#ifdef DEBUG #define _GLIBCXX_DEBUG #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE ) #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 #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK int auto_checked; AutoCheck( auto_checked ); if( auto_checked == 3 ){ Jikken(); return 0; } else if( auto_checked == 4 ){ Debug(); return 0; } else if( auto_checked != 0 ){ return 0; }; #else #pragma GCC optimize ( "O3" ) #pragma GCC optimize ( "unroll-loops" ) #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ) #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE ) #define CERR( ... ) #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << "\n" #define CERR_A( A , N ) #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << "\n" #define CERR_ITR( A ) #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #define AUTO_CHECK #endif #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using ld = long double; using lld = __float128; template using T2 = pair; template using T3 = tuple; template using T4 = tuple; using path = pair; // #define RANDOM_TEST #if defined( DEBUG ) && defined( RANDOM_TEST ) ll GetRand( const ll& Rand_min , const ll& Rand_max ); #define SET_ASSERT( A , MIN , MAX ) CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ) #define CIN( LL , ... ) LL __VA_ARGS__; static_assert( false ) #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = bound_T; static_assert( bound_T > 1 ) #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ANSWER , "==" , guchoku ); goto END_MAIN; } else { CERR( ANSWER , "!=" , guchoku ); return 0; } #else #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ ) #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); } #define RETURN( ANSWER ) COUT( ANSWER ); QUIT #endif #define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) ) #define TYPE_OF( VAR ) decay_t #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX ) #define CIN_A( LL , A , N ) LL A[N]; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; } #define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ ) #define GETLINE( ... ) GETLINE_SEPARATE( " " , ... ) #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 FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- ) #define AUTO_ITR( ARRAY ) auto itr_ ## ARRAY = ARRAY .begin() , end_ ## ARRAY = ARRAY .end() #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.begin() , END_FOR_OUTPUT_ITR = A.end(); bool VARIABLE_FOR_OUTPUT_ITR = ITERATOR_FOR_COUT_ITR != END_FOR_COUT_ITR; while( 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 QUIT goto END_MAIN #define START_MAIN REPEAT( T ){ { if constexpr( bound_T > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_T , ":" ); } #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 FINISH_MAIN QUIT; } END_MAIN: CERR( "" ); } // 入出力用関数 template inline basic_istream& VariadicCin( basic_istream& is ) { return is; } template inline basic_istream& VariadicCin( basic_istream& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator ) { return is; } template inline basic_istream& VariadicGetline( basic_istream& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg& arg ) { return os << arg; } template inline basic_ostream& VariadicCout( basic_ostream& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); } // 算術用関数 template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); } inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); } inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); } inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); } #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ static_assert( ! is_same::value && ! is_same::value ); \ TYPE_OF( ARGUMENT ) ANSWER{ 1 }; \ { \ TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT ); \ TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ while( 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 = ( ( MODULO ) + ( ( ARGUMENT ) % ( MODULO ) ) ) % ( MODULO ); \ TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT ); \ while( 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 , CONSTEXPR_LENGTH , MODULO ) \ static ll ANSWER[CONSTEXPR_LENGTH]; \ static ll ANSWER_INV[CONSTEXPR_LENGTH]; \ static ll INVERSE[CONSTEXPR_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 ); \ } \ } \ // 二分探索テンプレート // EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \ static_assert( ! is_same::value && ! is_same::value ); \ ll ANSWER = MINIMUM; \ if( MINIMUM <= MAXIMUM ){ \ ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM; \ ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM; \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH; \ while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \ CERR( "二分探索中： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << "-" << TARGET << "=" << VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L; \ } \ ANSWER = UPDATE_ANSWER; \ } \ CERR( "二分探索終了： " << VARIABLE_FOR_BINARY_SEARCH_L << "<=" << ANSWER << "<=" << VARIABLE_FOR_BINARY_SEARCH_U << ":" << EXPRESSION << ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) << TARGET ); \ if( EXPRESSION DESIRED_INEQUALITY TARGET ){ \ CERR( "二分探索成功" ); \ } else { \ CERR( "二分探索失敗" ); \ ANSWER = MAXIMUM + 1; \ } \ } else { \ CERR( "二分探索失敗： " << MINIMUM << ">" << MAXIMUM ); \ ANSWER = MAXIMUM + 1; \ } \ // 単調増加の時にEXPRESSION >= TARGETの最小解を格納。 #define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調増加の時にEXPRESSION <= TARGETの最大解を格納。 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION >= TARGETの最大解を格納。 #define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \ // 単調減少の時にEXPRESSION <= TARGETの最小解を格納。 #define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 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。 template inline typename set::iterator MaximumLeq( set& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // 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。 template inline typename set::iterator MaximumLt( set& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; } // 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。 template inline typename set::iterator MinimumGeq( set& S , const T& t ) { return 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。 template inline typename set::iterator MinimumGt( set& S , const T& t ) { return S.upper_bound( t ); } // データ構造用関数 template inline T add( const T& t0 , const T& t1 ) { return t0 + t1; } template inline T xor_add( const T& t0 , const T& t1 ){ return t0 ^ t1; } template inline T multiply( const T& t0 , const T& t1 ) { return t0 * t1; } template inline const T& zero() { static const T z = 0; return z; } template inline const T& one() { static const T o = 1; return o; }\ template inline T add_inv( const T& t ) { return -t; } template inline T id( const T& v ) { return v; } // グリッド問題用関数 int H , W , H_minus , W_minus , HW; inline pair EnumHW( const int& v ) { return { v / W , v % W }; } inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; } const string direction[4] = {"U","R","D","L"}; // (i,j)->(k,h)の方向番号を取得 inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return ik?0:jh?3:(assert(false),-1);} // v->wの方向番号を取得 inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);} // 方向番号の反転U<->D、R<->L inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;} inline void SetEdgeOnGrid( const string& Si , const int& i , list ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+10){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1 > ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+10){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1 list E( const int& i ); // 本体をmain()の後に定義 template vector > e; // デバッグ用関数 #ifdef DEBUG inline void 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。" ); } void AutoCheck( int& auto_checked ); void Jikken(); void Debug(); #endif // 圧縮用 #define TE template #define TY typename #define US using #define ST static #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 MO move #define TH this #define CRI CO int& #define CRUI CO uint& #define CRL CO ll& /* C-x 3 C-x o C-x C-fによるファイル操作用 BIT: c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/compress.txt BFS: c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt DFS on Tree: c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepththFirstSearch/Tree/compress.txt Divisor: c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt Mod: c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/compress.txt Polynomial c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt */ // VVV ライブラリは以下に挿入する。 TE CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();CE CO INT& OP[](CRI n) CO;CE CO INT& Get(CRI n) CO;CE CO bool& IsComposite(CRI i) CO;CE CRI LE() CO NE;}; TE CE PrimeEnumeration::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){INT j = i;WH((j += i)< val_limit){m_is_composite[j] = true;}m_val[m_LE++] = i;if(m_LE >= LE_max){break;}}}}TE CE CO INT& PrimeEnumeration::OP[](CRI n)CO{assert(n < m_LE);RE m_val[n];}TE CE CO INT& PrimeEnumeration::Get(CRI n)CO{RE OP[](n);}TE CE CO bool& PrimeEnumeration::IsComposite(CRI i)CO{assert(i < val_limit);RE m_is_composite[i];}TE CE CRI PrimeEnumeration::LE()CO NE{RE m_LE;} TE VO SetPrimeFactorisation(CO PrimeEnumeration& prime,CO INT& n,VE& P,VE& EX){INT n_copy = n;int i = 0;WH(i < prime.m_LE){CO INT& p = prime[i];if(p * p > n_copy){break;}if(n_copy % p == 0){P.push_back(p);EX.push_back(1);INT& EX_back = EX.back();n_copy /= p;WH(n_copy % p == 0){EX_back++;n_copy /= p;}}i++;}if(n_copy != 1){P.push_back(n_copy);EX.push_back(1);}RE;} #define SFINAE_FOR_MA(DEFAULT) TY Arg,enable_if_t::value>* DEFAULT TE CL MA{PU:T m_M[Y][X];IN MA()NE;IN MA(CO T& t)NE;IN MA(CRI t)NE;TE IN MA(Arg0&& t0,Arg1&& t1,Args&&... args)NE;IN MA(CO MA& mat)NE;IN MA(MA&& mat)NE;TE IN MA(CO T (&mat)[Y][X])NE;TE IN MA(T (&&mat)[Y][X])NE;IN MA& OP=(CO MA& mat)NE;IN MA& OP=(MA&& mat)NE;IN MA& OP=(CO T (&mat)[Y][X])NE;IN MA& OP=(T (&&mat)[Y][X])NE;IN MA& OP+=(CO MA& mat)NE;IN MA& OP-=(CO MA& mat)NE;IN MA& OP*=(CO T& scalar)NE;IN MA& OP*=(CO MA& mat)NE;IN MA& OP/=(CO T& scalar);IN MA& OP%=(CO T& scalar);IN bool OP==(CO MA& mat) CO NE;TE IN MA OP*(CO MA& mat) CO NE;IN MA Transpose() CO NE;IN T Trace() CO NE;IN CO T (&GetTable() CO NE)[Y][X];IN T (&RefTable()NE)[Y][X];ST IN CO MA& Zero()NE;ST IN CO MA& Unit()NE;ST IN MA Scalar(CO T& t)NE;ST IN VO SetArray(T (&M)[Y][X],T (&&array)[Y * X])NE;}; TE IN MA::MA()NE:m_M(){}TE IN MA::MA(CO T& t)NE:m_M(){OP=(Scalar(t));}TE IN MA::MA(CRI t)NE:MA(T(t)){}TE TE IN MA::MA(Arg0&& t0,Arg1&& t1,Args&&... args)NE:m_M(){T array[Y * X] ={T(forward(t0)),T(forward(t1)),T(forward(args))...};SetArray(m_M,MO(array));}TE IN MA::MA(CO MA& mat)NE:m_M(){OP=(mat.m_M);}TE IN MA::MA(MA&& mat)NE:m_M(){swap(m_M,mat.m_M);}TE TE IN MA::MA(CO T (&mat)[Y][X])NE:m_M(){OP=(mat);}TE TE IN MA::MA(T (&&mat)[Y][X])NE:m_M(){swap(m_M,mat);}TE IN MA& MA::OP=(CO MA& mat)NE{RE OP=(mat.m_M);}TE IN MA& MA::OP=(MA&& mat)NE{RE OP=(MO(mat.m_M));}TE IN MA& MA::OP=(CO T (&mat)[Y][X])NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];CO T (&mat_y)[X] = mat[y];for(uint x = 0;x < X;x++){m_M_y[x] = mat_y[x];}}RE *TH;}TE IN MA& MA::OP=(T (&&mat)[Y][X])NE{swap(m_M,mat);RE *TH;}TE IN MA& MA::OP+=(CO MA& mat)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];T (&mat_y)[X] = mat.m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] += mat_y[x];}}RE *TH;}TE IN MA& MA::OP-=(CO MA& mat)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];T (&mat_y)[X] = mat.m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] -= mat_y[x];}}RE *TH;}TE IN MA& MA::OP*=(CO T& scalar)NE{for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] *= scalar;}}RE *TH;}TE IN MA& MA::OP*=(CO MA& mat)NE{RE OP=(MO(*TH * mat));}TE IN MA& MA::OP/=(CO T& scalar){RE OP*=(T(1) / scalar);}TE IN MA& MA::OP%=(CO T& scalar){for(uint y = 0;y < Y;y++){T (&m_M_y)[X] = m_M[y];for(uint x = 0;x < X;x++){m_M_y[x] %= scalar;}}RE *TH;}TE TE IN MA MA::OP*(CO MA& mat) CO NE{MA prod{};for(uint y = 0;y < Y;y++){CO T (&m_M_y)[X] = m_M[y];T (&prod_y)[Z] = prod.m_M[y];for(uint x = 0;x < X;x++){CO T &m_M_yx = m_M_y[x];CO T (&mat_x)[Z] = mat.m_M[x];for(uint z = 0;z < Z;z++){prod_y[z] += m_M_yx * mat_x[z];}}}RE prod;}TE IN bool MA::OP==(CO MA& mat) CO NE{for(uint y = 0;y < Y;y++){CO T (&m_M_y)[X] = m_M[y];CO T (&mat_y)[X] = mat[y];for(uint x = 0;x < X;x++){if(m_M_y[x] != mat_y[x]){RE false;}}}RE true;}TE IN MA MA::Transpose() CO NE{MA M_t{};for(uint x = 0;x < X;x++){CO T (&M_t_x)[Y] = M_t.m_M[x];for(uint y = 0;y < Y;y++){M_t_x[y] = m_M[y][x];}}RE M_t;}TE IN T MA::Trace() CO NE{CE CO uint minXY = Y < X?Y:X;T AN{};for(uint y = 0;y < minXY;y++){AN += m_M[y][y];}RE AN;}TE IN T (&MA::RefTable()NE)[Y][X]{RE m_M;}TE IN CO T (&MA::GetTable() CO NE)[Y][X]{RE m_M;}TE IN CO MA& MA::Zero()NE{ST CO MA zero{};RE zero;}TE IN CO MA& MA::Unit()NE{ST CO MA unit{1};RE unit;}TE IN MA MA::Scalar(CO T& t)NE{CE CO uint minXY = Y < X?Y:X;MA M{};for(uint y = 0;y < minXY;y++){M.m_M[y][y] = t;}RE M;}TE IN VO MA::SetArray(T (&M)[Y][X],T (&&array)[Y * X])NE{uint i = 0;for(uint y = 0;y < Y;y++){T (&M_y)[X] = M[y];for(uint x = 0;x < X;x++){M_y[x] = MO(array[i + x]);}i += X;}}TE IN MA OP!=(CO MA& mat1,CO MA& mat2)NE{RE !(mat1 == mat2);}TE IN MA OP+(CO MA& mat1,CO MA& mat2)NE{RE MO(MA(mat1) += mat2);}TE IN MA OP-(CO MA& mat1,CO MA& mat2)NE{RE MO(MA(mat1) -= mat2);}TE IN MA OP*(CO MA& mat,CO T& scalar)NE{RE MO(MA(mat) *= scalar);}TE IN MA OP*(CO T& scalar,CO MA& mat)NE{RE MO(MA(mat) *= scalar);}TE IN MA OP/(CO MA& mat,CO T& scalar){RE MO(MA(mat) /= scalar);}TE IN MA OP%(CO MA& mat,CO T& scalar){RE MO(MA(mat) %= scalar);} CEXPR(uint,P,998244353);TE CE INT& RS(INT& n)NE{RE n < 0?((((++n)*= -1)%= M)*= -1)+= M - 1:n %= M;}TE CE uint& RS(uint& n)NE{RE n %= M;}TE CE ull& RS(ull& n)NE{RE n %= M;}TE CE INT& RSP(INT& n)NE{CE CO uint trunc = (1 << 23)- 1;INT n_u = n >> 23;n &= trunc;INT n_uq = (n_u / 7)/ 17;n_u -= n_uq * 119;n += n_u << 23;RE n < n_uq?n += P - n_uq:n -= n_uq;}TE <> CE ull& RS(ull& n)NE{CE CO ull Pull = P;CE CO ull Pull2 = (Pull - 1)* (Pull - 1);RE RSP(n > Pull2?n -= Pull2:n);}TE CE INT RS(INT&& n)NE{RE MO(RS(n));}TE CE INT RS(CO INT& n)NE{RE RS(INT(n));} #define SFINAE_FOR_MOD(DEFAULT)TY T,enable_if_t >::value>* DEFAULT #define DC_OF_CM_FOR_MOD(FUNC)CE bool OP FUNC(CO Mod& n)CO NE #define DC_OF_AR_FOR_MOD(FUNC)CE Mod OP FUNC(CO Mod& n)CO NE;TE CE Mod OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MOD(FUNC)TE CE bool Mod::OP FUNC(CO Mod& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MOD(FUNC,FORMULA)TE CE Mod Mod::OP FUNC(CO Mod& n)CO NE{RE MO(Mod(*TH)FUNC ## = n);}TE TE CE Mod Mod::OP FUNC(T&& n)CO NE{RE FORMULA;}TE CE Mod OP FUNC(T&& n0,CO Mod& n1)NE{RE MO(Mod(forward(n0))FUNC ## = n1);} TE CL Mod{PU:uint m_n;CE Mod()NE;CE Mod(CO Mod& n)NE;CE Mod(Mod& n)NE;CE Mod(Mod&& n)NE;TE CE Mod(CO T& n)NE;TE CE Mod(T& n)NE;TE CE Mod(T&& n)NE;CE Mod& OP=(CO Mod& n)NE;CE Mod& OP=(Mod&& n)NE;CE Mod& OP+=(CO Mod& n)NE;CE Mod& OP-=(CO Mod& n)NE;CE Mod& OP*=(CO Mod& n)NE;IN Mod& OP/=(CO Mod& n);CE Mod& OP<<=(int n)NE;CE Mod& OP>>=(int n)NE;CE Mod& OP++()NE;CE Mod OP++(int)NE;CE Mod& OP--()NE;CE Mod OP--(int)NE;DC_OF_CM_FOR_MOD(==);DC_OF_CM_FOR_MOD(!=);DC_OF_CM_FOR_MOD(<);DC_OF_CM_FOR_MOD(<=);DC_OF_CM_FOR_MOD(>);DC_OF_CM_FOR_MOD(>=);DC_OF_AR_FOR_MOD(+);DC_OF_AR_FOR_MOD(-);DC_OF_AR_FOR_MOD(*);DC_OF_AR_FOR_MOD(/);CE Mod OP<<(int n)CO NE;CE Mod OP>>(int n)CO NE;CE Mod OP-()CO NE;CE Mod& SignInvert()NE;CE Mod& Double()NE;CE Mod& Halve()NE;IN Mod& Invert();TE CE Mod& PositivePW(T&& EX)NE;TE CE Mod& NonNegativePW(T&& EX)NE;TE CE Mod& PW(T&& EX);CE VO swap(Mod& n)NE;CE CRUI RP()CO NE;ST CE Mod DeRP(CRUI n)NE;ST CE uint& Normalise(uint& n)NE;ST IN CO Mod& Inverse(CRUI n)NE;ST IN CO Mod& Factorial(CRUI n)NE;ST IN CO Mod& FactorialInverse(CRUI n)NE;ST IN Mod Combination(CRUI n,CRUI i)NE;ST IN CO Mod& zero()NE;ST IN CO Mod& one()NE;TE CE Mod& Ref(T&& n)NE;}; #define SFINAE_FOR_MN(DEFAULT)TY T,enable_if_t,decay_t >::value>* DEFAULT #define DC_OF_AR_FOR_MN(FUNC)IN MN OP FUNC(CO MN& n)CO NE;TE IN MN OP FUNC(T&& n)CO NE; #define DF_OF_CM_FOR_MN(FUNC)TE IN bool MN::OP FUNC(CO MN& n)CO NE{RE m_n FUNC n.m_n;} #define DF_OF_AR_FOR_MN(FUNC,FORMULA)TE IN MN MN::OP FUNC(CO MN& n)CO NE{RE MO(MN(*TH)FUNC ## = n);}TE TE IN MN MN::OP FUNC(T&& n)CO NE{RE FORMULA;}TE IN MN OP FUNC(T&& n0,CO MN& n1)NE{RE MO(MN(forward(n0))FUNC ## = n1);} TE CL MN:PU Mod{PU:CE MN()NE;CE MN(CO MN& n)NE;CE MN(MN& n)NE;CE MN(MN&& n)NE;TE CE MN(CO T& n)NE;TE CE MN(T&& n)NE;CE MN& OP=(CO MN& n)NE;CE MN& OP=(MN&& n)NE;CE MN& OP+=(CO MN& n)NE;CE MN& OP-=(CO MN& n)NE;CE MN& OP*=(CO MN& n)NE;IN MN& OP/=(CO MN& n);CE MN& OP<<=(int n)NE;CE MN& OP>>=(int n)NE;CE MN& OP++()NE;CE MN OP++(int)NE;CE MN& OP--()NE;CE MN OP--(int)NE;DC_OF_AR_FOR_MN(+);DC_OF_AR_FOR_MN(-);DC_OF_AR_FOR_MN(*);DC_OF_AR_FOR_MN(/);CE MN OP<<(int n)CO NE;CE MN OP>>(int n)CO NE;CE MN OP-()CO NE;CE MN& SignInvert()NE;CE MN& Double()NE;CE MN& Halve()NE;CE MN& Invert();TE CE MN& PositivePW(T&& EX)NE;TE CE MN& NonNegativePW(T&& EX)NE;TE CE MN& PW(T&& EX);CE uint RP()CO NE;CE Mod Reduce()CO NE;ST CE MN DeRP(CRUI n)NE;ST IN CO MN& Formise(CRUI n)NE;ST IN CO MN& Inverse(CRUI n)NE;ST IN CO MN& Factorial(CRUI n)NE;ST IN CO MN& FactorialInverse(CRUI n)NE;ST IN MN Combination(CRUI n,CRUI i)NE;ST IN CO MN& zero()NE;ST IN CO MN& one()NE;ST CE uint Form(CRUI n)NE;ST CE ull& Reduction(ull& n)NE;ST CE ull& ReducedMU(ull& n,CRUI m)NE;ST CE uint MU(CRUI n0,CRUI n1)NE;ST CE uint BaseSquareTruncation(uint& n)NE;TE CE MN& Ref(T&& n)NE;};TE CE MN Twice(CO MN& n)NE;TE CE MN Half(CO MN& n)NE;TE CE MN Inverse(CO MN& n);TE CE MN PW(MN n,T EX);TE CE MN<2> PW(CO MN<2>& n,CO T& p);TE CE T Square(CO T& t);TE <> CE MN<2> Square >(CO MN<2>& t);TE CE VO swap(MN& n0,MN