#line 1 "h.cpp" /** * author: nok0 * created: 2022.04.08 22:20:56 **/ #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/maxflow.hpp" #include #include #include #include #include #line 1 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_queue.hpp" #line 5 "/Users/nok0/Documents/Programming/nok0/atcoder/internal_queue.hpp" namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder #line 11 "/Users/nok0/Documents/Programming/nok0/atcoder/maxflow.hpp" namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} explicit mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #line 1 "/Users/nok0/Documents/Programming/nok0/cftemp.hpp" #include using namespace std; #pragma region Macros // rep macro #define foa(v, a) for(auto &v : a) #define REPname(a, b, c, d, e, ...) e #define REP(...) REPname(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__) #define REP0(x) for(int i = 0; i < (x); ++i) #define REP1(i, x) for(int i = 0; i < (x); ++i) #define REP2(i, l, r) for(int i = (l); i < (r); ++i) #define REP3(i, l, r, c) for(int i = (l); i < (r); i += (c)) #define REPSname(a, b, c, ...) c #define REPS(...) REPSname(__VA_ARGS__, REPS1, REPS0)(__VA_ARGS__) #define REPS0(x) for(int i = 1; i <= (x); ++i) #define REPS1(i, x) for(int i = 1; i <= (x); ++i) #define RREPname(a, b, c, d, e, ...) e #define RREP(...) RREPname(__VA_ARGS__, RREP3, RREP2, RREP1, RREP0)(__VA_ARGS__) #define RREP0(x) for(int i = (x)-1; i >= 0; --i) #define RREP1(i, x) for(int i = (x)-1; i >= 0; --i) #define RREP2(i, r, l) for(int i = (r)-1; i >= (l); --i) #define RREP3(i, r, l, c) for(int i = (r)-1; i >= (l); i -= (c)) #define RREPSname(a, b, c, ...) c #define RREPS(...) RREPSname(__VA_ARGS__, RREPS1, RREPS0)(__VA_ARGS__) #define RREPS0(x) for(int i = (x); i >= 1; --i) #define RREPS1(i, x) for(int i = (x); i >= 1; --i) // name macro #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define popcnt(x) __builtin_popcountll(x) template using V = std::vector; template using VV = std::vector>; template using pqup = std::priority_queue, std::greater>; using ll = long long; using ld = long double; using int128 = __int128_t; using pii = std::pair; using pll = std::pair; // input macro template std::istream &operator>>(std::istream &is, std::pair &p) { is >> p.first >> p.second; return is; } template std::istream &operator>>(std::istream &is, std::vector &v) { for(T &i : v) is >> i; return is; } std::istream &operator>>(std::istream &is, __int128_t &a) { std::string s; is >> s; __int128_t ret = 0; for(int i = 0; i < s.length(); i++) if('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0'; a = ret * (s[0] == '-' ? -1 : 1); return is; } namespace scanner { void scan(int &a) { std::cin >> a; } void scan(long long &a) { std::cin >> a; } void scan(std::string &a) { std::cin >> a; } void scan(char &a) { std::cin >> a; } void scan(char a[]) { std::scanf("%s", a); } void scan(double &a) { std::cin >> a; } void scan(long double &a) { std::cin >> a; } template void scan(std::pair &p) { std::cin >> p; } template void scan(std::vector &a) { std::cin >> a; } void INPUT() {} template void INPUT(Head &head, Tail &...tail) { scan(head); INPUT(tail...); } } // namespace scanner #define VEC(type, name, size) \ std::vector name(size); \ scanner::INPUT(name) #define VVEC(type, name, h, w) \ std::vector> name(h, std::vector(w)); \ scanner::INPUT(name) #define INT(...) \ int __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LL(...) \ long long __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define STR(...) \ std::string __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define DOUBLE(...) \ double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) #define LD(...) \ long double __VA_ARGS__; \ scanner::INPUT(__VA_ARGS__) // output-macro template std::ostream &operator<<(std::ostream &os, const std::pair &p) { os << p.first << " " << p.second; return os; } template std::ostream &operator<<(std::ostream &os, const std::vector &a) { for(int i = 0; i < int(a.size()); ++i) { if(i) os << " "; os << a[i]; } return os; } std::ostream &operator<<(std::ostream &dest, __int128_t &value) { std::ostream::sentry s(dest); if(s) { __uint128_t tmp = value < 0 ? -value : value; char buffer[128]; char *d = std::end(buffer); do { --d; *d = "0123456789"[tmp % 10]; tmp /= 10; } while(tmp != 0); if(value < 0) { --d; *d = '-'; } int len = std::end(buffer) - d; if(dest.rdbuf()->sputn(d, len) != len) { dest.setstate(std::ios_base::badbit); } } return dest; } template void print(const T a) { std::cout << a << '\n'; } template void print(Head H, Tail... T) { std::cout << H << ' '; print(T...); } template void printel(const T a) { std::cout << a << '\n'; } template void printel(const std::vector &a) { for(const auto &v : a) std::cout << v << '\n'; } template void printel(Head H, Tail... T) { std::cout << H << '\n'; printel(T...); } void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); } void No() { std::cout << "No\n"; } void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); } void NO() { std::cout << "NO\n"; } void err(const bool b = true) { if(b) { std::cout << "-1\n", exit(0); } } //debug macro namespace debugger { template void view(const std::vector &a) { std::cerr << "{ "; for(const auto &v : a) { std::cerr << v << ", "; } std::cerr << "\b\b }"; } template void view(const std::vector> &a) { std::cerr << "{\n"; for(const auto &v : a) { std::cerr << "\t"; view(v); std::cerr << "\n"; } std::cerr << "}"; } template void view(const std::vector> &a) { std::cerr << "{\n"; for(const auto &p : a) std::cerr << "\t(" << p.first << ", " << p.second << ")\n"; std::cerr << "}"; } template void view(const std::map &m) { std::cerr << "{\n"; for(const auto &p : m) std::cerr << "\t[" << p.first << "] : " << p.second << "\n"; std::cerr << "}"; } template void view(const std::pair &p) { std::cerr << "(" << p.first << ", " << p.second << ")"; } template void view(const std::set &s) { std::cerr << "{ "; for(auto &v : s) { view(v); std::cerr << ", "; } std::cerr << "\b\b }"; } template void view(const T &e) { std::cerr << e; } } // namespace debugger #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { debugger::view(H); std::cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ std::cerr << "\b\b]\n"; \ } while(false) #else #define debug(...) (void(0)) #endif // vector macro template int lb(const std::vector &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); } template int ub(const std::vector &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); } template void UNIQUE(std::vector &a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template std::vector press(std::vector &a) { auto res = a; UNIQUE(res); for(auto &v : a) v = lb(res, v); return res; } #define SORTname(a, b, c, ...) c #define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__) #define SORT0(a) std::sort((a).begin(), (a).end()) #define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; }) template void ADD(std::vector &a, const T x = 1) { for(auto &v : a) v += x; } template void SUB(std::vector &a, const T x = 1) { for(auto &v : a) v -= x; } std::vector> rle(const string &s) { int n = s.size(); std::vector> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and s[l] == s[r]; r++) {} ret.emplace_back(s[l], r - l); l = r; } return ret; } template std::vector> rle(const std::vector &v) { int n = v.size(); std::vector> ret; for(int l = 0; l < n;) { int r = l + 1; for(; r < n and v[l] == v[r]; r++) {} ret.emplace_back(v[l], r - l); l = r; } return ret; } std::vector iota(int n) { std::vector p(n); std::iota(p.begin(), p.end(), 0); return p; } template struct cum_vector { public: cum_vector() = default; template cum_vector(const std::vector &vec) : cum((int)vec.size() + 1) { for(int i = 0; i < (int)vec.size(); i++) cum[i + 1] = cum[i] + vec[i]; } T prod(int l, int r) { return cum[r] - cum[l]; } private: std::vector cum; }; // math macro template inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; } template inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; } template T divup(T x, T y) { return (x + y - 1) / y; } template T POW(T a, long long n) { T ret = 1; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } // modpow long long POW(long long a, long long n, const int mod) { long long ret = 1; a = (a % mod + mod) % mod; while(n) { if(n & 1) (ret *= a) %= mod; (a *= a) %= mod; n >>= 1; } return ret; } template T bin_search(T ok, T ng, const F &f) { while(abs(ok - ng) > 1) { T mid = (ok + ng) >> 1; (f(mid) ? ok : ng) = mid; } return ok; } template T bin_search(T ok, T ng, const F &f, int loop) { for(int i = 0; i < loop; i++) { T mid = (ok + ng) / 2; (f(mid) ? ok : ng) = mid; } return ok; } // others struct fast_io { fast_io() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } fast_io_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion void main_(); int main() { main_(); return 0; } #line 7 "h.cpp" void main_() { INT(n); VEC(int, a, n); V<> lef, rig; REP(i, n) { if(popcnt(a[i]) % 2) lef.pb(a[i]); else rig.pb(a[i]); } int l = SZ(lef), r = SZ(rig); atcoder::mf_graph mf(l + r + 2); const int s = l + r, t = s + 1; REP(i, l) { REP(j, r) { if(popcnt(lef[i] ^ rig[j]) == 1) { debug(i, j); mf.add_edge(i, l + j, 1); } } } REP(i, l) { mf.add_edge(s, i, 1); } REP(i, r) { mf.add_edge(l + i, t, 1); } print(n - mf.flow(s, t)); }