#ifdef LOCAL #define _GLIBCXX_DEBUG #define __clock__ #else #pragma GCC optimize("Ofast") // #define NDEBUG #endif #define __precision__ 10 #define buffer_check true #define iostream_untie true #define debug_stream std::cerr #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define all(v) std::begin(v), std::end(v) #define rall(v) std::rbegin(v), std::rend(v) #define odd(n) ((n) & 1) #define even(n) (not __odd(n)) #define __popcount(n) __builtin_popcountll(n) #define __clz32(n) __builtin_clz(n) #define __clz64(n) __builtin_clzll(n) #define __ctz32(n) __builtin_ctz(n) #define __ctz64(n) __builtin_ctzll(n) using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t; using pii = std::pair; using pll = std::pair; template using heap = std::priority_queue; template using rheap = std::priority_queue, std::greater>; template using hashset = std::unordered_set; template using hashmap = std::unordered_map; namespace execution { using namespace std::chrono; system_clock::time_point start_time, end_time; long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast(end_time - start_time).count(); } void print_elapsed_time() { std::cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n"; } struct setupper { setupper() { if(iostream_untie) std::ios::sync_with_stdio(false), std::cin.tie(nullptr); std::cout << std::fixed << std::setprecision(__precision__); #ifdef stderr_path if(freopen(stderr_path, "a", stderr)) { std::cerr << std::fixed << std::setprecision(__precision__); } #endif #ifdef stdout_path if(not freopen(stdout_path, "w", stdout)) { freopen("CON", "w", stdout); std::cerr << "Failed to open the stdout file\n\n"; } std::cout << ""; #endif #ifdef stdin_path if(not freopen(stdin_path, "r", stdin)) { freopen("CON", "r", stdin); std::cerr << "Failed to open the stdin file\n\n"; } #endif #ifdef LOCAL std::cerr << "----- stderr at LOCAL -----\n\n"; atexit(print_elapsed_time); #else fclose(stderr); #endif #ifdef __clock__ start_time = system_clock::now(); #endif } } __setupper; class myclock_t { system_clock::time_point built_pt, last_pt; int built_ln, last_ln; std::string built_func, last_func; bool is_built; public: myclock_t() : is_built(false) {} void build(int crt_ln, const std::string &crt_func) { is_built = true, last_pt = built_pt = system_clock::now(), last_ln = built_ln = crt_ln, last_func = built_func = crt_func; } void set(int crt_ln, const std::string &crt_func) { if(is_built) last_pt = system_clock::now(), last_ln = crt_ln, last_func = crt_func; else debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::set failed (yet to be built!)\n"; } void get(int crt_ln, const std::string &crt_func) { if(is_built) { system_clock::time_point crt_pt(system_clock::now()); long long diff = duration_cast(crt_pt - last_pt).count(); debug_stream << diff << " ms elapsed from" << " [ " << last_ln << " : " << last_func << " ]"; if(last_ln == built_ln) debug_stream << " (when built)"; debug_stream << " to" << " [ " << crt_ln << " : " << crt_func << " ]" << "\n"; last_pt = built_pt, last_ln = built_ln, last_func = built_func; } else { debug_stream << "[ " << crt_ln << " : " << crt_func << " ] " << "myclock_t::get failed (yet to be built!)\n"; } } }; } // namespace execution #ifdef __clock__ execution::myclock_t __myclock; #define build_clock() __myclock.build(__LINE__, __func__) #define set_clock() __myclock.set(__LINE__, __func__) #define get_clock() __myclock.get(__LINE__, __func__) #else #define build_clock() ((void)0) #define set_clock() ((void)0) #define get_clock() ((void)0) #endif namespace std { // hash template size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); } template struct hash> { size_t operator()(pair const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } }; template ::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc::apply(seed, t), get(t)); } }; template struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } }; template struct hash> { size_t operator()(tuple const &t) const { return tuple_hash_calc>::apply(0, t); } }; // iostream template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template ostream &operator<<(ostream &os, const pair &p) { return os << p.first << ' ' << p.second; } template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos::apply(os, t); return os << ' ' << get(t); } }; template struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } }; template ostream &operator<<(ostream &os, const tuple &t) { return tupleos, tuple_size>::value - 1>::apply(os, t); } template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; } template , string>::value, nullptr_t> = nullptr> istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; } template , string>::value, nullptr_t> = nullptr> ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; } } // namespace std #ifdef LOCAL #define dump(...) \ debug_stream << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]\n", \ dump_func(#__VA_ARGS__, __VA_ARGS__) template void dump_func(const char *ptr, const T &x) { debug_stream << '\t'; for(char c = *ptr; c != '\0'; c = *++ptr) if(c != ' ') debug_stream << c; debug_stream << " : " << x << '\n'; } template void dump_func(const char *ptr, const T &x, rest_t... rest) { debug_stream << '\t'; for(char c = *ptr; c != ','; c = *++ptr) if(c != ' ') debug_stream << c; debug_stream << " : " << x << ",\n"; dump_func(++ptr, rest...); } #else #define dump(...) ((void)0) #endif template void read_range(P __first, P __second) { for(P i = __first; i != __second; ++i) std::cin >> *i; } template void write_range(P __first, P __second) { for(P i = __first; i != __second; std::cout << (++i == __second ? '\n' : ' ')) std::cout << *i; } // substitue y for x if x > y. template inline bool sbmin(T &x, const T &y) { return x > y ? x = y, true : false; } // substitue y for x if x < y. template inline bool sbmax(T &x, const T &y) { return x < y ? x = y, true : false; } // binary search. i64 bin(const std::function &pred, i64 ok, i64 ng) { while(std::abs(ok - ng) > 1) { i64 mid = (ok + ng) / 2; (pred(mid) ? ok : ng) = mid; } return ok; } double bin(const std::function &pred, double ok, double ng, const double eps) { while(std::abs(ok - ng) > eps) { double mid = (ok + ng) / 2; (pred(mid) ? ok : ng) = mid; } return ok; } // be careful that val is type-sensitive. template void init(A (&array)[N], const T &val) { std::fill((T *)array, (T *)(array + N), val); } // reset all bits. template void reset(A &array) { memset(array, 0, sizeof(array)); } /* The main code follows. */ using namespace std; main() { void __solve(); u32 t = 1; #ifdef LOCAL t = 1; #endif // t = -1; // cin >> t; while(t--) __solve(); char chec; if(buffer_check && cin >> chec) { cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; return EXIT_FAILURE; } } template // K must be a field. struct matrix { std::vector> mat; matrix() {} matrix(size_t n) { assign(n, n);} matrix(size_t h, size_t w) { assign(h, w); } matrix(const matrix &x) : mat(x.mat) {} matrix(const std::vector> _mat) : mat(_mat) {} void resize(size_t h, size_t w, const K v = K(0)) { mat.resize(h, std::vector(w, v)); } void assign(size_t h, size_t w, const K v = K()) { mat.assign(h, std::vector(w, v)); } size_t height() const { return mat.size(); } size_t width() const { return mat.empty() ? 0 : mat[0].size(); } bool is_square() const { return height() == width(); } std::vector &operator[](const size_t i) { return mat[i]; } static matrix identity(size_t n) { matrix ret(n, n); for(size_t i = 0; i < n; ++i) ret[i][i] = K(1); return ret; } matrix operator-() const { size_t h = height(), w = width(); matrix res(*this); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { res[i][j] = -mat[i][j]; } } return res; } matrix operator&(const matrix &x) const { return matrix(*this) &= x; } matrix operator|(const matrix &x) const { return matrix(*this) |= x; } matrix operator^(const matrix &x) const { return matrix(*this) ^= x; } matrix operator+(const matrix &x) const { return matrix(*this) += x; } matrix operator-(const matrix &x) const { return matrix(*this) -= x; } matrix operator*(const matrix &x) const { return matrix(*this) *= x; } matrix &operator&=(const matrix &x) { size_t h = height(), w = width(); assert(h == x.height() and w == x.width()); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { mat[i][j] &= x.mat[i][j]; } } return *this; } matrix &operator|=(const matrix &x) { size_t h = height(), w = width(); assert(h == x.height() and w == x.width()); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { mat[i][j] |= x.mat[i][j]; } } return *this; } matrix &operator^=(const matrix &x) { size_t h = height(), w = width(); assert(h == x.height() and w == x.width()); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { mat[i][j] ^= x.mat[i][j]; } } return *this; } matrix &operator+=(const matrix &x) { size_t h = height(), w = width(); assert(h == x.height() and w == x.width()); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { mat[i][j] += x.mat[i][j]; } } return *this; } matrix &operator-=(const matrix &x) { size_t h = height(), w = width(); assert(h == x.height() and w == x.width()); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) { mat[i][j] -= x.mat[i][j]; } } return *this; } matrix &operator*=(const matrix &x) { size_t l = height(), m = width(), n = x.width(); assert(m == x.height()); matrix res(l, n); for(size_t i = 0; i < l; ++i) { for(size_t j = 0; j < m; ++j) { for(size_t k = 0; k < n; ++k) { res[i][k] += mat[i][j] * x.mat[j][k]; } } } return *this = res; } friend matrix pow(matrix x, int_fast64_t n) { assert(x.is_square()); matrix res = identity(x.height()); while(n) { if(n & 1) res *= x; x *= x, n >>= 1; } return res; } friend matrix inverse(const matrix &x) { assert(x.is_square()); size_t n = x.height(); matrix ext_x(x), e(identity(n)), res(n); for(size_t i = 0; i < n; ++i) ext_x[i].insert(end(ext_x[i]), begin(e[i]), end(e[i])); ext_x = ext_x.row_canonical_form(); for(size_t i = 0; i < n; ++i) { if(std::vector(begin(ext_x[i]), begin(ext_x[i]) + n) != e[i]) return matrix(); res[i] = std::vector(begin(ext_x[i]) + n, end(ext_x[i])); } return res; } matrix row_canonical_form() { size_t h = height(), w = width(), rank = 0; matrix res(*this); for(size_t j = 0; j < w; ++j) { bool piv = false; for(size_t i = rank; i < h; ++i) { if(res[i][j] != K(0)) { if(piv) { K r = -res[i][j]; for(size_t k = j; k < w; ++k) res[i][k] += res[rank][k] * r; } else { swap(res[rank], res[i]); K r = res[rank][j]; for(size_t k = j; k < w; ++k) res[rank][k] /= r; for(size_t k = 0; k < rank; ++k) { r = -res[k][j]; for(size_t l = j; l < w; ++l) res[k][l] += res[rank][l] * r; } piv = true; } } } if(piv) ++rank; } return res; } K determinant() const { matrix x(*this); assert(is_square()); size_t n = height(); K res(1); for(size_t j = 0; j < n; ++j) { bool piv = false; for(size_t i = j; i < n; ++i) { if(x[i][j] != K(0)) { if(piv) { const K r = -x[i][j]; for(size_t k = j; k < n; ++k) x[i][k] += x[j][k] * r; } else { swap(x[i], x[j]); if(i != j) res = -res; const K r = x[j][j]; res *= r; for(size_t k = j; k < n; ++k) x[j][k] /= r; piv = true; } } } if(not piv) return K(0); } return res; } friend std::istream &operator>>(std::istream &s, matrix &x) { size_t h = x.height(), w = x.width(); for(size_t i = 0; i < h; ++i) { for(size_t j = 0; j < w; ++j) s >> x[i][j]; } return s; } friend std::ostream &operator<<(std::ostream &s, const matrix &x) { size_t h = x.height(), w = x.width(); for(size_t i = 0; i < h; ++i) { if(i) s << "\n"; for(size_t j = 0; j < w; ++j) s << (j ? " " : "") << x.mat[i][j]; } return s; } }; namespace math { template class modint { int dat; public: constexpr modint() : dat{0} {} constexpr modint(long long y) : dat((y %= mod) < 0 ? mod + y : y) {} constexpr long long get() const { return dat; } constexpr modint &operator+=(const modint &other) { return (dat += other.dat) < mod ? 0 : dat -= mod, *this; } constexpr modint &operator++() { return ++dat, *this; } constexpr modint operator++(int) { modint t = *this; return ++dat, t; } constexpr modint &operator-=(const modint &other) { return (dat += mod - other.dat) < mod ? 0 : dat -= mod, *this; } constexpr modint &operator--() { return --dat, *this; } constexpr modint operator--(int) { modint t = *this; return --dat, t; } constexpr modint &operator*=(const modint &other) { return dat = (long long)dat * other.dat % mod, *this; } constexpr modint &operator/=(const modint &other) { return *this *= inverse(other); } constexpr modint operator-() const { return modint(-dat); } constexpr modint operator+(const modint &other) const { return modint(*this) += other; } constexpr modint operator-(const modint &other) const { return modint(*this) -= other; } constexpr modint operator*(const modint &other) const { return modint(*this) *= other; } constexpr modint operator/(const modint &other) const { return modint(*this) /= other; } constexpr bool operator==(const modint &other) const { return dat == other.dat; } constexpr bool operator!=(const modint &other) const { return dat != other.dat; } constexpr bool operator!() const { return !dat; } friend constexpr modint inverse(const modint &other) { int a{mod}, b{other.dat}, u{}, v{1}, t{}; while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v; return modint{u}; } friend constexpr modint pow(modint other, long long e) { if(e < 0) e = e % (mod - 1) + mod - 1; modint res{1}; while(e) { if(e & 1) res *= other; other *= other, e >>= 1; } return res; } friend std::ostream &operator<<(std::ostream &s, const modint &other) { return s << other.dat; } friend std::istream &operator>>(std::istream &s, modint &other) { long long dat; other = modint{(s >> dat, dat)}; return s; } }; // class modint } // namespace math // using F_2=math::modint<2>; struct F_2 { bool x; F_2() : x(0) {} F_2(bool y) : x(y) {} F_2 operator-() { return *this; } bool operator!=(F_2 y) { return y.x!=x; } bool operator==(F_2 y) { return y.x==x; } F_2 &operator/=(F_2 y) { return *this; } F_2 &operator+=(F_2 y) { return x^=y.x,*this; } F_2 &operator*=(F_2 y) { return x &= y.x,*this; } F_2 operator*(F_2 y) { return x&&(y.x); } F_2 operator+(F_2 y) { return x ^ y.x; } }; void __solve() { int n; cin>>n; vector a(n); cin>>a; i64 sum[1<<17]={}; for(int i=0; i base(n*17,17); for(int i=0; i=(1<<17)) break; for(int k=0; k<17; ++k) { base[i*17+j][k]=now>>k&1; } now<<=1; } } base=base.row_canonical_form(); int piv[17]; init(piv,-1); for(int i=0,j=0; i>j&1) { if(~piv[j]) { for(int k=0; k<17; ++k) { if(base[piv[j]][k].x) { tt^=1<