#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( MESSAGE ) cerr << MESSAGE << endl; #define COUT( ANSWER ) cout << "出力: " << ANSWER << endl #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " << ( MIN ) << ( ( MIN ) <= A ? "<=" : ">" ) << A << ( A <= ( MAX ) ? "<=" : ">" ) << ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) ) #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( MESSAGE ) #define COUT( ANSWER ) cout << ANSWER << "\n" #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) ) #endif #include using namespace std; using ll = long long; #define TYPE_OF( VAR ) decay_t #define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE #define CIN( LL , A ) LL A; cin >> A #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX ) #define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_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 REPEAT( HOW_MANY_TIMES ) FOR( VARIABLE_FOR_REPEAT_ ## HOW_MANY_TIMES , 0 , HOW_MANY_TIMES ) #define QUIT return 0 #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。" ); } #endif template inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); } #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; \ } \ } \ // 入力フォーマットチェック用 // 1行中の変数の個数をSEPARATOR区切りで確認 #define GETLINE_COUNT( S , VARIABLE_NUMBER , SEPARATOR ) GETLINE( S ); int VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S = 0; int VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S = S.size(); { int size = S.size(); int count = 0; for( int i = 0 ; i < size ; i++ ){ if( S.substr( i , 1 ) == SEPARATOR ){ count++; } } assert( count + 1 == VARIABLE_NUMBER ); } // 余計な入力の有無を確認 #ifdef DEBUG #define CHECK_REDUNDANT_INPUT #else #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; cin >> VARIABLE_FOR_CHECK_REDUNDANT_INPUT; assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin ) // #define CHECK_REDUNDANT_INPUT string VARIABLE_FOR_CHECK_REDUNDANT_INPUT = ""; getline( cin , VARIABLE_FOR_CHECK_REDUNDANT_INPUT ); assert( VARIABLE_FOR_CHECK_REDUNDANT_INPUT == "" ); assert( ! cin ) #endif // |N| <= BOUNDを満たすNをSから構築 #define STOI( S , N , BOUND ) TYPE_OF( BOUND ) N = 0; { bool VARIABLE_FOR_POSITIVITY_FOR_GETLINE = true; assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); if( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) == "-" ){ VARIABLE_FOR_POSITIVITY_FOR_GETLINE = false; VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); } assert( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) != " " ); string VARIABLE_FOR_LETTER_FOR_GETLINE{}; int VARIABLE_FOR_DIGIT_FOR_GETLINE{}; while( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ? ( VARIABLE_FOR_LETTER_FOR_GETLINE = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) ) != " " : false ){ VARIABLE_FOR_DIGIT_FOR_GETLINE = stoi( VARIABLE_FOR_LETTER_FOR_GETLINE ); assert( N < BOUND / 10 ? true : N == BOUND / 10 && VARIABLE_FOR_DIGIT_FOR_GETLINE <= BOUND % 10 ); N = N * 10 + VARIABLE_FOR_DIGIT_FOR_GETLINE; VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } if( ! VARIABLE_FOR_POSITIVITY_FOR_GETLINE ){ N *= -1; } if( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } } // SをSEPARATORで区切りTを構築 #define SEPARATE( S , T , SEPARATOR ) string T{}; { assert( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ); int VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev = VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S; assert( S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) != SEPARATOR ); string VARIABLE_FOR_LETTER_FOR_GETLINE{}; while( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ? ( VARIABLE_FOR_LETTER_FOR_GETLINE = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S , 1 ) ) != SEPARATOR : false ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } T = S.substr( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev , VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S - VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S_prev ); if( VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S < VARIABLE_FOR_SIZE_FOR_GETLINE_FOR_ ## S ){ VARIABLE_FOR_INDEX_FOR_GETLINE_FOR_ ## S ++; } } int main() { UNTIE; DEXPR( int , bound_T , 100000 , 100 ); CIN_ASSERT( T , 1 , bound_T ); CEXPR( int , bound_N_sum , 300000 ); CEXPR( int , bound_xy , 20000 ); CEXPR( ll , P , 998244353 ); int N_sum = 0; REPEAT( T ){ // |Z/z_j - zj/Z|^2 // = |(Z^2 - zj^2)/(zj Z)|^2 // = |Z - zj|^2 |Z + zj|^2/(|zj|^2 |Z|^2) // = ((X - xj)^2 + (Y - yj)^2)((X + xj)^2 + (Y + yj)^2) // /((xj^2 + yj^2)(X^2 + Y^2)) // = (X^2 - 2xj X + Y^2 - 2yj Y + xj^2 + yj^2) // (X^2 + 2xj X + Y^2 + 2yj Y + xj^2 + yj^2) // /((xj^2 + yj^2)(X^2 + Y^2)) // = ((X^2 + Y^2 + xj^2 + yj^2)^2 - (2xj X + 2yj Y)^2) // /((xj^2 + yj^2)(X^2 + Y^2)) // = ( // (X^2 + Y^2)^2 + 2(xj^2 + yj^2)(X^2 + Y^2) + (xj^2 + yj^2)^2 // - 4xj^2 X^2 - 8xj yj X Y + 4yj^2 Y^2 // ) // /((xj^2 + yj^2)(X^2 + Y^2)) // = (1/(xj^2 + yj^2)) * (X^2 + Y^2) // +2 // +(xj^2 + yj^2) * 1/(X^2 + Y^2) // -(4xj^2/(xj^2 + yj^2)) * X^2/(X^2 + Y^2) // -(8xjyj/(xj^2 + yj^2)) * XY/(X^2 + Y^2) // -(4yj^2/(xj^2 + yj^2)) * Y^2/(X^2 + Y^2) ll sum0 = 0; ll sum1 = 0; ll sum2 = 0; ll sum3 = 0; ll sum4 = 0; ll sum5 = 0; ll answer = 0; CIN_ASSERT( N , 2 , bound_N_sum ); N_sum += N; FOR( i , 0 , N ){ CIN_ASSERT( x , -bound_xy , bound_xy ); CIN_ASSERT( y , -bound_xy , bound_xy ); int x2 = x * x; int xy = x * y; int y2 = y * y; int x2y2 = x2 + y2; assert( x2y2 != 0 ); POWER_MOD( x2y2inv , x2y2 , P - 2 , P ); answer += sum0 * x2y2 % P + sum1 + sum2 * x2y2inv % P - sum3 * x2 % P * x2y2inv % P - sum4 * xy % P * x2y2inv % P - sum5 * y2 % P * x2y2inv % P; ( sum0 += x2y2inv ) < P ? sum0 : sum0 -= P; ( sum1 += 2 ); ( sum2 += x2y2 ) < P ? sum2 : sum2 -= P; ( sum3 += 4 * ( x2 * x2y2inv ) ) %= P; ( sum4 += 8 * ( xy * x2y2inv ) ) %= P; ( sum5 += 4 * ( y2 * x2y2inv ) ) %= P; } COUT( Residue( answer , P ) ); } CHECK_REDUNDANT_INPUT; assert( N_sum <= bound_N_sum ); cerr << "入力の強さ確認: " << T << "," << N_sum << "\n"; QUIT; }