#line 1 ".lib/template.hpp" #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define allof(obj) (obj).begin(), (obj).end() #define range(i, l, r) for(int i=l;i>1)|y_bit)) #define bit_kth(i, k) ((i >> k)&1) #define bit_highest(i) (i?63-__builtin_clzll(i):-1) #define bit_lowest(i) (i?__builtin_ctzll(i):-1) #define sleepms(t) std::this_thread::sleep_for(std::chrono::milliseconds(t)) using ll = long long; using ld = long double; using ul = uint64_t; using pi = std::pair; using pl = std::pair; using namespace std; template std::ostream &operator<<(std::ostream &dest, const std::pair &p){ dest << p.first << ' ' << p.second; return dest; } template std::ostream &operator<<(std::ostream &dest, const std::vector> &v){ int sz = v.size(); if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::vector &v){ int sz = v.size(); if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::array &v){ if(sz==0) return dest; for(int i=0;i std::ostream &operator<<(std::ostream &dest, const std::set &v){ for(auto itr=v.begin();itr!=v.end();){ dest << *itr; itr++; if(itr!=v.end()) dest << ' '; } return dest; } template std::ostream &operator<<(std::ostream &dest, const std::map &v){ for(auto itr=v.begin();itr!=v.end();){ dest << '(' << itr->first << ", " << itr->second << ')'; itr++; if(itr!=v.end()) dest << '\n'; } return dest; } template vector make_vec(size_t sz, T val){return std::vector(sz, val);} template auto make_vec(size_t sz, Tail ...tail){ return std::vector(tail...))>(sz, make_vec(tail...)); } template vector read_vec(size_t sz){ std::vector v(sz); for(int i=0;i<(int)sz;i++) std::cin >> v[i]; return v; } template auto read_vec(size_t sz, Tail ...tail){ auto v = std::vector(tail...))>(sz); for(int i=0;i<(int)sz;i++) v[i] = read_vec(tail...); return v; } void io_init(){ std::cin.tie(nullptr); std::ios::sync_with_stdio(false); } #line 1 ".lib/math/mod.hpp" #line 6 ".lib/math/mod.hpp" #include #line 8 ".lib/math/mod.hpp" #include #line 1 ".lib/math/minior/mod_base.hpp" #line 4 ".lib/math/minior/mod_base.hpp" // @param m `1 <= m` constexpr long long safe_mod(long long x, long long m){ x %= m; if (x < 0) x += m; return x; } struct barrett{ unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1){} unsigned int umod()const{return _m;} unsigned int mul(unsigned int a, unsigned int b)const{ unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z) * im) >> 64); #endif unsigned long long y = x * _m; return (unsigned int)(z - y + (z < y ? _m : 0)); } }; // @param n `0 <= n` // @param m `1 <= m` constexpr long long pow_mod_constexpr(long long x, long long n, int m){ if(m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while(n){ if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for(long long a : bases){ long long t = d; long long y = pow_mod_constexpr(a, t, n); while(t != n - 1 && y != 1 && y != n - 1){ y = y * y % n; t <<= 1; } if(y != n - 1 && t % 2 == 0){ return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr int primitive_root_constexpr(int m){ if(m == 2) return 1; if(m == 167772161) return 3; if(m == 469762049) return 3; if(m == 754974721) return 11; if(m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for(int i = 3; (long long)(i)*i <= x; i += 2){ if(x % i == 0){ divs[cnt++] = i; while(x % i == 0){ x /= i; } } } if(x > 1) divs[cnt++] = x; for(int g = 2;; g++){ bool ok = true; for(int i = 0; i < cnt; i++){ if(pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1){ ok = false; break; } } if(ok)return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); int ceil_pow2(int n){ int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } int bsf(unsigned int n){ return __builtin_ctz(n); } // @param b `1 <= b` // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g constexpr std::pair inv_gcd(long long a, long long b){ a = safe_mod(a, b); if(a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t){ long long u = s / t; s -= t * u; m0 -= m1 * u; auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if(m0 < 0) m0 += b / s; return {s, m0}; } #line 13 ".lib/math/mod.hpp" template long long modpow(long long a, long long b){ assert(0 <= b); assert(0 < m); a = safe_mod(a, m); long long ret = 1; while(b){ if(b & 1) ret = (ret * a) % m; a = (a * a) % m; b >>= 1; } return ret; } // @param 0 <= b, 0 < m long long modpow(long long a, long long b, int m){ assert(0 <= b); assert(0 < m); a = safe_mod(a, m); long long ret = 1; while(b){ if(b & 1) ret = (ret * a) % m; a = (a * a) % m; b >>= 1; } return ret; } struct modint_base {}; struct static_modint_base : modint_base {}; template * = nullptr> struct static_modint : static_modint_base{ using mint = static_modint; public: static constexpr int mod(){return m;} static mint raw(int v) { mint x; x._v = v; return x; } static_modint(): _v(0){} template static_modint(T v){ long long x = v % (long long)umod(); if (x < 0) x += umod(); _v = x; } unsigned int val()const{return _v;} mint& operator++(){ _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--(){ if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int){ mint result = *this; ++*this; return result; } mint operator--(int){ mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs){ _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs){ _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs){ unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs){return *this = *this * rhs.inv();} mint operator+()const{return *this;} mint operator-()const{return mint() - *this;} mint pow(long long n)const{ assert(0 <= n); mint x = *this, r = 1; while(n){ if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv()const{ if(prime){ assert(_v); return pow(umod() - 2); }else{ auto eg = inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs){return mint(lhs) += rhs;} friend mint operator-(const mint& lhs, const mint& rhs){return mint(lhs) -= rhs;} friend mint operator*(const mint& lhs, const mint& rhs){return mint(lhs) *= rhs;} friend mint operator/(const mint& lhs, const mint& rhs){return mint(lhs) /= rhs;} friend bool operator==(const mint& lhs, const mint& rhs){return lhs._v == rhs._v;} friend bool operator!=(const mint& lhs, const mint& rhs){return lhs._v != rhs._v;} private: unsigned int _v; static constexpr unsigned int umod(){return m;} static constexpr bool prime = is_prime; }; template struct dynamic_modint : modint_base{ using mint = dynamic_modint; public: static int mod(){return (int)(bt.umod());} static void set_mod(int m){ assert(1 <= m); bt = barrett(m); } static mint raw(int v){ mint x; x._v = v; return x; } dynamic_modint(): _v(0){} template dynamic_modint(T v){ long long x = v % (long long)(mod()); if (x < 0) x += mod(); _v = x; } unsigned int val()const{return _v;} mint& operator++(){ _v++; if(_v == umod()) _v = 0; return *this; } mint& operator--(){ if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int){ mint result = *this; ++*this; return result; } mint operator--(int){ mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs){ _v += rhs._v; if(_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs){ _v += mod() - rhs._v; if(_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs){ _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs){return *this = *this * rhs.inv();} mint operator+()const{return *this;} mint operator-()const{return mint() - *this;} mint pow(long long n)const{ assert(0 <= n); mint x = *this, r = 1; while(n){ if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv()const{ auto eg = inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs){return mint(lhs) += rhs;} friend mint operator-(const mint& lhs, const mint& rhs){return mint(lhs) -= rhs;} friend mint operator*(const mint& lhs, const mint& rhs){return mint(lhs) *= rhs;} friend mint operator/(const mint& lhs, const mint& rhs){return mint(lhs) /= rhs;} friend bool operator==(const mint& lhs, const mint& rhs){return lhs._v == rhs._v;} friend bool operator!=(const mint& lhs, const mint& rhs){return lhs._v != rhs._v;} private: unsigned int _v; static barrett bt; static unsigned int umod(){return bt.umod();} }; template barrett dynamic_modint::bt(998244353); using modint = dynamic_modint<-1>; using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; template std::ostream &operator<<(std::ostream &dest, const static_modint &a){ dest << a.val(); return dest; } template std::ostream &operator<<(std::ostream &dest, const dynamic_modint &a){ dest << a.val(); return dest; } // 0 <= n < m <= int_max // 前処理 O(n + log(m)) // 各種計算 O(1) // 変数 <= n template* = nullptr> struct modcomb{ private: int n; std::vector f, i, fi; void init(int _n){ assert(0 <= _n && _n < mint::mod()); if(_n < f.size()) return; n = _n; f.resize(n + 1), i.resize(n + 1), fi.resize(n + 1); f[0] = fi[0] = mint(1); if(n) f[1] = fi[1] = i[1] = mint(1); for(int j = 2; j <= n; j++) f[j] = f[j - 1] * j; fi[n] = f[n].inv(); for(int j = n; j >= 2; j--){ fi[j - 1] = fi[j] * j; i[j] = f[j - 1] * fi[j]; } } public: modcomb(): n(-1){} modcomb(int _n){ init(_n); } void recalc(int _n){ init(std::min(mint::mod() - 1, 1 << ceil_pow2(_n))); } mint comb(int a, int b){ if((a < 0) || (b < 0) || (a < b)) return 0; return f[a] * fi[a - b] * fi[b]; } mint perm(int a, int b){ if((a < 0) || (b < 0) || (a < b)) return 0; return f[a] * fi[a - b]; } mint fac(int x){ assert(0 <= x && x <= n); return f[x]; } mint inv(int x){ assert(0 < x && x <= n); return i[x]; } mint finv(int x){ assert(0 <= x && x <= n); return fi[x]; } }; template* = nullptr> struct modpow_table{ std::vector v; // x^maxkまで計算できる modpow_table(){} void init(int x, int maxk){ v.resize(maxk + 1); v[0] = 1; for(int i = 1; i <= maxk; i++) v[i] = v[i - 1] * x; } mint pow(int k){ assert(0 <= k && k < v.size()); return v[k]; } }; #line 3 "a.cpp" int main(){ io_init(); int n; std::cin >> n; auto v = read_vec(1 << n); auto no = [&](){ std::cout << "No" << '\n'; exit(0); }; if(v[0]) no(); range(i, 1, 1 << n){ ll x = 0; for(int j = n - 1; j >= 0; j--){ if((i >> j) & 1){ x ^= v[1 << j]; } } if(x != v[i]) no(); } std::cout << "Yes" << '\n'; }