// 入力フォーマットチェック
#ifndef INCLUDE_MODE
#define INCLUDE_MODE
// #define REACTIVE
#define USE_GETLINE
#endif
#ifdef INCLUDE_MAIN
inline void Solve()
{
CEXPR( uint , P , 998244353 );
CEXPR( ll , bound , P - 1 );
GETLINE_COUNT( ABC_str , 3 , " " );
STOI( ABC_str , A , bound );
STOI( ABC_str , B , bound );
STOI( ABC_str , C , bound );
// cos theta = sqrt((A^2+B^2)/(A^2+B^2+C^2))
// (sin theta)^2 = C^2/(A^2+B^2+C^2)
// S = pi*1^2/sin theta
// (S/pi)^2 = 1/(sin theta)^2 = 1+(A^2+B^2)/C^2
RETURN( Mod
( A * A + B * B ) / ( C * C ) + 1 );
}
REPEAT_MAIN(300000);
#else // INCLUDE_MAIN
#ifdef INCLUDE_LIBRARY
// https://github.com/p-adic/cpp
// VVV ライブラリは以下に挿入する。
template inline constexpr INT Residue( INT n ) noexcept { return move( n < 0 ? ( ( ( ( ++n ) *= -1 ) %= M ) *= -1 ) += M - 1 : n %= M ); }
template inline constexpr INT1 Residue( INT1 n , const INT2& M ) noexcept { return move( n < 0 ? ( ( ( ( ++n ) *= -1 ) %= M ) *= -1 ) += M - 1 : n %= M ); }
template inline constexpr INT& Residue998244353( INT& n ) noexcept { constexpr const 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; return n < n_uq ? n += 998244353 - n_uq : n -= n_uq; }
using INT_TYPE_FOR_MOD = uint;
template class Mod;
template
class ConstantsForMod
{
friend class Mod;
private:
ConstantsForMod() = delete;
static constexpr const INT_TYPE_FOR_MOD g_memory_bound = 1000000;
static constexpr const INT_TYPE_FOR_MOD g_memory_length = M < g_memory_bound ? M : g_memory_bound;
static constexpr INT_TYPE_FOR_MOD g_M_minus = M - 1;
static constexpr INT_TYPE_FOR_MOD g_M_minus_2 = M - 2;
static constexpr INT_TYPE_FOR_MOD g_M_minus_2_neg = 2 - M;
};
#define DECLARATION_OF_COMPARISON_FOR_MOD( FUNC ) \
inline constexpr bool operator FUNC( const Mod& n ) const noexcept \
#define DECLARATION_OF_ARITHMETIC_FOR_MOD( FUNC ) \
inline constexpr Mod operator FUNC( const Mod& n ) const noexcept; \
#define DEFINITION_OF_COMPARISON_FOR_MOD( FUNC ) \
template inline constexpr bool Mod::operator FUNC( const Mod& n ) const noexcept { return m_n FUNC n.m_n; } \
#define DEFINITION_OF_ARITHMETIC_FOR_MOD( FUNC ) \
template inline constexpr Mod Mod::operator FUNC( const Mod& n ) const noexcept { return move( Mod( *this ) FUNC ## = n ); } \
template inline constexpr Mod operator FUNC( T n0 , const Mod& n1 ) noexcept { return move( Mod( move( n0 ) ) FUNC ## = n1 ); } \
template
class Mod
{
protected:
INT_TYPE_FOR_MOD m_n;
public:
inline constexpr Mod() noexcept;
inline constexpr Mod( const Mod& n ) noexcept;
inline constexpr Mod( Mod&& n ) noexcept;
template inline constexpr Mod( T n ) noexcept;
inline constexpr Mod& operator=( Mod n ) noexcept;
inline constexpr Mod& operator+=( const Mod& n ) noexcept;
inline constexpr Mod& operator-=( const Mod& n ) noexcept;
inline constexpr Mod& operator*=( const Mod& n ) noexcept;
inline Mod& operator/=( const Mod& 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。
inline constexpr Mod& operator<<=( int n ) noexcept;
// 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。
inline constexpr Mod& operator>>=( int n ) noexcept;
inline constexpr Mod& operator++() noexcept;
inline constexpr Mod operator++( int ) noexcept;
inline constexpr Mod& operator--() noexcept;
inline constexpr Mod operator--( int ) noexcept;
DECLARATION_OF_COMPARISON_FOR_MOD( == );
DECLARATION_OF_COMPARISON_FOR_MOD( != );
DECLARATION_OF_COMPARISON_FOR_MOD( < );
DECLARATION_OF_COMPARISON_FOR_MOD( <= );
DECLARATION_OF_COMPARISON_FOR_MOD( > );
DECLARATION_OF_COMPARISON_FOR_MOD( >= );
DECLARATION_OF_ARITHMETIC_FOR_MOD( + );
DECLARATION_OF_ARITHMETIC_FOR_MOD( - );
DECLARATION_OF_ARITHMETIC_FOR_MOD( * );
DECLARATION_OF_ARITHMETIC_FOR_MOD( / );
// 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。
inline constexpr Mod operator<<( int n ) const noexcept;
// 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。
inline constexpr Mod operator>>( int n ) const noexcept;
inline constexpr Mod operator-() const noexcept;
// -1倍する。
inline constexpr Mod& SignInvert() noexcept;
// Mが素数である場合のみサポート。-1乗する。
inline Mod& Invert();
// 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 Mod& 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( Mod& n ) noexcept;
inline constexpr const INT_TYPE_FOR_MOD& Represent() const noexcept;
// 0 <= n < Mの場合のみサポート。
static inline constexpr Mod Derepresent( const INT_TYPE_FOR_MOD& n ) noexcept;
// Mが素数かつn < g_memory_lengthである場合のみサポート。
static inline const Mod& Inverse( const INT_TYPE_FOR_MOD& n ) noexcept;
// n < g_memory_lengthである場合のみサポート。
static inline const Mod& Factorial( const INT_TYPE_FOR_MOD& n ) noexcept;
// Mが素数かつn < g_memory_lengthである場合のみサポート。
static inline const Mod& FactorialInverse( const INT_TYPE_FOR_MOD& n ) noexcept;
// Mが素数かつn < g_memory_lengthである場合のみサポート。
static inline Mod Combination( const INT_TYPE_FOR_MOD& n , const INT_TYPE_FOR_MOD& i ) noexcept;
static inline const Mod& zero() noexcept;
static inline const Mod& one() noexcept;
private:
template inline constexpr Mod& PositivePower( INT exponent ) noexcept;
template inline constexpr Mod& NonNegativePower( INT exponent ) noexcept;
template inline constexpr Mod& Ref( T&& n ) noexcept;
// 0 <= n < Mの場合のみサポート。
static inline constexpr INT_TYPE_FOR_MOD& Normalise( INT_TYPE_FOR_MOD& n ) noexcept;
};
// Mが素数でありnが0でない場合にのみサポート。
template inline Mod Inverse( const Mod& n );
template inline constexpr Mod Inverse_constexpr( Mod n );
// Mが素数であるかexponent>=0である場合にのみサポート。
template inline constexpr Mod Power( Mod n , T exponent );
template inline constexpr void swap( Mod& n0 , Mod& n1 ) noexcept;
template inline string to_string( const Mod& n ) noexcept;
template inline basic_istream& operator>>( basic_istream& is , Mod& n );
template inline basic_ostream& operator<<( basic_ostream& os , const Mod& n );
template inline constexpr Mod::Mod() noexcept : m_n() {}
template inline constexpr Mod::Mod( const Mod& n ) noexcept : m_n( n.m_n ) {}
template inline constexpr Mod::Mod( Mod&& n ) noexcept : m_n( move( n.m_n ) ) {}
template template inline constexpr Mod::Mod( T n ) noexcept : m_n( Residue( move( n ) ) ) { static_assert( is_constructible_v > ); }
template inline constexpr Mod& Mod::operator=( Mod n ) noexcept { return Ref( m_n = move( n.m_n ) ); }
template inline constexpr Mod& Mod::operator+=( const Mod& n ) noexcept { return Ref( Normalise( m_n += n.m_n ) ); }
template inline constexpr Mod& Mod::operator-=( const Mod& n ) noexcept { return Ref( m_n < n.m_n ? ( m_n += M ) -= n.m_n : m_n -= n.m_n ); }
template inline constexpr Mod& Mod::operator*=( const Mod& n ) noexcept { return Ref( m_n = Residue( ull( m_n ) * n.m_n ) ); }
template <> inline constexpr Mod<998244353>& Mod<998244353>::operator*=( const Mod<998244353>& n ) noexcept { ull m_n_copy = m_n; return Ref( m_n = move( ( m_n_copy *= n.m_n ) < 998244353 ? m_n_copy : Residue998244353( m_n_copy ) ) ); }
template inline Mod& Mod::operator/=( const Mod& n ) { return operator*=( Mod( n ).Invert() ); }
template inline constexpr Mod& Mod::operator<<=( int n ) noexcept { assert( n >= 0 ); return *this *= Derepresent( 2 ).NonNegativePower( move( n ) ); }
template inline constexpr Mod& Mod::operator>>=( int n ) noexcept { assert( n >=0 ); while( n-- > 0 ){ ( ( m_n & 1 ) == 0 ? m_n : m_n += M ) >>= 1; } return *this; }
template inline constexpr Mod& Mod::operator++() noexcept { return Ref( m_n < ConstantsForMod::g_M_minus ? ++m_n : m_n = 0 ); }
template inline constexpr Mod Mod::operator++( int ) noexcept { Mod n{ *this }; operator++(); return n; }
template inline constexpr Mod& Mod::operator--() noexcept { return Ref( m_n == 0 ? m_n = ConstantsForMod::g_M_minus : --m_n ); }
template inline constexpr Mod Mod::operator--( int ) noexcept { Mod n{ *this }; operator--(); return n; }
DEFINITION_OF_COMPARISON_FOR_MOD( == );
DEFINITION_OF_COMPARISON_FOR_MOD( != );
DEFINITION_OF_COMPARISON_FOR_MOD( > );
DEFINITION_OF_COMPARISON_FOR_MOD( >= );
DEFINITION_OF_COMPARISON_FOR_MOD( < );
DEFINITION_OF_COMPARISON_FOR_MOD( <= );
DEFINITION_OF_ARITHMETIC_FOR_MOD( + );
DEFINITION_OF_ARITHMETIC_FOR_MOD( - );
DEFINITION_OF_ARITHMETIC_FOR_MOD( * );
DEFINITION_OF_ARITHMETIC_FOR_MOD( / );
template inline constexpr Mod Mod::operator<<( int n ) const noexcept { return move( Mod( *this ) <<= n ); }
template inline constexpr Mod Mod::operator>>( int n ) const noexcept { return move( Mod( *this ) >>= n ); }
template inline constexpr Mod Mod::operator-() const noexcept { return move( Mod( *this ).SignInvert() ); }
template inline constexpr Mod& Mod::SignInvert() noexcept { return Ref( m_n > 0 ? m_n = M - m_n : m_n ); }
template inline Mod& Mod::Invert() { assert( m_n != 0 ); INT_TYPE_FOR_MOD m_n_neg; return m_n < ConstantsForMod::g_memory_length ? Ref( m_n = Inverse( m_n ).m_n ) : ( ( m_n_neg = M - m_n ) < ConstantsForMod::g_memory_length ) ? Ref( m_n = M - Inverse( m_n_neg ).m_n ) : PositivePower( INT_TYPE_FOR_MOD( ConstantsForMod::g_M_minus_2 ) ); }
template template inline constexpr Mod& Mod::PositivePower( INT exponent ) noexcept { Mod power{ *this }; exponent--; while( exponent != 0 ){ ( exponent & 1 ) == 1 ? operator*=( power ) : *this; exponent >>= 1; power *= power; } return *this; }
template template inline constexpr Mod& Mod::NonNegativePower( INT exponent ) noexcept { return exponent == 0 ? Ref( m_n = 1 ) : Ref( PositivePower( move( exponent ) ) ); }
template template inline constexpr Mod& Mod::Power( INT exponent ) { bool neg = exponent < 0; assert( !( neg && m_n == 0 ) ); return neg ? PositivePower( move( exponent *= ConstantsForMod::g_M_minus_2_neg ) ) : NonNegativePower( move( exponent ) ); }
template inline constexpr void Mod::swap( Mod& n ) noexcept { std::swap( m_n , n.m_n ); }
template inline const Mod& Mod::Inverse( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod memory[ConstantsForMod::g_memory_length] = { zero() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ memory[length_curr].m_n = M - memory[M % length_curr].m_n * ull( M / length_curr ) % M; length_curr++; } return memory[n]; }
template inline const Mod& Mod::Factorial( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod memory[ConstantsForMod::g_memory_length] = { one() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ ( memory[length_curr] = memory[length_curr - 1] ) *= length_curr; length_curr++; } return memory[n]; }
template inline const Mod& Mod::FactorialInverse( const INT_TYPE_FOR_MOD& n ) noexcept { static Mod memory[ConstantsForMod::g_memory_length] = { one() , one() }; static INT_TYPE_FOR_MOD length_curr = 2; while( length_curr <= n ){ ( memory[length_curr] = memory[length_curr - 1] ) *= Inverse( length_curr ); length_curr++; } return memory[n]; }
template inline Mod Mod::Combination( const INT_TYPE_FOR_MOD& n , const INT_TYPE_FOR_MOD& i ) noexcept { return Factorial( n ) * FactorialInverse( i ) * FactorialInverse( n - i ); }
template inline constexpr const INT_TYPE_FOR_MOD& Mod::Represent() const noexcept { return m_n; }
template inline constexpr Mod Mod::Derepresent( const INT_TYPE_FOR_MOD& n ) noexcept { Mod n_copy{}; n_copy.m_n = n; return n_copy; }
template inline const Mod& Mod::zero() noexcept { static constexpr const Mod z{}; return z; }
template inline const Mod& Mod::one() noexcept { static constexpr const Mod o{ Derepresent( 1 ) }; return o; }
template template inline constexpr Mod& Mod::Ref( T&& n ) noexcept { return *this; }
template inline constexpr INT_TYPE_FOR_MOD& Mod::Normalise( INT_TYPE_FOR_MOD& n ) noexcept { return n < M ? n : n -= M; }
template inline Mod Inverse( const Mod& n ) { return move( Mod( n ).Invert() ); }
template inline constexpr Mod Inverse_constrexpr( Mod n ) noexcept { return move( n.NonNegativePower( M - 2 ) ); }
template inline constexpr Mod Power( Mod n , INT exponent ) { return move( n.Power( move( exponent ) ) ); }
template inline constexpr void swap( Mod& n0 , Mod& n1 ) noexcept { n0.swap( n1 ); }
template inline string to_string( const Mod& n ) noexcept { return to_string( n.Represent() ) + " + " + to_string( M ) + "Z"; }
template inline basic_istream& operator>>( basic_istream& is , Mod& n ) { ll m; is >> m; n = m; return is; }
template inline basic_ostream& operator<<( basic_ostream& os , const Mod& n ) { return os << n.Represent(); }
// AAA ライブラリは以上に挿入する。
#define INCLUDE_MAIN
#include __FILE__
#else // INCLUDE_LIBRARY
#ifdef DEBUG
#define _GLIBCXX_DEBUG
#define SIGNAL signal( SIGABRT , &AlertAbort );
#define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック: " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
#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 SIGNAL
#define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
#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 , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#else
#define SET_LL( A ) cin >> A
#define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
#define SET_A( A , N ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ cin >> A[VARIABLE_FOR_SET_A]; }
#define CIN_A( LL , A , N ) vector A( N ); SET_A( A , N );
#endif
#include
using namespace std;
#define REPEAT_MAIN( BOUND ) int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr ); SIGNAL; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( 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 ); } REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } CHECK_REDUNDANT_INPUT; }
#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 ) constexpr LL BOUND = VALUE
#define SET_ASSERT( A , MIN , MAX ) SET_LL( A ); ASSERT( A , MIN , MAX )
#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 .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 RETURN( ... ) COUT( __VA_ARGS__ ); return
// 型のエイリアス
#define decldecay_t( VAR ) decay_t
template using ret_t = decltype( declval()( declval()... ) );
template using inner_t = typename T::type;
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