#ifndef INCLUDE_MODE #define INCLUDE_MODE // #define REACTIVE // #define USE_GETLINE #endif #ifdef INCLUDE_MAIN IN VO Solve() { DEXPR( int , bound_N , 5000 , 100 ); CIN_ASSERT( N , 1 , bound_N ); CEXPR( ll , PLL , P ); using type = QuotientRing<>; type::SetModulo( &PLL ); SecondStirlingNumberCalculator ssn{}; type overlapping[N+1][N+1] = {}; overlapping[0][1] = type::one(); overlapping[1][1] = type( 2 ); FOREQ( j , 2 , N ){ overlapping[j][1] = overlapping[j-1][1] * overlapping[1][1]; } FOREQ( j , 0 , N ){ auto& overlapping_j = overlapping[j]; overlapping_j[0] = type::one(); overlapping_j[1] -= type::Derepresent( j ); FOREQ( i , 2 , N ){ overlapping_j[i] = overlapping_j[i-1] * overlapping_j[1]; } } type answer{}; FOREQ( i , 0 , N ){ FOREQ( j , 0 , i ){ answer += ssn.CountDisjointCover( N , i , j ) * overlapping[j][N-i]; } } RETURN( answer ); } REPEAT_MAIN(1); #else // INCLUDE_MAIN #ifdef INCLUDE_SUB // COMPAREに使用。圧縮時は削除する。 ll Naive( ll N , ll M , ll K ) { ll answer = N + M + K; return answer; } // COMPAREに使用。圧縮時は削除する。 ll Answer( ll N , ll M , ll K ) { // START_WATCH; ll answer = N + M + K; // // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。 // CEXPR( double , TL , 2000.0 ); // while( CHECK_WATCH( TL ) ){ // } return answer; } // 圧縮時は中身だけ削除する。 IN VO Experiment() { // CEXPR( int , bound , 10 ); // FOREQ( N , 0 , bound ){ // FOREQ( M , 0 , bound ){ // FOREQ( K , 0 , bound ){ // COUT( N , M , K , ":" , Naive( N , M , K ) ); // } // } // // cout << Naive( N ) << ",\n"[N==bound]; // } } // 圧縮時は中身だけ削除する。 IN VO SmallTest() { // CEXPR( int , bound , 10 ); // FOREQ( N , 0 , bound ){ // FOREQ( M , 0 , bound ){ // FOREQ( K , 0 , bound ){ // COMPARE( N , M , K ); // } // } // } } // 圧縮時は中身だけ削除する。 IN VO RandomTest() { // CEXPR( int , bound_N , 1e5 ); CIN_ASSERT( N , 1 , bound_N ); // CEXPR( ll , bound_M , 1e18 ); CIN_ASSERT( M , 1 , bound_M ); // CEXPR( ll , bound_K , 1e9 ); CIN_ASSERT( K , 1 , bound_K ); // COMPARE( N , M , N ); } #define INCLUDE_MAIN #include __FILE__ #else // INCLUDE_SUB #ifdef INCLUDE_LIBRARY /* C-x 3 C-x o C-x C-fによるファイル操作用 BFS (5KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt CoordinateCompress (3KB) c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/CoordinateCompress/compress.txt DFSOnTree (11KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepthFirstSearch/Tree/a.hpp Divisor (4KB) c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt IntervalAddBIT (9KB) c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/IntervalAdd/compress.txt Polynomial (21KB) c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt UnionFind (3KB) c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/UnionFindForest/compress.txt */ // VVV 常設でないライブラリは以下に挿入する。 template class SecondStirlingNumberCalculator { private: // N元集合の非交叉非空部分集合i個による被覆の個数をm_val[N][i]に格納する。 T m_val[length][length]; public: // （コンパイル時に）計算量O(length^2)で構築する。 constexpr inline SecondStirlingNumberCalculator(); constexpr inline const T ( &operator[]( const int& i ) const )[length]; // 以下Nと表せる場合のみサポート。 // N元集合の長さiの非交叉非空部分集合列による被覆の個数を返す。（O(log min{N,i})） // （i彩色の個数はこれらを足し合わせればよい） inline T CountDisjointCoverSequence( const int& N , const int& i ) const; // N元集合の長さiの非交叉非空部分集合列の個数を返す。（O(log min{N,i})） inline T CountDisjointSubsetSequence( const int& N , const int& i ) const; // 以下Mがlength以上の素数である場合のみサポート。 // N元集合の要素数nの部分集合の非交叉非空部分集合i個による被覆の個数を返す。（O(log N)） inline T CountDisjointCover( const int& N , const int& n , const int& i ) const; // N元集合の要素数nの部分集合の長さiの非交叉非空部分集合列による被覆の個数を返す。（O(log N)） inline T CountDisjointCoverSequence( const int& N , const int& n , const int& i ) const; }; template constexpr inline SecondStirlingNumberCalculator::SecondStirlingNumberCalculator() : m_val() { m_val[0][0] = 1; for( int i = 1 ; i < length ; i++ ){ auto& m_val_i = m_val[i]; const auto& m_val_i_minus = m_val[i - 1]; for( int j = 1 ; j < i ; j++ ){ ( ( m_val_i[j] = m_val_i_minus[j] ) *= j ) += m_val_i_minus[j - 1]; } m_val_i[i] = 1; } } template constexpr inline const T ( &SecondStirlingNumberCalculator::operator[]( const int& i ) const )[length] { assert( i < length ); return m_val[i]; } template constexpr inline T SecondStirlingNumberCalculator::CountDisjointCover( const int& N , const int& i ) const { assert( N < length ); return i <= N ? m_val[N][i] : T(); } template constexpr inline T SecondStirlingNumberCalculator::CountDisjointSubset( const int& N , const int& i ) const { assert( N < length ); return i < N ? m_val[N][i] + m_val[N][i+1] : i == N ? m_val[N][i] : T(); } template inline T SecondStirlingNumberCalculator::CountDisjointCoverSequence( const int& N , const int& i ) const { return CountDisjointCover( N , i ) * T::Factorial( i ); } template inline T SecondStirlingNumberCalculator::CountDisjointSubsetSequence( const int& N , const int& i ) const { return CountDisjointSubset( N , i ) * T::Factorial( i ); } template inline T SecondStirlingNumberCalculator::CountDisjointCover( const int& N , const int& n , const int& i ) const { return CountDisjointCover( n , i ) * T::Combination( N , n ); } template inline T SecondStirlingNumberCalculator::CountDisjointCoverSequence( const int& N , const int& n , const int& i ) const { return CountDisjointCoverSequence( n , i ) * T::Combination( N , n ); } template class QuotientRing; template class StaticModuloForQuotientRing { friend class QuotientRing; private: static const INT* g_p; StaticModuloForQuotientRing() = delete; }; template const INT* StaticModuloForQuotientRing::g_p = nullptr; #define DECLARATION_OF_ARITHMETIC_FOR_QUOTIENT( OPR , EX ) \ inline constexpr QuotientRing operator OPR( QuotientRing n ) const EX; \ #define DEFINITION_OF_ARITHMETIC_FOR_QUOTIENT( OPR , EX , LEFT , OPR2 ) \ template inline constexpr QuotientRing QuotientRing::operator OPR( QuotientRing n ) const EX { return move( LEFT OPR2 ## = *this ); } \ template inline constexpr QuotientRing operator OPR( T n0 , const QuotientRing& n1 ) EX { return move( QuotientRing( move( n0 ) ) OPR ## = n1 ); } \ // インスタンスごとに異なる法を定めたい場合は // MultiBase/a.hpp // のクラスを用いる。 template class QuotientRing { protected: U m_n; public: inline constexpr QuotientRing() noexcept; inline constexpr QuotientRing( const QuotientRing& n ) noexcept; inline constexpr QuotientRing( QuotientRing&& n ) noexcept; inline constexpr QuotientRing( U n ) noexcept; inline constexpr QuotientRing& operator=( QuotientRing n ) noexcept; inline constexpr QuotientRing& operator+=( const QuotientRing& n ) noexcept; inline constexpr QuotientRing& operator-=( const QuotientRing& n ) noexcept; inline constexpr QuotientRing& operator*=( const QuotientRing& n ) noexcept; inline QuotientRing& operator/=( QuotientRing n ); // n>=0である場合のみサポート。計算量O(log n)で2^n倍する。 template inline constexpr QuotientRing& operator<<=( INT n ); // n>=0かつMが奇数である場合のみサポート。計算量O(n)で2^{-n}倍する。 template inline constexpr QuotientRing& operator>>=( INT n ); inline constexpr QuotientRing& operator++() noexcept; inline constexpr QuotientRing operator++( int ) noexcept; inline constexpr QuotientRing& operator--() noexcept; inline constexpr QuotientRing operator--( int ) noexcept; inline constexpr bool operator==( QuotientRing n ) const noexcept; inline constexpr bool operator!=( QuotientRing n ) const noexcept; DECLARATION_OF_ARITHMETIC_FOR_QUOTIENT( + , noexcept ); DECLARATION_OF_ARITHMETIC_FOR_QUOTIENT( - , noexcept ); DECLARATION_OF_ARITHMETIC_FOR_QUOTIENT( * , noexcept ); DECLARATION_OF_ARITHMETIC_FOR_QUOTIENT( / , ); // Mが素数であるかexponent>=0である場合にのみサポート。exponent乗する。 template inline constexpr QuotientRing operator^( INT exponent ) const; // n>=0である場合のみサポート。計算量O(log n)で2^n倍を返す。 template inline constexpr QuotientRing operator<<( INT n ) const; // n>=0かつMが奇数である場合のみサポート。計算量O(n)で2^{-n}倍を返す。 template inline constexpr QuotientRing operator>>( INT n ) const; inline constexpr QuotientRing operator-() const noexcept; // -1倍する。 inline constexpr QuotientRing& SignInvert() noexcept; // *g_pが素数である場合のみサポート。-1乗する。 inline QuotientRing& Invert(); // *g_pが素数であるかexponent>=0である場合にのみサポート。exponent乗する。 template inline constexpr QuotientRing& Power( INT exponent ); // グローバルスコープでswapを定義するためのもの。 inline constexpr void swap( QuotientRing& n ) noexcept; inline constexpr const U& Represent() noexcept; inline constexpr U Represent() const noexcept; // 0 <= n < *g_pの場合のみサポート。定数倍高速化のためにassertなし。 static inline constexpr QuotientRing Derepresent( U n ) noexcept; // *g_pが素数である場合のみサポート。 static inline const QuotientRing& Inverse( const U& n ); // Uが整数型である場合にのみサポート。 static inline const QuotientRing& Factorial( const U& n ); // *g_pが素数である場合のみサポート。 static inline const QuotientRing& FactorialInverse( const U& n ); // *g_pが素数である場合のみサポート。 static inline QuotientRing Combination( const U& n , const U& i ); static inline const QuotientRing& zero() noexcept; static inline const QuotientRing& one() noexcept; static inline const U& GetModulo() noexcept; static inline void SetModulo( const U* p ) noexcept; private: template inline constexpr QuotientRing& PositivePower( INT exponent ) noexcept; template inline constexpr QuotientRing& NonNegativePower( INT exponent ) noexcept; template inline constexpr QuotientRing& Ref( T&& n ) noexcept; }; template inline constexpr QuotientRing::QuotientRing() noexcept : m_n() {} template inline constexpr QuotientRing::QuotientRing( const QuotientRing& n ) noexcept : m_n( n.m_n ) {} template inline constexpr QuotientRing::QuotientRing( QuotientRing&& n ) noexcept : m_n( move( n.m_n ) ) {} template inline constexpr QuotientRing::QuotientRing( U n ) noexcept : m_n( move( ( ( n %= *StaticModuloForQuotientRing::g_p ) += *StaticModuloForQuotientRing::g_p ) %= *StaticModuloForQuotientRing::g_p ) ) {} template inline constexpr QuotientRing& QuotientRing::operator=( QuotientRing n ) noexcept { return Ref( m_n = move( n.m_n ) ); } template inline constexpr QuotientRing& QuotientRing::operator+=( const QuotientRing& n ) noexcept { return Ref( m_n += n.m_n ); } template inline constexpr QuotientRing& QuotientRing::operator-=( const QuotientRing& n ) noexcept { return *this += -n; } template inline constexpr QuotientRing& QuotientRing::operator*=( const QuotientRing& n ) noexcept { return Ref( ( ( m_n %= *StaticModuloForQuotientRing::g_p ) *= n.m_n % *StaticModuloForQuotientRing::g_p ) %= *StaticModuloForQuotientRing::g_p ); } template inline QuotientRing& QuotientRing::operator/=( QuotientRing n ) { return operator*=( n.Invert() ); } template template inline constexpr QuotientRing& QuotientRing::operator<<=( INT n ) { assert( n >= 0 ); return *this *= QuotientRing( 2 ).NonNegativePower( move( n ) ); } template template inline constexpr QuotientRing& QuotientRing::operator>>=( INT n ) { assert( n >=0 ); while( n-- > 0 ){ ( ( m_n & 1 ) == 0 ? m_n : m_n += *StaticModuloForQuotientRing::g_p ) >>= 1; } return *this; } template inline constexpr QuotientRing& QuotientRing::operator++() noexcept { return Ref( ++m_n ); } template inline constexpr QuotientRing QuotientRing::operator++( int ) noexcept { QuotientRing n{ *this }; operator++(); return n; } template inline constexpr QuotientRing& QuotientRing::operator--() noexcept { return Ref( --( m_n == 0 ? m_n += *StaticModuloForQuotientRing::g_p : m_n ) ); } template inline constexpr QuotientRing QuotientRing::operator--( int ) noexcept { QuotientRing n{ *this }; operator--(); return n; } template inline constexpr bool QuotientRing::operator==( QuotientRing n ) const noexcept { return ( n -= *this ).m_n % *StaticModuloForQuotientRing::g_p == 0; } template inline constexpr bool QuotientRing::operator!=( QuotientRing n ) const noexcept { return !( *this == n ); } DEFINITION_OF_ARITHMETIC_FOR_QUOTIENT( + , noexcept , n , + ); DEFINITION_OF_ARITHMETIC_FOR_QUOTIENT( - , noexcept , n.SignInvert() , + ); DEFINITION_OF_ARITHMETIC_FOR_QUOTIENT( * , noexcept , n , * ); DEFINITION_OF_ARITHMETIC_FOR_QUOTIENT( / , , n.Invert() , * ); template template inline constexpr QuotientRing QuotientRing::operator^( INT exponent ) const { return move( QuotientRing( *this ).Power( move( exponent ) ) ); } template template inline constexpr QuotientRing QuotientRing::operator<<( INT n ) const { return move( QuotientRing( *this ) <<= move( n ) ); } template template inline constexpr QuotientRing QuotientRing::operator>>( INT n ) const { return move( QuotientRing( *this ) >>= move( n ) ); } template inline constexpr QuotientRing QuotientRing::operator-() const noexcept { return move( QuotientRing( *this ).SignInvert() ); } template inline constexpr QuotientRing& QuotientRing::SignInvert() noexcept { return Ref( m_n = *StaticModuloForQuotientRing::g_p - ( m_n %= *StaticModuloForQuotientRing::g_p ) ); } template inline QuotientRing& QuotientRing::Invert() { assert( ( m_n %= *StaticModuloForQuotientRing::g_p ) != 0 ); return NonNegativePower( U( *StaticModuloForQuotientRing::g_p - 2 ) ); } template template inline constexpr QuotientRing& QuotientRing::PositivePower( INT exponent ) noexcept { U power{ this->m_n }; exponent--; while( exponent != 0 ){ ( exponent & 1 ) == 1 ? ( *this *= power ).m_n %= *StaticModuloForQuotientRing::g_p : *this; exponent >>= 1; ( power *= power ) %= *StaticModuloForQuotientRing::g_p; } return *this; } template template inline constexpr QuotientRing& QuotientRing::NonNegativePower( INT exponent ) noexcept { return exponent == 0 ? Ref( m_n = *StaticModuloForQuotientRing::g_p == 1 ? 0 : 1 ) : Ref( PositivePower( move( exponent ) ) ); } template template inline constexpr QuotientRing& QuotientRing::Power( INT exponent ) { bool neg = exponent < 0; assert( !( ( m_n %= *StaticModuloForQuotientRing::g_p ) == 0 && neg ) ); return neg ? PositivePower( move( exponent *= -( *StaticModuloForQuotientRing::g_p - 2 ) ) ) : NonNegativePower( move( exponent ) ); } template inline constexpr void QuotientRing::swap( QuotientRing& n ) noexcept { std::swap( m_n , n.m_n ); } template inline const QuotientRing& QuotientRing::Inverse( const U& n ) { static vector> memory = { zero() , one() }; static U length_curr = 2; while( length_curr <= n ){ memory.push_back( zero() ); memory.back().m_n = *StaticModuloForQuotientRing::g_p - memory[*StaticModuloForQuotientRing::g_p % length_curr].m_n * ( *StaticModuloForQuotientRing::g_p / length_curr ) % *StaticModuloForQuotientRing::g_p; length_curr++; } return memory[n]; } template inline const QuotientRing& QuotientRing::Factorial( const U& n ) { static vector> memory = { one() , one() }; static U length_curr = 2; while( length_curr <= n ){ memory.push_back( memory[length_curr - 1] * length_curr ); length_curr++; } return memory[n]; } template inline const QuotientRing& QuotientRing::FactorialInverse( const U& n ) { static vector> memory = { one() , one() }; static U length_curr = 2; while( length_curr <= n ){ memory.push_back( memory[length_curr - 1] * Inverse( length_curr ) ); length_curr++; } return memory[n]; } template inline QuotientRing QuotientRing::Combination( const U& n , const U& i ) { return i <= n ? Factorial( n ) * FactorialInverse( i ) * FactorialInverse( n - i ) : zero(); } template inline constexpr const U& QuotientRing::Represent() noexcept { return m_n %= *StaticModuloForQuotientRing::g_p; } template inline constexpr U QuotientRing::Represent() const noexcept { return m_n % *StaticModuloForQuotientRing::g_p; } template inline constexpr QuotientRing QuotientRing::Derepresent( U n ) noexcept { QuotientRing n_copy{}; n_copy.m_n = move( n ); return n_copy; } template inline const QuotientRing& QuotientRing::zero() noexcept { static constexpr const QuotientRing z{}; return z; } template inline const QuotientRing& QuotientRing::one() noexcept { static constexpr const QuotientRing o = QuotientRing::Derepresent( 1 ); return o; } template inline const U& QuotientRing::GetModulo() noexcept { return *StaticModuloForQuotientRing::g_p; } template inline void QuotientRing::SetModulo( const U* p ) noexcept { assert( p != nullptr && *p != 0 ); StaticModuloForQuotientRing::g_p = p; } template template inline constexpr QuotientRing& QuotientRing::Ref( T&& n ) noexcept { return *this; } template inline QuotientRing Inverse( const QuotientRing& n ) { return move( QuotientRing( n ).Invert() ); } template inline constexpr QuotientRing Power( QuotientRing n , INT exponent ) { return move( n.Power( move( exponent ) ) ); } template inline constexpr void swap( QuotientRing& n0 , QuotientRing& n1 ) noexcept { n0.swap( n1 ); } template inline string to_string( QuotientRing& n ) noexcept { return to_string( n.Represent() ) + " + " + to_string( QuotientRing::GetModulo() ) + "Z"; } template inline basic_istream& operator>>( basic_istream& is , QuotientRing& n ) { ll m; is >> m; n = m; return is; } template inline basic_ostream& operator<<( basic_ostream& os , const QuotientRing& n ) { return os << n.Represent(); } // AAA 常設でないライブラリは以上に挿入する。 #define INCLUDE_SUB #include __FILE__ #else // INCLUDE_LIBRARY #ifdef DEBUG #define _GLIBCXX_DEBUG #define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode , use_getline ); CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if( exec_mode == solve_mode ){ if CE( bound_test_case_num > 1 ){ CERR( "テストケースの個数を入力してください。" ); SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else { if( exec_mode == experiment_mode ){ Experiment(); } else if( exec_mode == small_test_mode ){ SmallTest(); } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); SET_LL( test_case_num ); REPEAT( test_case_num ){ RandomTest(); } } RE 0; } FINISH_MAIN #define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE2 ) #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); AS( ( MIN ) <= A && A <= ( MAX ) ) #define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ SET_LL( A ); ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { AS( false ); } #define SOLVE_ONLY ST_AS( __FUNCTION__[0] == 'S' ) #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl #define COUT( ... ) VariadicCout( cout << "出力： " , __VA_ARGS__ ) << endl #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << endl #define COUT_A( A , N ) cout << "出力： "; OUTPUT_ARRAY( cout , A , N ) << endl #define CERR_ITR( A ) OUTPUT_ITR( cerr , A ) << endl #define COUT_ITR( A ) cout << "出力： "; OUTPUT_ITR( cout , A ) << endl #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize ( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if CE( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN #define DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 ) #define ASSERT( A , MIN , MAX ) AS( ( MIN ) <= A && A <= ( MAX ) ) #define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX ) #define SOLVE_ONLY #define CERR( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << ENDL #endif #ifdef REACTIVE #define ENDL endl #else #define ENDL "\n" #endif #ifdef USE_GETLINE #define SET_LL( A ) { GETLINE( A ## _str ); A = stoll( A ## _str ); } #define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ ) #else #define SET_LL( A ) cin >> A #define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; } #define CIN_A( LL , A , N ) VE A( N ); SET_A( A , N ); #endif #include using namespace std; #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define FINISH_MAIN REPEAT( test_case_num ){ if CE( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } } #define START_WATCH chrono::system_clock::time_point watch = chrono::system_clock::now() #define CURRENT_TIME static_cast( chrono::duration_cast( chrono::system_clock::now() - watch ).count() / 1000.0 ) #define CHECK_WATCH( TL_MS ) ( CURRENT_TIME < TL_MS - 100.0 ) #define CEXPR( LL , BOUND , VALUE ) CE LL BOUND = VALUE #define SET_A_ASSERT( A , N , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A] , MIN , MAX ); } #define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define CIN_A_ASSERT( A , N , MIN , MAX ) vector A( N ); SET_A_ASSERT( A , N , MIN , MAX ) #define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( decldecay_t( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ ) #define FOREQ( VAR , INITIAL , FINAL ) for( decldecay_t( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ ) #define FOREQINV( VAR , INITIAL , FINAL ) for( decldecay_t( INITIAL ) VAR = INITIAL ; VAR + 1 > FINAL ; VAR -- ) #define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .BE() , end_ ## ARRAY = ARRAY .EN() #define FOR_ITR( ARRAY ) for( AUTO_ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define SET_PRECISION( DECIMAL_DIGITS ) cout << fixed << setprecision( DECIMAL_DIGITS ) #define OUTPUT_ARRAY( OS , A , N ) FOR( VARIABLE_FOR_OUTPUT_ARRAY , 0 , N ){ OS << A[VARIABLE_FOR_OUTPUT_ARRAY] << (VARIABLE_FOR_OUTPUT_ARRAY==N-1?"":" "); } OS #define OUTPUT_ITR( OS , A ) { auto ITERATOR_FOR_OUTPUT_ITR = A.BE() , EN_FOR_OUTPUT_ITR = A.EN(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; WH( VARIABLE_FOR_OUTPUT_ITR ){ OS << *ITERATOR_FOR_COUT_ITR; ( VARIABLE_FOR_OUTPUT_ITR = ++ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR ) ? OS : OS << " "; } } OS #define RETURN( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); RE #define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( "(" , #__VA_ARGS__ , ") == (" , __VA_ARGS__ , ") : Naive == " , naive , match ? "==" : "!=" , answer , "== Answer" ); if( !match ){ RE; } // 圧縮用 #define TE template #define TY typename #define US using #define ST static #define AS assert #define IN inline #define CL class #define PU public #define OP operator #define CE constexpr #define CO const #define NE noexcept #define RE return #define WH while #define VO void #define VE vector #define LI list #define BE begin #define EN end #define SZ size #define LE length #define PW Power #define MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& #define VI virtual #define ST_AS static_assert #define reMO_CO remove_const #define is_COructible_v is_constructible_v #define rBE rbegin #define reSZ resize // 型のエイリアス #define decldecay_t(VAR)decay_t TE US ret_t = decltype(declval()(declval()...)); TE US inner_t = TY T::type; US uint = unsigned int; US ll = long long; US ull = unsigned long long; US ld = long double; US lld = __float128; TE US T2 = pair; TE US T3 = tuple; TE US T4 = tuple; US path = pair; // 入出力用 #define DF_OF_COUT_FOR_VE(V)TE IN basic_ostream& OP<<(basic_ostream& os,CO V& arg){auto BE = arg.BE(),EN = arg.EN();auto IT = BE;WH(IT != EN){(IT == BE?os:os << " ")<< *IT;IT++;}RE os;} TE IN basic_istream& VariadicCin(basic_istream& is){RE is;} TE IN basic_istream& VariadicCin(basic_istream& is,Arg& arg,ARGS&... args){RE VariadicCin(is >> arg,args...);} TE IN basic_istream& VariadicGetline(basic_istream& is,CO char& separator){RE is;} TE IN basic_istream& VariadicGetline(basic_istream& is,CO char& separator,Arg& arg,ARGS&... args){RE VariadicGetline(getline(is,arg,separator),separator,args...);} DF_OF_COUT_FOR_VE(VE); DF_OF_COUT_FOR_VE(LI); DF_OF_COUT_FOR_VE(set); DF_OF_COUT_FOR_VE(unordered_set); TE IN basic_ostream& OP<<(basic_ostream& os,CO pair& arg){RE os << arg.first << " " << arg.second;} TE IN basic_ostream& VariadicCout(basic_ostream& os,CO Arg& arg){RE os << arg;} TE IN basic_ostream& VariadicCout(basic_ostream& os,CO Arg1& arg1,CO Arg2& arg2,CO ARGS&... args){RE VariadicCout(os << arg1 << " ",arg2,args...);} // 算術用 TE CE T PositiveBaseRS(CO T& a,CO T& p){RE a >= 0?a % p:p - 1 -((-(a + 1))% p);} TE CE T RS(CO T& a,CO T& p){RE PositiveBaseRS(a,p < 0?-p:p);} TE CE T PositiveBaseQuotient(CO T& a,CO T& p){RE(a - PositiveBaseRS(a,p))/ p;} TE CE T Quotient(CO T& a,CO T& p){RE p < 0?PositiveBaseQuotient(-a,-p):PositiveBaseQuotient(a,p);} #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ ST_AS( ! is_same::value && ! is_same::value ); \ decldecay_t( ARGUMENT ) ANSWER{ 1 }; \ { \ decldecay_t( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \ decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ WH( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER; \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ #define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO ) \ ll ANSWER{ 1 }; \ { \ ll ARGUMENT_FOR_SQUARE_FOR_POWER = ( ( ARGUMENT ) % ( MODULO ) ) % ( MODULO ); \ ARGUMENT_FOR_SQUARE_FOR_POWER < 0 ? ARGUMENT_FOR_SQUARE_FOR_POWER += ( MODULO ) : ARGUMENT_FOR_SQUARE_FOR_POWER; \ decldecay_t( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ WH( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){ \ if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){ \ ANSWER = ( ANSWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \ } \ ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT_FOR_SQUARE_FOR_POWER * ARGUMENT_FOR_SQUARE_FOR_POWER ) % ( MODULO ); \ EXPONENT_FOR_SQUARE_FOR_POWER /= 2; \ } \ } \ #define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CE_LENGTH , MODULO ) \ ll ANSWER[CE_LENGTH]; \ ll ANSWER_INV[CE_LENGTH]; \ ll INVERSE[CE_LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_INDEX ){ \ ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \ } \ ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ FOREQ( i , 2 , MAX_INDEX ){ \ ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \ } \ } \ // 二分探索用 // EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= CO_TARGETの整数解を格納。 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , CO_TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \ ST_AS( ! is_same::value && ! is_same::value ); \ ll ANSWER = MINIMUM; \ { \ ll L_BS = MINIMUM; \ ll U_BS = MAXIMUM; \ ANSWER = UPDATE_ANSWER; \ ll EXPRESSION_BS; \ CO ll CO_TARGET_BS = ( CO_TARGET ); \ ll DIFFERENCE_BS; \ WH( L_BS < U_BS ){ \ DIFFERENCE_BS = ( EXPRESSION_BS = ( EXPRESSION ) ) - CO_TARGET_BS; \ CERR( "二分探索中：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS :" , #EXPRESSION , "=" , EXPRESSION_BS , DIFFERENCE_BS > 0 ? ">" : DIFFERENCE_BS < 0 ? "<" : "=" , CO_TARGET_BS , "=" , #CO_TARGET ); \ if( DIFFERENCE_BS INEQUALITY_FOR_CHECK 0 ){ \ U_BS = UPDATE_U; \ } else { \ L_BS = UPDATE_L; \ } \ ANSWER = UPDATE_ANSWER; \ } \ if( L_BS > U_BS ){ \ CERR( "二分探索失敗：" , "L_BS =" , L_BS , ">" , U_BS , "= U_BS :" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \ CERR( "二分探索マクロにミスがある可能性があります。変更前の版に戻してください。" ); \ ANSWER = MAXIMUM + 1; \ } else { \ CERR( "二分探索終了：" , "L_BS =" , L_BS , "<=" , #ANSWER , "=" , ANSWER , "<=" , U_BS , "= U_BS" ); \ CERR( "二分探索が成功したかを確認するために" , #EXPRESSION , "を計算します。" ); \ CERR( "成功判定が不要な場合はこの計算を削除しても構いません。" ); \ EXPRESSION_BS = ( EXPRESSION ); \ CERR( "二分探索結果：" , #EXPRESSION , "=" , EXPRESSION_BS , ( EXPRESSION_BS > CO_TARGET_BS ? ">" : EXPRESSION_BS < CO_TARGET_BS ? "<" : "=" ) , CO_TARGET_BS ); \ if( EXPRESSION_BS DESIRED_INEQUALITY CO_TARGET_BS ){ \ CERR( "二分探索成功：" , #ANSWER , ":=" , ANSWER ); \ } else { \ CERR( "二分探索失敗：" , #ANSWER , ":=" , #MAXIMUM , "+ 1 =" , MAXIMUM + 1 ); \ CERR( "単調でないか、単調増加性と単調減少性を逆にしてしまったか、探索範囲内に解が存在しません。" ); \ ANSWER = MAXIMUM + 1; \ } \ } \ } \ // 単調増加の時にEXPRESSION >= CO_TARGETの最小解を格納。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , >= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) // 単調増加の時にEXPRESSION <= CO_TARGETの最大解を格納。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , > , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) // 単調減少の時にEXPRESSION >= CO_TARGETの最大解を格納。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , CO_TARGET , < , ANSWER - 1 , ANSWER , ( L_BS + 1 + U_BS ) / 2 ) // 単調減少の時にEXPRESSION <= CO_TARGETの最小解を格納。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , CO_TARGET ) BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , CO_TARGET , <= , ANSWER , ANSWER + 1 , ( L_BS + U_BS ) / 2 ) // t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。 TE IN TY set::iterator MaximumLeq(set& S,CO T& t){CO auto EN = S.EN();if(S.empty()){RE EN;}auto IT = S.upper_bound(t);RE IT == EN?S.find(*(S.rBE())):IT == S.BE()?EN:--IT;} // t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。 TE IN TY set::iterator MaximumLt(set& S,CO T& t){CO auto EN = S.EN();if(S.empty()){RE EN;}auto IT = S.lower_bound(t);RE IT == EN?S.find(*(S.rBE())):IT == S.BE()?EN:--IT;} // t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。 TE IN TY set::iterator MinimumGeq(set& S,CO T& t){RE S.lower_bound(t);} // tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。 TE IN TY set::iterator MinimumGt(set& S,CO T& t){RE S.upper_bound(t);} // 尺取り法用 // VAR_TPA_LとVAR_TPA_RをINITで初期化し、VAR_TPA_RがCONTINUE_CONDITIONを満たす限り、 // 閉区間[VAR_TPA_L,VAR_TPA_R]が条件ON_CONDITIONを満たすか否かを判定し、 // trueになるかVAR_TAR_LがVAR_TAR_Rに追い付くまでVAR_TPA_Lの更新操作UPDATE_Lを繰り返し、 // その後VAR_TPA_Rの更新操作UPDATE_Rを行う。 // ON_CONDITIONがtrueとなる極大閉区間とその時点でのINFOをANSWERに格納する。 #define TPA( ANSWER , VAR_TPA , INIT , CONTINUE_CONDITION , UPDATE_L , UPDATE_R , ON_CONDITION , INFO ) \ VE> ANSWER{}; \ { \ auto init_TPA = INIT; \ decldecay_t( ANSWER.front() ) ANSWER ## _temp = { init_TPA , init_TPA , INFO }; \ auto ANSWER ## _prev = ANSWER ## _temp; \ auto& VAR_TPA ## _L = get<0>( ANSWER ## _temp ); \ auto& VAR_TPA ## _R = get<1>( ANSWER ## _temp ); \ auto& VAR_TPA ## _info = get<2>( ANSWER ## _temp ); \ bool on_TPA_prev = false; \ WH( true ){ \ bool continuing = CONTINUE_CONDITION; \ bool on_TPA = continuing && ( ON_CONDITION ); \ CERR( continuing ? "尺取り中" : "尺取り終了" , "： [L,R] = [" , VAR_TPA ## _L , "," , VAR_TPA ## _R , "] ," , on_TPA_prev ? "on" : "off" , "->" , on_TPA ? "on" : "off" , ", info =" , VAR_TPA ## _info ); \ if( on_TPA_prev && ! on_TPA ){ \ ANSWER.push_back( ANSWER ## _prev ); \ } \ if( continuing ){ \ if( on_TPA || VAR_TPA ## _L == VAR_TPA ## _R ){ \ ANSWER ## _prev = ANSWER ## _temp; \ UPDATE_R; \ } else { \ UPDATE_L; \ } \ } else { \ break; \ } \ on_TPA_prev = on_TPA; \ } \ } \ // データ構造用 TE TY V> IN auto OP+(CO V& a0,CO V& a1)-> decldecay_t((declval>().push_back(declval()),a0)){if(a0.empty()){RE a1;}if(a1.empty()){RE a0;}AS(a0.SZ()== a1.SZ());V AN{};for(auto IT0 = a0.BE(),IT1 = a1.BE(),EN0 = a0.EN();IT0 != EN0;IT0++,IT1++){AN.push_back(*IT0 + *IT1);}RE AN;} TE IN pair OP+(CO pair& t0,CO pair& t1){RE{t0.first + t1.first,t0.second + t1.second};} TE IN tuple OP+(CO tuple& t0,CO tuple& t1){RE{get<0>(t0)+ get<0>(t1),get<1>(t0)+ get<1>(t1),get<2>(t0)+ get<2>(t1)};} TE IN tuple OP+(CO tuple& t0,CO tuple& t1){RE{get<0>(t0)+ get<0>(t1),get<1>(t0)+ get<1>(t1),get<2>(t0)+ get<2>(t1),get<3>(t0)+ get<3>(t1)};} TE IN T Addition(CO T& t0,CO T& t1){RE t0 + t1;} TE IN T Xor(CO T& t0,CO T& t1){RE t0 ^ t1;} TE IN T MU(CO T& t0,CO T& t1){RE t0 * t1;} TE IN CO T& Zero(){ST CO T z{};RE z;} TE IN CO T& One(){ST CO T o = 1;RE o;}TE IN T AdditionInv(CO T& t){RE -t;} TE IN T Id(CO T& v){RE v;} TE IN T Min(CO T& a,CO T& b){RE a < b?a:b;} TE IN T Max(CO T& a,CO T& b){RE a < b?b:a;} // グラフ用 TE TY V> IN auto Get(CO V& a){RE[&](CRI i = 0){RE a[i];};} TE IN VE id(CRI SZ){VE AN(SZ);FOR(i,0,SZ){AN[i]= i;}RE AN;} // グリッド問題用 int H,W,H_minus,W_minus,HW; VE wall_str;VE > non_wall; char walkable = '.',unwalkable = '#'; IN T2 EnumHW(CRI v){RE{v / W,v % W};} IN int EnumHW_inv(CO T2& ij){auto&[i,j]= ij;RE i * W + j;} CO string direction[4]={"U","R","D","L"}; IN int DirectionNumberOnGrid(CRI i,CRI j,CRI k,CRI h){RE ik?0:jh?3:(AS(false),-1);} IN int DirectionNumberOnGrid(CRI v,CRI w){auto[i,j]=EnumHW(v);auto[k,h]=EnumHW(w);RE DirectionNumberOnGrid(i,j,k,h);} IN int ReverseDirectionNumberOnGrid(CRI n){AS(0<=n&&n<4);RE(n+2)%4;} IN VE EdgeOnGrid(CRI v){VEAN{};auto[i,j]=EnumHW(v);if(i>0&&wall_str[i-1][j]==walkable){AN.push_back(EnumHW_inv({i-1,j}));}if(i+10&&wall_str[i][j-1]==walkable){AN.push_back(EnumHW_inv({i,j-1}));}if(j+1 WeightedEdgeOnGrid(CRI v){VEAN{};auto[i,j]=EnumHW(v);if(i>0&&wall_str[i-1][j]==walkable){AN.push_back({EnumHW_inv({i-1,j}),1});}if(i+10&&wall_str[i][j-1]==walkable){AN.push_back({EnumHW_inv({i,j-1}),1});}if(j+1& S){if(S.empty()){S.reSZ(H);}cin>>S[i];AS(int(S[i].SZ())==W);} IN VO SetWallOnGrid(CRI i,VE>& b){if(b.empty()){b.reSZ(H,VE(W));}auto&S_i=wall_str[i];auto&b_i=b[i];FOR(j,0,W){b_i[j]=S_i[j]==walkable?false:(AS(S_i[j]==unwalkable),true);}} // デバッグ用 #ifdef DEBUG IN VO AlertAbort( int n ) { CERR( "abort関数が呼ばれました。assertマクロのメッセージが出力されていない場合はオーバーフローの有無を確認をしてください。" ); } VO AutoCheck( int& exec_mode , CO bool& use_getline ); IN VO Solve(); IN VO Experiment(); IN VO SmallTest(); IN VO RandomTest(); ll GetRand( CRL Rand_min , CRL Rand_max ); IN VO BreakPoint( CRI LINE ) {} int exec_mode; CEXPR( int , solve_mode , 0 ); CEXPR( int , sample_debug_mode , 1 ); CEXPR( int , submission_debug_mode , 2 ); CEXPR( int , library_search_mode , 3 ); CEXPR( int , experiment_mode , 4 ); CEXPR( int , small_test_mode , 5 ); CEXPR( int , random_test_mode , 6 ); #ifdef USE_GETLINE CEXPR( bool , use_getline , true ); #else CEXPR( bool , use_getline , false ); #endif #else ll GetRand( CRL Rand_min , CRL Rand_max ) { ll answer = time( NULL ); RE answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; } #endif // VVV 常設ライブラリは以下に挿入する。 // Map (1KB) // c:/Users/user/Documents/Programming/Mathematics/Function/Map/compress.txt CL is_ordered{PU:is_ordered()= delete;TE ST CE auto Check(CO T& t)-> decltype(t < t,true_type());ST CE false_type Check(...);TE ST CE CO bool value = is_same_v< decltype(Check(declval())),true_type >;}; TE US Map = conditional_t>,unordered_map,conditional_t,map,VO>>; // Algebra (4KB) // c:/Users/user/Documents/Programming/Mathematics/Algebra/compress.txt #define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE #define DC_OF_POINT(POINT)IN U& POINT()NE #define DF_OF_CPOINT(POINT)TE IN CO U& VirtualPointedSet::POINT()CO NE{RE Point();} #define DF_OF_POINT(POINT)TE IN U& VirtualPointedSet::POINT()NE{RE Point();} TE CL UnderlyingSet{PU:US type = U;};TE CL VirtualPointedSet:VI PU UnderlyingSet{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE CL PointedSet:VI PU VirtualPointedSet{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE CL VirtualNSet:VI PU UnderlyingSet{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE CL AbstractNSet:VI PU VirtualNSet{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN U Transfer(CO U& u);};TE