#line 1 "/home/maspy/compro/library/my_template.hpp" #include using namespace std; using ll = long long; using pi = pair; using vi = vector; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; template using pq = priority_queue; template using pqg = priority_queue, greater>; #define vec(type, name, ...) vector name(__VA_ARGS__) #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) #define FOR_(n) for (ll _ = 0; (_) < (ll)(n); ++(_)) #define FOR(i, n) for (ll i = 0; (i) < (ll)(n); ++(i)) #define FOR3(i, m, n) for (ll i = (m); (i) < (ll)(n); ++(i)) #define FOR_R(i, n) for (ll i = (ll)(n)-1; (i) >= 0; --(i)) #define FOR3_R(i, m, n) for (ll i = (ll)(n)-1; (i) >= (ll)(m); --(i)) #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 template T SUM(vector &A) { T sum = T(0); for (auto &&a: A) sum += a; return sum; } #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()) 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); } // (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 T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template pair divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } ll binary_search(function check, ll ok, ll ng) { assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; if (check(x)) ok = x; else ng = x; } return ok; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } vi s_to_vi(const string& S, char first_char) { vi A(S.size()); FOR(i, S.size()) { A[i] = S[i] - first_char; } return A; } template vector cumsum(vector &A, int off = 1) { int N = A.size(); vector B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } template vc bincount(const vc &A, int size) { vc C(size); for (auto &&x: A) { ++C[x]; } return C; } template vector argsort(const vector &A) { // stable vector ids(A.size()); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return A[i] < A[j] || (A[i] == A[j] && i < j); }); return ids; } // A[I[0]], A[I[1]], ... template vc rearrange(const vc &A, const vc &I) { int n = len(A); assert(len(I) == n); vc B(n); FOR(i, n) B[i] = A[I[i]]; return B; } #line 1 "/home/maspy/compro/library/other/io.hpp" // based on yosupo's fastio #include namespace detail { template std::true_type check_value(int); template std::false_type check_value(long); } // namespace detail template struct is_modint : decltype(detail::check_value(0)) {}; template using is_modint_t = enable_if_t::value>; template using is_not_modint_t = enable_if_t::value>; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template ::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template * = nullptr> bool read_single(T &ref) { long long val = 0; bool f = read_single(val); ref = T(val); return f; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template bool read_single(vector &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template bool read_single(pair &p) { return (read_single(p.first) && read_single(p.second)); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p))); } template bool read_single(tuple &p) { return (read_single(get<0>(p)) && read_single(get<1>(p)) && read_single(get<2>(p)) && read_single(get<3>(p))); } void read() {} template void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char &val) { if (pos == SIZE) flush(); line[pos++] = val; } template ::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string &s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double &x) { ostringstream oss; oss << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double &x) { ostringstream oss; oss << setprecision(15) << x; string s = oss.str(); write(s); } template * = nullptr> void write(T &ref) { write(ref.val); } template void write(const vector &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template void write(const pair &val) { write(val.first); write(' '); write(val.second); } template void write(const tuple &val) { auto &[a, b, c] = val; write(a), write(' '), write(b), write(' '), write(c); } template void write(const tuple &val) { auto &[a, b, c, d] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d); } template void write(const tuple &val) { auto &[a, b, c, d, e] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e); } template void write(const tuple &val) { auto &[a, b, c, d, e, f] = val; write(a), write(' '), write(b), write(' '), write(c), write(' '), write(d), write(' '), write(e), write(' '), write(f); } template void write(const array &val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if(val < 0){ negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if(negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward(tail)...); } void read() {} template void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __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 name(size); \ read(name) #define VV(type, name, h, w) \ vector> name(h, vector(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 2 "/home/maspy/compro/library/graph/base.hpp" template struct Edge { int frm, to; T cost; int id; }; template struct Graph { int N, M; using cost_type = T; using edge_type = Edge; vector edges; vector indptr; vector csr_edges; 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: int l, r; const Graph* G; }; bool is_prepared() { return prepared; } constexpr bool is_directed() { return directed; } Graph() : N(0), M(0), prepared(0) {} Graph(int N) : N(N), M(0), prepared(0) {} void add(int frm, int to, T cost = 1, int i = -1) { assert(!prepared && 0 <= frm && 0 <= to && to < N); if (i == -1) i = M; auto e = edge_type({frm, to, cost, i}); edges.eb(e); ++M; } // 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_(M) { INT(a, b); a -= off, b -= off; if (!wt) { add(a, b); } else { T c; read(c); add(a, b, c); } } build(); } void read_parent(int off = 1) { FOR3(v, 1, N) { INT(p); p -= off; add(p, v); } build(); } 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(v, N) 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]}; } 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); } } }; #line 2 "/home/maspy/compro/library/ds/unionfind.hpp" struct UnionFind { int num; int comp; vc size, par; UnionFind(int n) : num(n), comp(n), size(n, 1), par(n) { iota(par.begin(), par.end(), 0); } int find(int x) { while (par[x] != x) { par[x] = par[par[x]]; x = par[x]; } return x; } int operator[](int x) { return find(x); } bool merge(ll x, ll y) { x = find(x); y = find(y); if (x == y) { return false; } comp--; if (size[x] < size[y]) swap(x, y); size[x] += size[y]; size[y] = 0; par[y] = x; return true; } vc find_all() { vc A(num); FOR(i, num) A[i] = find(i); return A; } void reset(){ comp = num; size.assign(num, 1); iota(all(par), 0); } }; #line 3 "/home/maspy/compro/library/graph/check_bipartite.hpp" // 二部グラフ判定 + 復元 // 二部グラフでなかった場合には empty template vc check_bipartite(Graph& G) { assert(G.is_prepared()); int n = G.N; UnionFind uf(2 * n); for (auto&& e: G.edges) { int u = e.frm, v = e.to; if (e.cost == 0) uf.merge(u, v), uf.merge(u + n, v + n); if (e.cost != 0) uf.merge(u + n, v), uf.merge(u, v + n); } vc 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 "/home/maspy/compro/library/flow/bipartite.hpp" template struct BipartiteMatching { int N; Graph& G; vc color; vc dist, match; vc vis; BipartiteMatching(Graph& G) : G(G), N(G.N), dist(G.N, -1), match(G.N, -1) { color = check_bipartite(G); 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; } } void bfs() { dist.assign(N, -1); queue 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> matching() { vc> res; FOR(v, N) if (v < match[v]) res.eb(v, match[v]); return res; } vc vertex_cover() { vc res; FOR(v, N) if (color[v] ^ (dist[v] == -1)) { res.eb(v); } return res; } vc independent_set() { vc res; FOR(v, N) if (!(color[v] ^ (dist[v] == -1))) { res.eb(v); } return res; } vc edge_cover() { vc done(N); vc 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; } void debug() { print("match", match); print("min vertex covor", vertex_cover()); print("max indep set", independent_set()); print("min edge cover", edge_cover()); } }; #line 4 "main.cpp" void solve() { LL(N); VEC(ll, A, N); Graph G(N); FOR(i, N) FOR(j, N) { ll x = A[i] ^ A[j]; if (x == 0) continue; if ((x & (x - 1)) == 0) G.add(i, j); } G.build(); BipartiteMatching BM(G); print(len(BM.independent_set())); } signed main() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << setprecision(15); ll T = 1; // LL(T); FOR(_, T) solve(); return 0; }