#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; } int main() { UNTIE; CEXPR( int , bound , 1000000000 ); int hw[2][4]; int sum[2] = {}; FOR( k , 0 , 2 ){ int ( &hw_k )[4] = hw[k]; int& sum_k = sum[k]; FOR( i , 0 , 4 ){ CIN_ASSERT( hwi , 4 , bound ); sum_k += hw_k[i] = hwi - 4; } } if( sum[0] != sum[1] ){ RETURN( 0 ); } // 次の繰り上がり計算に使う3以下のデータ6個を2進法で12桁のデータに纏めたもの（以下「桁和」）の上限値 CEXPR( int , assign_sum_lim , 1 << 12 ); // 桁和から元のデータを復元する static int assign_sum[assign_sum_lim][2][3] = {}; int t_copy; FOR( t , 0 , assign_sum_lim ){ t_copy = t; int ( &assign_sum_t )[2][3] = assign_sum[t]; FOR( k , 0 , 2 ){ int ( &assign_sum_t_k )[3] = assign_sum_t[k]; FOR( i , 0 , 3 ){ assign_sum_t_k[i] = t_copy % 4; t_copy /= 4; } } } // 次の桁を表す1以下のデータ9個を2進法で9桁のデータに纏めてたもの（以下「桁値」）の上限 CEXPR( int , assign_lim , 1 << 9 ); // 桁値を動かした時の次の桁和の重複を格納 static int multiple[assign_sum_lim] = {}; int assign[3][3] = {}; int assign_sum_curr; FOR( t , 0 , assign_lim ){ t_copy = t; FOR( i , 0 , 3 ){ int ( &assign_i )[3] = assign[i]; FOR( j , 0 , 3 ){ assign_i[j] = t_copy % 2; t_copy /= 2; } } assign_sum_curr = 0; { FOR( i , 0 , 3 ){ assign_sum_curr *= 4; int ( &assign_i )[3] = assign[i]; FOR( j , 0 , 3 ){ assign_sum_curr += assign_i[j]; } } } { FOR( j , 0 , 3 ){ assign_sum_curr *= 4; FOR( i , 0 , 3 ){ assign_sum_curr += assign[i][j]; } } } multiple[assign_sum_curr]++; } // multipleが正の桁和の抽出 int valid_sum_num = 0; static int valid_sum[assign_lim]; FOR( t , 0 , assign_sum_lim ){ if( multiple[t] > 0 ){ valid_sum[valid_sum_num] = t; valid_sum_num++; } } // hwの成分を2進法表記した時の特定の桁のデータ int hw_r[2][4]; // 繰り上がりの値である(4-1)以下のデータ8個を2進法で16桁のデータ（以下「状態」）に纏めたものの上限値 CEXPR( int , state_lim , 1 << 16 ); // 状態から元のデータを復元する static int state[state_lim][2][4] = {}; FOR( s , 0 , state_lim ){ int ( &state_s )[2][4] = state[s]; t_copy = s; FOR( k , 0 , 2 ){ int ( &state_s_k )[4] = state_s[k]; FOR( i , 0 , 4 ){ state_s_k[i] = t_copy % 4; t_copy /= 4; } } } // 次の状態を格納 int hw_next[2][4]; // 各状態ごとの、特定の桁までの数え上げ vector count[2] = {}; vector count_init( state_lim ); { vector& count0 = count[0]; count0 = count_init; count0[0] = 1; } int i_prev = 0; int i_curr = 1; int valid_sum_t , rest_assign_sum , diff , sa_sum , s_next; CEXPR( ll , P , 998244353 ); bool computing = true; while( computing ){ vector& count_prev = count[i_prev]; vector& count_curr = count[i_curr]; count_curr = count_init; FOR( k , 0 , 2 ){ int ( &hw_k )[4] = hw[k]; int ( &hw_r_k )[4] = hw_r[k]; FOR( i , 0 , 4 ){ hw_r_k[i] = hw_k[i] % 2; } } FOR( s , 0 , state_lim ){ ll& count_prev_s = count_prev[s]; if( count_prev_s != 0 ){ int ( &state_s )[2][4] = state[s]; FOR( t , 0 , valid_sum_num ){ valid_sum_t = valid_sum[t]; int ( &assign_sum_t )[2][3] = assign_sum[valid_sum_t]; // 桁和から次の状態を計算する（つまり残りの16-9個の変数を決定し和を8個取る） { int k = 0; int ( &hw_r_k )[4] = hw_r[k]; int ( &hw_next_k )[4] = hw_next[k]; int ( &assign_sum_t_k )[3] = assign_sum_t[k]; int ( &state_s_k )[4] = state_s[k]; rest_assign_sum = 0; FOR( i , 0 , 3 ){ int& hw_next_k_i = hw_next_k[i]; sa_sum = state_s_k[i] + assign_sum_t_k[i]; rest_assign_sum += diff = ( hw_r_k[i] + sa_sum ) % 2; hw_next_k_i = ( sa_sum + diff ) / 2; } } { int k = 1; int ( &hw_r_k )[4] = hw_r[k]; int ( &hw_next_k )[4] = hw_next[k]; int ( &assign_sum_t_k )[3] = assign_sum_t[k]; int ( &state_s_k )[4] = state_s[k]; { int i = 3; int& hw_next_k_i = hw_next_k[i]; sa_sum = state_s_k[i] + rest_assign_sum; diff = ( hw_r_k[i] + sa_sum ) % 2; hw_next_k_i = ( sa_sum + diff ) / 2; } rest_assign_sum = 0; FOR( i , 0 , 3 ){ int& hw_next_k_i = hw_next_k[i]; sa_sum = state_s_k[i] + assign_sum_t_k[i]; rest_assign_sum += diff = ( hw_r_k[i] + sa_sum ) % 2; hw_next_k_i = ( sa_sum + diff ) / 2; } } { int k = 0; int ( &hw_r_k )[4] = hw_r[k]; int ( &hw_next_k )[4] = hw_next[k]; int ( &state_s_k )[4] = state_s[k]; { int i = 3; int& hw_next_k_i = hw_next_k[i]; sa_sum = state_s_k[i] + rest_assign_sum; diff = ( hw_r_k[i] + sa_sum ) % 2; hw_next_k_i = ( sa_sum + diff ) / 2; } } s_next = 0; FOREQINV( k , 1 , 0 ){ int ( &hw_next_k )[4] = hw_next[k]; FOREQINV( i , 3 , 0 ){ s_next = s_next * 4 + hw_next_k[i]; } } count_curr[s_next] += count_prev_s * multiple[valid_sum_t]; } } } FOR( s , 0 , state_lim ){ count_curr[s] %= P; } computing = false; FOR( k , 0 , 2 ){ int ( &hw_k )[4] = hw[k]; FOR( i , 0 , 4 ){ if( ( hw_k[i] /= 2 ) != 0 ){ computing = true; } } } swap( i_prev , i_curr ); } // 最終的には繰り上がりがなくなっていないと一致しないので、状態は0のみ RETURN( count[i_prev][0] ); }