>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                   // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;             // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                         // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;
template <class T, size_t N> void FILL(T (&a)[N], const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, size_t N, size_t M, class T>
void FILL(ARY (&a)[N][M], const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
template <class T> void FILL(std::vector<T> &a, const T &val) {
  for (auto &x : a)
    x = val;
}
template <class ARY, class T>
void FILL(std::vector<std::vector<ARY>> &a, const T &val) {
  for (auto &b : a)
    FILL(b, val);
}
// ------------>8---------

unsigned long long popCount(unsigned long long x) {
  x = ((x & 0xaaaaaaaaaaaaaaaaUL) >> 1) + (x & 0x5555555555555555UL);
  x = ((x & 0xccccccccccccccccUL) >> 2) + (x & 0x3333333333333333UL);
  x = ((x & 0xf0f0f0f0f0f0f0f0UL) >> 4) + (x & 0x0f0f0f0f0f0f0f0fUL);
  x = ((x & 0xff00ff00ff00ff00UL) >> 8) + (x & 0x00ff00ff00ff00ffUL);
  x = ((x & 0xffff0000ffff0000UL) >> 16) + (x & 0x0000ffff0000ffffUL);
  return x;
}

signed main() {
  INIT;

  VAR(int, n);
  VEC_ROW(int, n, x, y, P);

  std::map<int, int> X, Y;
  ++X[-30000];
  ++X[0];
  ++X[30000];
  ++Y[-30000];
  ++Y[0];
  ++Y[30000];

  V<i64> ans(n + 1, INFLL);
  auto rec = [&](auto &&f, int p, int bit) -> void {
    if (p == n) {
      i64 sum = 0;
      REP(i, n) {
        if (bit & 1 << i)
          continue;
        int mi = INFINT;
        {
          auto it = X.lower_bound(x[i]);
          CHMIN(mi, it->first - x[i]);
          if (mi == 0)
            continue;
          --it;
          CHMIN(mi, x[i] - it->first);
        }
        {
          auto it = Y.lower_bound(y[i]);
          CHMIN(mi, it->first - y[i]);
          if (mi == 0)
            continue;
          --it;
          CHMIN(mi, y[i] - it->first);
        }
        sum += (i64)mi * P[i];
      }
      CHMIN(ans[popCount(bit)], sum);
    } else {
      f(f, p + 1, bit);

      ++X[x[p]];
      f(f, p + 1, bit | 1 << p);
      if (--X[x[p]] == 0)
        X.erase(x[p]);

      ++Y[y[p]];
      f(f, p + 1, bit | 1 << p);
      if (--Y[y[p]] == 0)
        Y.erase(y[p]);
    }
  };
  rec(rec, 0, 0);
  REP(i, n + 1) { OUT(ans[i]) BR; }

  return 0;
}