#line 2 "library/KowerKoint/template.cpp" #ifndef ONLINE_JUDGE #define _GLIBCXX_DEBUG #endif #include using namespace std; #define REP(i, n) for(int i = 0; i < (int)(n); i++) #define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++) #define ALL(a) (a).begin(),(a).end() #define END(...) { print(__VA_ARGS__); return; } #ifdef ONLINE_JUDGE #define DBG(...) {} #else #define DBG(a) { cerr << #a << ": "; dbg(a); } #endif using VI = vector; using VVI = vector; using VVVI = vector; using ll = long long; using VL = vector; using VVL = vector; using VVVL = vector; using VD = vector; using VVD = vector; using VVVD = vector; using VS = vector; using VVS = vector; using VVVS = vector; using VC = vector; using VVC = vector; using VVVC = vector; using P = pair; using VP = vector

; using VVP = vector; using VVVP = vector; using LP = pair; using VLP = vector; using VVLP = vector; using VVVLP = vector; template using PQ = priority_queue; template using GPQ = priority_queue, greater>; constexpr int INF = 1001001001; constexpr ll LINF = 1001001001001001001ll; constexpr int DX[] = {1, 0, -1, 0}; constexpr int DY[] = {0, 1, 0, -1}; #ifdef aclmodint using MI7 = modint1000000007; using V7 = vector; using VV7 = vector; using VVV7 = vector; using MI3 = modint998244353; using V3 = vector; using VV3 = vector; using VVV3 = vector; ostream &operator<<(ostream &os, const modint &x) { os << x.val(); return os; } ostream &operator<<(ostream &os, const MI3 &x) { os << x.val(); return os; } ostream &operator<<(ostream &os, const MI7 &x) { os << x.val(); return os; } istream &operator>>(istream &is, modint &x) { int y; is >> y; x = y; return is; } istream &operator>>(istream &is, MI3 &x) { int y; is >> y; x = y; return is; } istream &operator>>(istream &is, MI7 &x) { int y; is >> y; x = y; return is; } #endif void print() { cout << '\n'; } template void print(const T &t) { cout << t << '\n'; } template void print(const Head &head, const Tail &... tail) { cout << head << ' '; print(tail...); } #ifdef ONLINE_JUDGE template void dbg(const Args &... args) {} #else void dbg() { cerr << '\n'; } template void dbg(const T &t) { cerr << t << '\n'; } template void dbg(const Head &head, const Tail &... tail) { cerr << head << ' '; dbg(tail...); } #endif template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 >& p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template pair> compress(const vector &a) { int n = a.size(); vector x; REP(i, n) x.push_back(a[i]); sort(ALL(x)); x.erase(unique(ALL(x)), x.end()); VI res(n); REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin(); return make_pair(res, x); } template pair, vector> factorial(int n) { vector res(n+1), rev(n+1); res[0] = 1; REP(i, n) res[i+1] = res[i] * (i+1); rev[n] = 1 / res[n]; for(int i = n; i > 0; i--) { rev[i-1] = rev[i] * i; } return make_pair(res, rev); } #ifdef aclsegtree template struct value_size { S value; int size; }; template S min_op(S l, S r) { return min(l, r); }; template S max_op(S l, S r) { return max(l, r); }; template S sum_op(S l, S r) { return l + r; }; template value_size sum_op_size(value_size l, value_size r) { return {l.value + r.value, l.size + r.size}; }; template S min_e() { return numeric_limits::max(); }; template S max_e() { return numeric_limits::min(); }; template S sum_e() { return 0; } template value_size sum_e_size() { return {0, 0}; } template value_size min_e_size() { return {numeric_limits::max(), 0}; } template value_size max_e_size() { return {numeric_limits::min(), 0}; } template S chmin_mapping(F f, S x) { return min(x, f); } template S chmax_mapping(F f, S x) { return max(x, f); } template S add_mapping(F f, S x) { return x + f; } template value_size add_mapping_size(F f, value_size x) { return {x.value + x.size * f, x.size}; } template S change_mapping(F f, S x) { return (f == ID? x : f); } template value_size change_mapping_size(F f, value_size x) { value_size ret = {f * x.size, x.size}; return (f == ID? x : ret); } template S linear_mapping(pair f, S x) { return x * f.first + f.second; } template value_size linear_mapping_size(pair f, value_size x) { return {x.value * f.first + x.size * f.second, x.size}; } template F chmin_composition(F f, F g) { return min(f, g); } template F chmax_composition(F f, F g) { return max(f, g); } template F add_composition(F f, F g) { return f + g; } template F change_composition(F f, F g) { return (f == ID? g : f); } template pair linear_composition(pair f, pair g) { return {f.first * g.first, f.first * g.second + f.second}; } template F chmin_id() { return numeric_limits::max(); } template F chmax_id() { return numeric_limits::min(); } template F add_id() { return 0; } template F change_id() { return ID; } template pair linear_id() { return {1, 0}; } template using RSumQ = segtree, sum_e>; template using RMaxQ = segtree, max_e>; template using RMinQ = segtree, min_e>; template using RAddSumQ = lazy_segtree, sum_op_size, sum_e_size, F, add_mapping_size, add_composition, add_id>; template using RAddMinQ = lazy_segtree, min_e, F, add_mapping, add_composition, add_id>; template using RAddMaxQ = lazy_segtree, max_e, F, add_mapping, add_composition, add_id>; template using RMinMinQ = lazy_segtree, min_e, F, chmin_mapping, chmin_composition, chmin_id>; template using RMaxMaxQ = lazy_segtree, max_e, F, chmax_mapping, chmax_composition, chmax_id>; template using RChangeMinQ = lazy_segtree, min_e, F, change_mapping, change_composition, change_id>; template using RChangeMaxQ = lazy_segtree, max_e, F, change_mapping, change_composition, change_id>; template using RChangeSumQ = lazy_segtree, sum_op_size, sum_e_size, F, change_mapping_size, change_composition, change_id>; template using RLinearMinQ = lazy_segtree, min_e, pair, linear_mapping, linear_composition, linear_id>; template using RLinearMaxQ = lazy_segtree, max_e, pair, linear_mapping, linear_composition, linear_id>; template using RLinearSumQ = lazy_segtree, sum_op_size, sum_e_size, pair, linear_mapping_size, linear_composition, linear_id>; #endif #line 1 "library/KowerKoint/internal_operator.hpp" namespace internal_operator { template T default_add(T a, T b) { return a + b; } template T default_sub(T a, T b) { return a - b; } template T zero() { return T(0); } template T default_div(T a, T b) { return a / b; } template T default_mult(T a, T b) { return a * b; } template T one() { return T(1); } template T default_xor(T a, T b) { return a ^ b; } template T default_and(T a, T b) { return a & b; } template T default_or(T a, T b) { return a | b; } } #line 4 "library/KowerKoint/math/matrix.hpp" template < typename T, T (*add)(T, T)=internal_operator::default_add, T (*zero)()=internal_operator::zero, T (*mult)(T, T)=internal_operator::default_mult, T (*one)()=internal_operator::one, T (*sub)(T, T)=internal_operator::default_sub, T (*div)(T, T)=internal_operator::default_div > struct Matrix { vector> A; Matrix(size_t n, size_t m) : A(n, vector(m, zero())) {} size_t height() const { return A.size(); } size_t width() const { return A[0].size(); } vector &operator[](int i) { return A.at(i); } static Matrix I(size_t n) { Matrix ret(n, n); REP(i, n) ret[i][i] = one(); return ret; } Matrix &operator+=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); REP(i, n) REP(j, m) A[i][j] = add(A[i][j], B[i][j]); return *this; } Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); } Matrix &operator-=(const Matrix &B) { size_t n = height(), m = width(); assert(n == B.height() && m == B.width()); REP(i, n) REP(j, m) A[i][j] = sub(A[i][j], B[i][j]); return *this; } Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); } Matrix &operator*=(const Matrix &B) { size_t n = height(), m = width(), l = B.width(); assert(m == B.height()); vector> res(n, vector(l, zero())); REP(i, n) REP(j, m) REP(k, l) res[i][k] = add(res[i][k], mult(A[i][j], B[j][k])); A.swap(res); return (*this); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } friend istream &operator>>(istream &is, Matrix &mat) { size_t n = mat.height(), m = mat.width(); REP(i, n) REP(j, m) is >> mat[i][j]; return is; } friend ostream &operator<<(ostream &os, Matrix &mat) { size_t n = mat.height(), m = mat.width(); REP(i, n) { REP(j, m) os << mat[i][j] << (j==m-1? '\n' : ' '); } return os; } pair gaussian_elimination() const { int n = height(), m = width(); Matrix mat(*this); T det = one(); VI columns; int i = 0; int j = 0; while(i < n && j < m) { int idx = -1; FOR(k, i, n) if(mat[k][j] != zero()) idx = k; if(idx == -1) { det = zero(); j++; continue; } if(i != idx) { det *= sub(zero(), one()); swap(mat[i], mat[idx]); } det *= mat[i][j]; T scale = mat[i][j]; REP(l, m) mat[i][l] = div(mat[i][l], scale); FOR(k, i+1, n) { T scale = mat[k][j]; REP(l, m) mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale)); } columns.push_back(j); i++; j++; } REP(i, columns.size()) { int j = columns[i]; REP(k, i) { T scale = mat[k][j]; FOR(l, j, m) { mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale)); } } } return make_pair(mat, det); } Matrix inv() const { int n = height(); Matrix and_i(n, n*2, zero()); REP(i, n) REP(j, n) and_i[i][j] = A[i][j]; REP(i, n) and_i[i][n+i] = one(); auto& [i_and, det] = and_i.gaussian_elimination(); assert(det != zero()); Matrix res(n, n); REP(i, n) REP(j, n) res[i][j] = i_and[i][n+i]; return res; } Matrix operator^=(ll n) { if(n < 0) { *this = this->inv(); n = -n; } Matrix res = Matrix::I(height()); while(n) { if(n & 1) res *= *this; *this *= *this; n >>= 1LL; } A.swap(res.A); return (*this); } Matrix operator^(const ll n) const { return (Matrix(*this) ^= n); } }; #line 2 "library/KowerKoint/test/yukicoder-184/main.cpp" int main(void) { int n; cin >> n; VL a(n); cin >> a; Matrix< int, internal_operator::default_xor, internal_operator::zero, internal_operator::default_and, internal_operator::one, internal_operator::default_xor, internal_operator::default_and > mat(61, n); REP(i, 61) REP(j, n) mat[i][j] = a[j] >> i & 1LL; auto basis = mat.gaussian_elimination().first; ll ans = 1; REP(i, 61) { REP(j, n) if(basis[i][j]) { ans <<= 1LL; break; } } print(ans); }