// #define _GLIBCXX_DEBUG #pragma GCC optimize ( "O3" ) #pragma GCC target ( "avx" ) #include using namespace std; using uint = unsigned int; using ll = long long; #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 GETLINE( A ) string A; getline( cin , A ) #define GETLINE_SEPARATE( A , SEPARATOR ) string A; getline( cin , A , SEPARATOR ) #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 FOR_ITR( ARRAY , ITR , END ) for( auto ITR = ARRAY .begin() , END = ARRAY .end() ; ITR != END ; ITR ++ ) #define REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #define COUT( ANSWER ) cout << ( ANSWER ) << "\n"; #define RETURN( ANSWER ) COUT( ANSWER ); QUIT #define DOUBLE( PRECISION , ANSWER ) cout << fixed << setprecision( PRECISION ) << ( ANSWER ) << "\n"; QUIT #define POWER( ANSWER , ARGUMENT , EXPONENT ) \ 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 ) \ TYPE_OF( ARGUMENT ) ANSWER{ 1 }; \ { \ TYPE_OF( ARGUMENT ) 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 , MAX_I , LENGTH , MODULO ) \ ll ANSWER[LENGTH]; \ ll ANSWER_INV[LENGTH]; \ { \ ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \ ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL; \ FOREQ( i , 1 , MAX_I ){ \ ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= MODULO; \ } \ POWER_MOD( FACTORIAL_MAX_INV , ANSWER[MAX_I] , MODULO - 2 , MODULO ); \ ANSWER_INV[MAX_I] = FACTORIAL_MAX_INV; \ FOREQINV( i , MAX_I - 1 , 0 ){ \ ANSWER_INV[i] = ( FACTORIAL_MAX_INV *= i + 1 ) %= MODULO; \ } \ } \ \ // 通常の二分探索 #define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ ll ANSWER = MAXIMUM; \ { \ ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM; \ ll VARIABLE_FOR_BINARY_SEARCH_U = ANSWER; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ } else { \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ while( VARIABLE_FOR_BINARY_SEARCH_L != ANSWER ){ \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ break; \ } else { \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){ \ VARIABLE_FOR_BINARY_SEARCH_L = ANSWER; \ } else { \ VARIABLE_FOR_BINARY_SEARCH_U = ANSWER; \ } \ ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \ } \ } \ } \ \ // 二進法の二分探索 #define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET ) \ ll ANSWER = MINIMUM; \ { \ ll VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 = 1; \ ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( MAXIMUM ) - ANSWER; \ while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 <= VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ){ \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 *= 2; \ } \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 /= 2; \ ll VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER; \ while( VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 != 0 ){ \ ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 + VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2; \ VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( TARGET ) - ( EXPRESSION ); \ if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH == 0 ){ \ VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER; \ break; \ } else if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH > 0 ){ \ VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2 = ANSWER; \ } \ VARIABLE_FOR_POWER_FOR_BINARY_SEARCH_2 /= 2; \ } \ ANSWER = VARIABLE_FOR_ANSWER_FOR_BINARY_SEARCH_2; \ } \ \ template inline T Absolute( const T& a ){ return a > 0 ? a : - a; } template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - ( - a - 1 ) % p - 1; } class DirectedGraph { public: int m_N; vector > m_e; inline DirectedGraph( int N ) : m_N( N ) , m_e( m_N ) {} inline void AddEdge( int i , int j ) { m_e[i].push_back( j ); } }; int main() { UNTIE; CIN( int , N1 ); CIN( int , N2 ); CIN( int , N3 ); int N12 = N1 + N2; int N123 = N12 + N3; CEXPR( int , bound_N123 , 300000 ); assert( 0 <= N1 && 0 <= N2 && 0 <= N2 && N123 <= bound_N123 ); CEXPR( int , bound_t , bound_N123 + 2 ); int s = N123 + 1; int t = s + 1; int startpoint[4] = { 1 , N1 + 1 , N12 + 1 , s }; int endpoint[4] = { N1 , N12 , N123 , t }; int sp_curr , ep_curr; DirectedGraph G{ t + 1 }; DirectedGraph G_inv{ t + 1 }; FOR( line , 0 , 3 ){ sp_curr = startpoint[line]; ep_curr = endpoint[line]; G.AddEdge( s , sp_curr ); G_inv.AddEdge( sp_curr , s ); FOR( i , sp_curr , ep_curr ){ G.AddEdge( i , i + 1 ); G_inv.AddEdge( i + 1 , i ); } G.AddEdge( ep_curr , t ); G_inv.AddEdge( t , ep_curr ); } CIN_ASSERT( M , 0 , bound_N123 ); FOR( i , 0 , M ){ CIN_ASSERT( Ui , 1 , t ); CIN_ASSERT( Vi , 1 , t ); G.AddEdge( Ui , Vi ); G.AddEdge( Vi , Ui ); G_inv.AddEdge( Ui , Vi ); G_inv.AddEdge( Vi , Ui ); } static bool used[bound_t + 1] = {}; used[0] = true; int count = 0; vector path{}; vector > branch{}; vector* p_branch_end; DirectedGraph* p_G = &G; int u , v; int enumv[bound_t]; while( count < t ){ u = 1; while( used[u] ){ u++; } used[u] = true; path.push_back( u ); branch.push_back( p_G->m_e[u] ); while( ! branch.empty() ){ u = path.back(); p_branch_end = &( branch.back() ); while( ! p_branch_end->empty() ? used[v = p_branch_end->back()] : false ){ p_branch_end->pop_back(); } if( p_branch_end->empty() ){ enumv[count] = u; count++; path.pop_back(); branch.pop_back(); } else { used[v] = true; p_branch_end->pop_back(); path.push_back( v ); branch.push_back( p_G->m_e[v] ); } } } u = 0; while( ++u <= t ){ used[u] = false; } count = 0; static int scc[bound_t]; int scc_count = 0; p_G = &G_inv; int u_start = t - 1; while( count < t ){ FOREQINV( i , u_start , 0 ){ u = enumv[i]; if( ! used[u] ){ u_start = i - 1; break; } } used[u] = true; path.push_back( u ); branch.push_back( p_G->m_e[u] ); while( ! branch.empty() ){ u = path.back(); p_branch_end = &( branch.back() ); while( ! p_branch_end->empty() ? used[v = p_branch_end->back()] : false ){ p_branch_end->pop_back(); } if( p_branch_end->empty() ){ scc[u] = scc_count; count++; path.pop_back(); branch.pop_back(); } else { used[v] = true; p_branch_end->pop_back(); path.push_back( v ); branch.push_back( p_G->m_e[v] ); } } scc_count++; } DirectedGraph Gscc{ scc_count }; DirectedGraph Gscc_inv{ scc_count }; int sccu , sccv; FOR( line , 0 , 3 ){ sp_curr = startpoint[line]; ep_curr = endpoint[line]; sccu = scc[s]; sccv = scc[sp_curr]; if( sccu != sccv ){ Gscc.AddEdge( sccu , sccv ); Gscc_inv.AddEdge( sccv , sccu ); } FOR( i , sp_curr , ep_curr ){ sccu = scc[i]; sccv = scc[i+1]; if( sccu != sccv ){ Gscc.AddEdge( sccu , sccv ); Gscc_inv.AddEdge( sccv , sccu ); } } sccu = scc[ep_curr]; sccv = scc[t]; if( sccu != sccv ){ Gscc.AddEdge( sccu , sccv ); Gscc_inv.AddEdge( sccv , sccu ); } } FOR( i , 0 , scc_count ){ used[i] = false; } int red_count = 0; static int redc[bound_t]; static int redc_inv[bound_t]; FOR( i , 0 , scc_count ){ vector& eu = Gscc.m_e[i]; vector& eu_inv = Gscc_inv.m_e[i]; if( eu.size() != 1 || eu_inv.size() != 1 ){ redc[red_count] = i; redc_inv[i] = red_count; red_count++; } } DirectedGraph Gred( red_count ); static vector length[bound_t]; int eu_size , redc_inv_i , pvk; vector *pv , *pv_inv; FOR( i , 0 , scc_count ){ vector& eu = Gscc.m_e[i]; vector& eu_inv = Gscc_inv.m_e[i]; eu_size = eu.size(); if( eu_size != 1 || eu_inv.size() != 1 ){ redc_inv_i = redc_inv[i]; vector& length_i = length[redc_inv_i]; length_i = vector( eu_size , 1 ); FOR( k , 0 , eu_size ){ pvk = eu[k]; pv = &( Gscc.m_e[pvk] ); pv_inv = &( Gscc_inv.m_e[pvk] ); int& length_i_k = length_i[k]; while( pv->size() == 1 && pv_inv->size() == 1 ){ used[pvk] = true; pvk = ( *pv )[0]; pv = &( Gscc.m_e[pvk] ); pv_inv = &( Gscc_inv.m_e[pvk] ); length_i_k++; } Gred.AddEdge( redc_inv_i , redc_inv[pvk] ); } } } static ll line_comb[bound_t]; FOR( i , 0 , red_count ){ line_comb[i] = 1; } line_comb[redc_inv[scc[t]]] = 0; int euv , length_u_v; FOR( i , 0 , red_count ){ u = redc[i]; vector& length_u = length[i]; vector& eu = Gred.m_e[i]; eu_size = eu.size(); FOR( j , 0 , eu_size ){ euv = eu[j]; length_u_v = length_u[j]; FOR( k , i , euv ){ line_comb[k] *= length_u_v; } } } ll answer = 0; FOR( i , 0 , red_count ){ answer += line_comb[i]; } RETURN( answer ); }