#pragma GCC optimize ( "O3" ) #pragma GCC optimize( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #include using namespace std; using ull = unsigned long long; #define MAIN main #define TYPE_OF( VAR ) remove_const::type >::type #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define CEXPR( LL , BOUND , VALUE ) constexpr const LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define CIN_ASSERT( A , MIN , MAX ) CIN( TYPE_OF( MAX ) , A ); ASSERT( A , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define COUT( ANSWER ) cout << ( ANSWER ) << "\n" template class SqrtCalculation { public: int m_val; inline constexpr SqrtCalculation(); }; template inline constexpr SqrtCalculation::SqrtCalculation() : m_val( 1 ) { int m_val2 = 1; while( ( m_val2 << 2 ) <= N ){ m_val <<= 1; m_val2 <<= 2; } while( m_val2 < N ){ m_val++; m_val2 = m_val * m_val; } } #define TEMPLATE_ARGUMENTS_FOR_DUAL_SQRT_DECOMPOSITION typename T , T m_T(const T&,const T&) , const T& e_T() , typename U , U o_U(const T&,const U&) , int N , int N_sqrt // (可換とも結合的とも単位的とも限らない)基点付きマグマ(T,m_T:T^2->T,e_T:1->T)と基点が恒等変換に対応するT作用付き集合(U,o_U:T×U->U)と非負整数Nをパラメータとする。 // 配列による初期化O(N) // 一点取得O(1) // 一点更新はなし // o_Uによる一点更新はo_Uによる区間更新で処理する(O(N^{1/2})) // o_Uによる区間更新O(N^{1/2}) template {}.m_val > class NonCommutativeDualSqrtDecomposition { private: U m_a[N]; T m_b[N_sqrt]; static constexpr int N_d = N / N_sqrt; static constexpr int N_m = N_d * N_sqrt; public: static const T& g_e; inline constexpr NonCommutativeDualSqrtDecomposition( const U ( &a )[N] ); inline constexpr NonCommutativeDualSqrtDecomposition( U ( &&a )[N] ); inline constexpr U Get( const int& i ) const; inline constexpr void IntervalAct( const int& i_start , const int& i_final , const T& n ); }; template const T& NonCommutativeDualSqrtDecomposition::g_e = e_T(); template inline constexpr NonCommutativeDualSqrtDecomposition::NonCommutativeDualSqrtDecomposition( const U ( &a )[N] ) : m_a() , m_b() { if( m_b[0] != g_e ){ for( int d = 0 ; d < N_d ; d++ ){ m_b[d] = g_e; } } for( int i = 0 ; i < N ; i++ ){ m_a[i] = a[i]; } } template inline constexpr NonCommutativeDualSqrtDecomposition::NonCommutativeDualSqrtDecomposition( U ( &&a )[N] ) : m_a() , m_b() { swap( m_a , a ); if( m_b[0] != g_e ){ for( int d = 0 ; d < N_d ; d++ ){ m_b[d] = g_e; } } } template inline constexpr U NonCommutativeDualSqrtDecomposition::Get( const int& i ) const { return i < N_m ? o_U( m_b[i/N_sqrt] , m_a[i] ) : m_a[i]; } template inline constexpr void NonCommutativeDualSqrtDecomposition::IntervalAct( const int& i_start , const int& i_final , const T& n ) { if( n != g_e ){ const int i_min = max( i_start , 0 ); const int i_ulim = min( i_final + 1 , N ); const int d_0 = ( i_min + N_sqrt - 1 ) / N_sqrt; const int d_1 = max( d_0 , i_ulim / N_sqrt ); const int d_0_N_sqrt = d_0 * N_sqrt ; const int i_0 = min( d_0_N_sqrt , i_ulim ) ; const int d_1_N_sqrt = d_1 * N_sqrt ; const int i_1 = max( i_0 , d_1_N_sqrt ); if( d_0 > 0 ){ T& m_bd = m_b[d_0-1]; if( m_bd != g_e ){ for( int i = d_0_N_sqrt - N_sqrt ; i < d_0_N_sqrt ; i++ ){ U& m_ai = m_a[i]; m_ai = o_U( m_bd , m_ai ); } m_bd = g_e; } } for( int i = i_min ; i < i_0 ; i++ ){ U& m_ai = m_a[i]; m_ai = o_U( n , m_ai ); } for( int d = d_0 ; d < d_1 ; d++ ){ T& m_bd = m_b[d]; m_bd = m_T( n , m_bd ); } if( d_1 < N_d ){ T& m_bd = m_b[d_1]; if( m_bd != g_e ){ for( int i = d_1_N_sqrt + N_sqrt - 1 ; i >= d_1_N_sqrt ; i-- ){ U& m_ai = m_a[i]; m_ai = o_U( m_bd , m_ai ); } m_bd = g_e; } } for( int i = i_1 ; i < i_ulim ; i++ ){ U& m_ai = m_a[i]; m_ai = o_U( n , m_ai ); } } return; } class M { public: ull m_a; ull m_b; bool m_neg; constexpr M( const ull& a = -1 , const ull& b = 0 , const bool& neg = false ) : m_a( a ) , m_b( b ) , m_neg( neg ) {} }; inline M prod( const M& m0 , const M& m1 ) { return m0.m_neg ? M( ( ~m1.m_b ) & m0.m_a , ( ( ~m1.m_a ) & ( ( ~m1.m_b ) & m0.m_a ) ) | m0.m_b , !m1.m_neg ) : M( m1.m_a & m0.m_a , ( m1.m_b & m0.m_a ) | m0.m_b , m1.m_neg ); } inline const M& unit() { static const M m{}; return m; } inline ull act( const M& m , const ull& n ) { return ( ( m.m_neg ? ~n : n ) & m.m_a ) | m.m_b; } inline bool operator==( const M& m0 , const M& m1 ) { return m0.m_a == m1.m_a && m0.m_b == m1.m_b && m0.m_neg == m1.m_neg; } inline bool operator!=( const M& m0 , const M& m1 ) { return !( m0 == m1 ); } inline CEXPR( int , c , 6 ); class Variable { public: ull m_val[c]; constexpr Variable() : m_val() { FOR( i , 0 , c ){ ull one{ 1 }; ull& m_val_i = m_val[i]; FOR( d , 0 , 64 ){ if( ( ( d >> i ) & 1 ) == 1 ){ m_val_i += one << d; } } } } }; int MAIN() { UNTIE; CEXPR( int , bound_N , 1000000 ); CIN_ASSERT( N , 1 , bound_N ); CEXPR( int , bound_Q , 100000 ); CIN_ASSERT( Q , 1 , bound_Q ); constexpr Variable P{}; static ull X_pre[bound_N] = {}; FOR( i , 0 , N ){ X_pre[i] = P.m_val[i % c]; } static NonCommutativeDualSqrtDecomposition X{ move( X_pre ) }; string land = "land"; string lor = "lor"; string Rightarrow = "Rightarrow"; string Yes = "Yes"; string No = "No"; N--; REPEAT( Q ){ CIN_ASSERT( h , 0 , N ); CIN( string , o ); CIN_ASSERT( l0 , 0 , N ); CIN_ASSERT( r0 , l0 , N ); CIN_ASSERT( l1 , 0 , N ); CIN_ASSERT( r1 , l1 , N ); if( o == land ){ X.IntervalAct( l0 , r0 , M( X.Get( h ) ) ); } else if( o == lor ){ X.IntervalAct( l0 , r0 , M( -1 , X.Get( h ) ) ); } else { assert( o == Rightarrow ); X.IntervalAct( l0 , r0 , M( -1 , X.Get( h ) , true ) ); } set X_interval{}; bool found = false; FOREQ( i , l1 , r1 ){ ull Xi = X.Get( i ); if( X_interval.count( Xi ) == 0 ){ X_interval.insert( Xi ); } else { found = true; break; } } COUT( found ? Yes : No ); } QUIT; }