#line 2 "library/KowerKoint/base.hpp" #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; } 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}; 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 vector> split(typename vector::const_iterator begin, typename vector::const_iterator end, T val) { vector> res; vector cur; for(auto it = begin; it != end; it++) { if(*it == val) { res.push_back(cur); cur.clear(); } else cur.push_back(val); } res.push_back(cur); return res; } vector split(typename string::const_iterator begin, typename string::const_iterator end, char val) { vector res; string cur = ""; for(auto it = begin; it != end; it++) { if(*it == val) { res.push_back(cur); cur.clear(); } else cur.push_back(val); } res.push_back(cur); return res; } 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); } #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/matrix.hpp" template < typename T, T (*add)(const T, const T)=internal_operator::default_add, T (*zero)()=internal_operator::zero, T (*mult)(const T, const T)=internal_operator::default_mult, T (*one)()=internal_operator::one, T (*sub)(const T, const T)=internal_operator::default_sub, T (*div)(const T, const T)=internal_operator::default_div > struct Matrix { int n, m; vector> A; Matrix() : n(0), m(0), A(vector>(0)) {} Matrix(size_t _n, size_t _m) : n(_n), m(_m), A(_n, vector(_m, zero())) {} Matrix(vector> _A) : n(_A.size()), m(_A[0].size()), A(_A) {} vector &operator[](int i) { return A.at(i); } const vector &operator[](int i) const { 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) { assert(n == B.n && m == B.m); 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) { assert(n == B.n && m == B.m); 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) { assert(m == B.n); vector> res(n, vector(B.m, zero())); REP(i, n) REP(j, m) REP(k, B.m) res[i][k] = add(res[i][k], mult(A[i][j], B[j][k])); A.swap(res); m = B.m; return (*this); } Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); } Matrix &operator|=(const Matrix &B) { assert(B.n == n); REP(i, n) { A[i].resize(m+B.m); REP(j, B.m) A[i][m+j] = B[i][j]; } m += B.m; return (*this); } Matrix operator|(const Matrix &B) const { return (Matrix(*this) |= B); } Matrix &operator|=(const vector &B) { assert(B.size() == n); REP(i, n) { A[i].push_back(B[i]); } m++; return (*this); } Matrix operator|(const vector &B) const { return (Matrix(*this) |= B); } Matrix &operator&=(const Matrix &B) { assert(B.m == m); A.resize(n+B.n); REP(i, B.n) { A[n+i] = B[i]; } n += B.n; return (*this); } Matrix operator&(const Matrix &B) const { return (Matrix(*this) &= B); } Matrix &operator&=(const vector &B) { assert(B.size() == m); A.push_back(B); n++; return (*this); } Matrix operator&(const vector &B) const { return (Matrix(*this) &= B); } friend istream &operator>>(istream &is, Matrix &mat) { REP(i, mat.n) REP(j, mat.m) is >> mat[i][j]; return is; } friend ostream &operator<<(ostream &os, const Matrix &mat) { REP(i, mat.n) { REP(j, mat.m) os << mat[i][j] << (j==mat.m-1? '\n' : ' '); } return os; } pair gaussian_elimination() const { 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); } void make_basis() { *this = gaussian_elimination().first; while(n && get_bra(n-1) == vector(m, zero())) pop_bra(); } Matrix inv() const { Matrix and_i = A | I(n); 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; } vector get_bra(int i) const { assert(0 <= i && i < n); return A[i]; } vector get_ket(int i) const { assert(0 <= i && i < m); vector res(n); REP(i, n) res[i] = A[i][i]; return res; } void pop_bra() { assert(n > 0); A.pop_back(); n--; } void pop_ket() { assert(m > 0); REP(i, n) A[i].pop_back(); m--; } Matrix transpose() const { Matrix res(m, n); REP(i, n) REP(j, m) res[j][i] = A[i][j]; return res; } Matrix operator^=(ll n) { if(n < 0) { *this = this->inv(); n = -n; } Matrix res = Matrix::I(n); 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); } }; using XorMatrix = Matrix< int, internal_operator::default_xor, internal_operator::zero, internal_operator::default_and, internal_operator::one, internal_operator::default_xor, internal_operator::default_and >; #line 2 "library/KowerKoint/test/yukicoder-184/main.cpp" int main(void) { int n; cin >> n; VL a(n); cin >> a; XorMatrix 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); }