// 入力制約チェック
#ifndef INCLUDE_MODE
  #define INCLUDE_MODE
  // #define REACTIVE
  // #define USE_GETLINE
#endif

#ifdef INCLUDE_MAIN

constexpr PrimeEnumeration<int,3163> pe{};
vector<double> memory( 10000001 , -1.0 );
double f( const int& N ){
  if( memory[N] < -0.5 ){
    memory[N] = N;
    RUN( EnumerateDivisor(pe,N) , d ){
      d > 1 ? memory[N] += f( N / d ) * get<0>( EulerFunction( pe , d ) ) : memory[N];
    };
    memory[N] /= N - 1 ;
  }
  return memory[N];
}

inline void Solve()
{
  CEXPR( int , bound_N , 1e7 );
  CIN_ASSERT( N , 1 , bound_N );
  memory[1] = 0.0;
  SET_PRECISION( 6 );
  RETURN( f( N ) );
}
REPEAT_MAIN(1);

#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。

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#define AS assert
#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 LE length
#define PW Power
#define MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&
#define VI virtual 
#define IS basic_istream<char,Traits>
#define OS basic_ostream<char,Traits>
#define ST_AS static_assert
#define reMO_CO remove_const
#define is_COructible_v is_constructible_v
#define rBE rbegin
#define reSZ resize

#ifdef DEBUG
  #include "c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/a_Body.hpp"
#else
// nの素因数分解：PrimeFactorisation(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,CO INT2& n)
// nの約数数え上げ：CountDivisor(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT n)
// nの約数辞書順列挙１：EnumerateDivisor(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT n)
// nの約数辞書順列挙２：EnumerateDivisor(CO LeastDivisor<INT,val_limit>& ld,INT n)
// SZ_max未満の数の約数全列挙：TotalEnumerateDivisor(CRI SZ)

TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();IN CO INT& OP[](CRI i)CO;CE CO INT& Get(CRI i)CO;CE CO bool& IsComposite(CRI n)CO;CE CRI LE()CO NE;};
TE <TY INT,INT val_limit,int LE_max> CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){if(i <=(val_limit - 1)/ i){for(INT j = i * i;j < val_limit;j += i){m_is_composite[j]= true;}}m_val[m_LE++]= i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> IN CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI i)CO{AS(0 <= i && i < m_LE);RE m_val[i];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI i)CO{RE m_val[i];}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI n)CO{RE m_is_composite[n];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}

TE <TY INT1,INT1 val_limit,int LE_max,TY INT2>pair<VE<INT1>,VE<int>> PrimeFactorisation(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT2 n){VE<INT1> P{};VE<int> E{};CRI LE = pe.LE();for(int i = 0;i < LE;i++){CO INT1& p = pe[i];if(n % p == 0){int e = 1;WH((n /= p)% p == 0){e++;}P.push_back(p);E.push_back(e);}else if(n / p < p){break;}}if(n != 1){P.push_back(n);E.push_back(1);}RE{MO(P),MO(E)};}

TE <TY INT,INT val_limit>CL LeastDivisor{PU:INT m_val[val_limit];CE LeastDivisor()NE;IN CO INT& OP[](CRI i)CO;CE CO INT& Get(CRI i)CO;};
TE <TY INT,INT val_limit> CE LeastDivisor<INT,val_limit>::LeastDivisor()NE:m_val{}{for(int d = 2;d < val_limit;d++){if(m_val[d]== 0){for(int n = d;n < val_limit;n += d){m_val[n]== 0?m_val[n]= d:d;}}}}TE <TY INT,INT val_limit> IN CO INT& LeastDivisor<INT,val_limit>::OP[](CRI i)CO{AS(0 <= i && i < val_limit);RE m_val[i];}TE <TY INT,INT val_limit> CE CO INT& LeastDivisor<INT,val_limit>::Get(CRI i)CO{RE m_val[i];}

TE <TY INT> INT CountDivisorBody(VE<int>& E)NE{CO int LE = E.SZ();INT AN = 1;for(int i = 0;i < LE;i++){AN *= ++E[i];}RE AN;}TE <TY INT>INT CountDivisor(INT n)NE{auto[P,E]= PrimeFactorisation(MO(n));RE CountDivisorBody<INT>(E);}TE <TY INT,TY PE>INT CountDivisor(CO PE& pe,INT n)NE{auto[P,E]= PrimeFactorisation(pe,MO(n));RE CountDivisorBody<INT>(E);}TE <TY INT> VE<INT> EnumerateDivisorBody(CO VE<INT>& P,VE<int>& E){CO int LE = P.SZ();VE AN(CountDivisorBody<INT>(E),1);int SZ = 1;for(int i = 0;i < LE;i++){auto& P_i = P[i];auto& E_i = E[i];INT q = 1;int j_shift = 0;for(int e = 1;e < E_i;e++){q *= P_i;j_shift += SZ;for(int j = 0;j < SZ;j++){AN[j + j_shift]= AN[j]* q;}}SZ *= E_i;}RE AN;}TE <TY INT>VE<INT> EnumerateDivisor(INT n)NE{auto[P,E]= PrimeFactorisation(MO(n));RE EnumerateDivisorBody(P,E);}TE <TY INT1,INT1 val_limit,int LE_max,TY INT2>VE<INT2> EnumerateDivisor(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT2 n){auto[P,E]= PrimeFactorisation(pe,MO(n));RE EnumerateDivisorBody(P,E);}TE <TY INT1,INT1 val_limit,TY INT2>VE<INT2> EnumerateDivisor(CO LeastDivisor<INT1,val_limit>& ld,INT2 n){VE<INT2> P{};VE<int> E{};WH(n > 1){auto& p = ld[n];int e = 1;WH((n /= p)% p == 0){e++;}P.push_back(p);E.push_back(e);}RE EnumerateDivisorBody(P,E);}TE <TY INT>VE<VE<INT>> TotalEnumerateDivisor(CO INT& SZ)NE{VE<VE<INT>> AN(SZ);for(INT d = 1;d < SZ;d++){for(INT n = 0;n < SZ;n += d){AN[n].push_back(d);}}RE AN;}
#endif

#ifdef DEBUG
  #include "c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/Function/Euler/a_Body.hpp"
#else
// nのオイラー関数値：EulerFunction(CO PrimeEnumeration<INT1,val_limit,LE_max>& prime,CO INT2& n);
// n_max以下のnのオイラー関数値：TotalEulerFunction(CO PrimeEnumeration<INT1,val_limit,LE_max>& prime,CO INT2& n_max);
// val_limitは(nの上限の平方根+1)以上に設定。

// TE <TY INT,INT val_limit,int LE_max = val_limit>CL PrimeEnumeration{PU:bool m_is_composite[val_limit];INT m_val[LE_max];int m_LE;CE PrimeEnumeration();IN CO INT& OP[](CRI i)CO;CE CO INT& Get(CRI i)CO;CE CO bool& IsComposite(CRI n)CO;CE CRI LE()CO NE;};
// TE <TY INT,INT val_limit,int LE_max> CE PrimeEnumeration<INT,val_limit,LE_max>::PrimeEnumeration():m_is_composite(),m_val(),m_LE(0){for(INT i = 2;i < val_limit;i++){if(! m_is_composite[i]){if(i <=(val_limit - 1)/ i){for(INT j = i * i;j < val_limit;j += i){m_is_composite[j]= true;}}m_val[m_LE++]= i;if(m_LE >= LE_max){break;}}}}TE <TY INT,INT val_limit,int LE_max> IN CO INT& PrimeEnumeration<INT,val_limit,LE_max>::OP[](CRI i)CO{AS(0 <= i && i < m_LE);RE m_val[i];}TE <TY INT,INT val_limit,int LE_max> CE CO INT& PrimeEnumeration<INT,val_limit,LE_max>::Get(CRI i)CO{RE m_val[i];}TE <TY INT,INT val_limit,int LE_max> CE CO bool& PrimeEnumeration<INT,val_limit,LE_max>::IsComposite(CRI n)CO{RE m_is_composite[n];}TE <TY INT,INT val_limit,int LE_max> CE CRI PrimeEnumeration<INT,val_limit,LE_max>::LE()CO NE{RE m_LE;}

// TE <TY INT1,INT1 val_limit,int LE_max,TY INT2>pair<VE<INT1>,VE<int>> PrimeFactorisation(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT2 n){VE<INT1> P{};VE<int> E{};CRI LE = pe.LE();for(int i = 0;i < LE;i++){CO INT1& p = pe[i];if(n % p == 0){int e = 1;WH((n /= p)% p == 0){e++;}P.push_back(p);E.push_back(e);}else if(n / p < p){break;}}if(n != 1){P.push_back(n);E.push_back(1);}RE{MO(P),MO(E)};}TE <TY INT1,INT1 val_limit,int LE_max,TY INT2>tuple<VE<INT1>,VE<int>,VE<INT2>> PrimePWFactorisation(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,INT2 n){VE<INT1> P{};VE<int> E{};VE<INT2> Q{};CRI LE = pe.LE();for(int i = 0;i < LE;i++){CO INT1& p = pe[i];if(n % p == 0){int e = 1;INT2 q = p;WH((n /= p)% p == 0){e++;q *= p;}P.push_back(p);E.push_back(e);Q.push_back(q);}else if(n / p < p){break;}}if(n != 1){P.push_back(n);E.push_back(1);Q.push_back(n);}RE{MO(P),MO(E),MO(Q)};}

TE <TY PF,TY INT>tuple<INT,VE<INT>,VE<int>> EulerFunction_Body(PF pf,CO INT& n){auto[P,E]= pf(n);INT AN = n;for(auto& p:P){AN -= AN / p;}RE{AN,MO(P),MO(E)};}TE <TY INT1,INT1 val_limit,int LE_max,TY INT2> IN tuple<INT2,VE<INT1>,VE<int>> EulerFunction(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,CO INT2& n){RE EulerFunction_Body([&](CRI i){RE PrimeFactorisation(pe,i);},n);}TE <TY INT1,INT1 val_limit,int LE_max,int SZ,TY INT2>VE<INT2> TotalEulerFunction(CO PrimeEnumeration<INT1,val_limit,LE_max>& pe,CO INT2& n_max){VE<INT2> AN(n_max + 1);for(INT2 n = 1;n <= n_max;n++){AN[n]= n;}auto quotient = AN;CRI LE = pe.LE();for(int i = 0;i < LE;i++){CO INT2& p_i = pe[i];INT2 n = 0;WH((n += p_i)<= n_max){INT2& AN_n = AN[n];INT2& quotient_n = quotient[n];AN_n -= AN_n / p_i;WH((quotient_n /= p_i)% p_i == 0){}}}for(INT2 n = val_limit;n <= n_max;n++){CO INT2& quotient_n = quotient[n];if(quotient_n != 1){INT2& AN_n = AN[n];AN_n -= AN_n / quotient_n;}}RE AN;}
#endif

// 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 DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE2 )
  #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 DEXPR( LL , BOUND , VALUE1 , VALUE2 ) CEXPR( LL , BOUND , VALUE1 )
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define CERR_A( N , A ) 
  #define COUT_A( N , A ) OUTPUT_ARRAY( cout , N , A ) << 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( I , N , ... ) VariadicResize( N + I , __VA_ARGS__ ); FOR( VARIABLE_FOR_SET_A , 0 , N ){ VariadicSet( cin , VARIABLE_FOR_SET_A + I , __VA_ARGS__ ); }
  #define CIN_A( LL , I , N , ... ) VE<LL> __VA_ARGS__; SET_A( I , N , __VA_ARGS__ );
  #define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) VE<VE<LL>> VAR( N0 + I0 ); FOR( VARIABLE_FOR_CIN_AA , 0 , N0 ){ SET_A( I1 , N1 , VAR[VARIABLE_FOR_CIN_AA + I0] ); }
#endif
#include <bits/stdc++.h>
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<double>( chrono::duration_cast<chrono::microseconds>( 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( I , N , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_A , 0 , N ){ SET_ASSERT( A[VARIABLE_FOR_SET_A + I] , MIN , MAX ); }
#define SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) FOR( VARIABLE_FOR_SET_AA0 , 0 , N0 ){ FOR( VARIABLE_FOR_SET_AA1 , 0 , N1 ){ SET_ASSERT( A[VARIABLE_FOR_SET_AA0 + I0][VARIABLE_FOR_SET_AA1 + I1] , MIN , MAX ); } }
#define CIN_ASSERT( A , MIN , MAX ) decldecay_t( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define CIN_A_ASSERT( I , N , A , MIN , MAX ) vector<decldecay_t( MAX )> A( N + I ); SET_A_ASSERT( I , N , A , MIN , MAX )
#define CIN_AA_ASSERT( I0 , N0 , I1 , N1 , A , MIN , MAX ) vector A( N0 + I0 , vector<decldecay_t( MAX )>( N1 + I1 ) ); SET_AA_ASSERT( I0 , N0 , I1 , N1 , A , 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 ITR( ARRAY ) auto begin_ ## ARRAY = ARRAY .BE() , itr_ ## ARRAY = begin_ ## ARRAY , end_ ## ARRAY = ARRAY .EN()
#define FOR_ITR( ARRAY ) for( ITR( ARRAY ) , itr = itr_ ## ARRAY ; itr_ ## ARRAY != end_ ## ARRAY ; itr_ ## ARRAY ++ , itr++ )
#define RUN( ARRAY , ... ) for( auto&& __VA_ARGS__ : ARRAY )
#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 RETURN( ... ) COUT( __VA_ARGS__ ); return

// 型のエイリアス
#define decldecay_t( VAR ) decay_t<decltype( VAR )>
template <typename F , typename...Args> using ret_t = decltype( declval<F>()( declval<Args>()... ) );
template <typename T> 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 <typename INT> using T2 = pair<INT,INT>;
template <typename INT> using T3 = tuple<INT,INT,INT>;
template <typename INT> using T4 = tuple<INT,INT,INT,INT>;
using path = pair<int,ll>;

// 入出力用
template <class Traits , typename T , typename U , template <typename...> typename V> inline auto operator>>( basic_istream<char,Traits>& is , V<T,U>& arg ) -> decltype((get<0>(arg),is))& { return is >> get<0>( arg ) >> get<1>( arg ); }
template <class Traits , typename T , typename U , typename V> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , tuple<T,U,V>& arg ) { return is >> get<0>( arg ) >> get<1>( arg ) >> get<2>( arg ); }
template <class Traits , typename T , typename U , typename V , typename W> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , tuple<T,U,V,W>& arg ) { return is >> get<0>( arg ) >> get<1>( arg ) >> get<2>( arg ) >> get<3>( arg ); }

template <class Traits , typename T , typename U , template <typename...> typename V> inline auto operator<<( basic_ostream<char,Traits>& os , const V<T,U>& arg ) -> decltype((get<0>(arg),os))& { return os << get<0>( arg ) << " " << get<1>( arg ); }
template <class Traits , typename T , typename U , typename V> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const tuple<T,U,V>& arg ) { return os << get<0>( arg ) << " " << get<1>( arg ) << " " << get<2>( arg ); }
template <class Traits , typename T , typename U , typename V , typename W> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const tuple<T,U,V,W>& arg ) { return os << get<0>( arg ) << " " << get<1>( arg ) << " " << get<2>( arg ) << " " << get<3>( arg ); }

#define DEFINITION_OF_COUT_FOR_VECTOR( V ) template <class Traits , typename Arg> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const V<Arg>& arg ) { auto begin = arg.begin() , end = arg.end(); auto itr = begin; while( itr != end ){ ( itr == begin ? os : os << " " ) << *itr; itr++; } return os; }
DEFINITION_OF_COUT_FOR_VECTOR( vector );
DEFINITION_OF_COUT_FOR_VECTOR( list );
DEFINITION_OF_COUT_FOR_VECTOR( set );
DEFINITION_OF_COUT_FOR_VECTOR( unordered_set );

inline void VariadicResize( const int& size ) {}
template <typename Arg , typename... ARGS> inline void VariadicResize( const int& size , Arg& arg , ARGS&... args ) { arg.resize( size ); VariadicResize( size , args... ); }

template <class Traits> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicCin( basic_istream<char,Traits>& is , Arg& arg , ARGS&... args ) { return VariadicCin( is >> arg , args... ); }
template <class Traits> inline basic_istream<char,Traits>& VariadicSet( basic_istream<char,Traits>& is , const int& i ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicSet( basic_istream<char,Traits>& is , const int& i , Arg& arg , ARGS&... args ) { return VariadicSet( is >> arg[i] , i , args... ); }

template <class Traits> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator ) { return is; }
template <class Traits , typename Arg , typename... ARGS> inline basic_istream<char,Traits>& VariadicGetline( basic_istream<char,Traits>& is , const char& separator , Arg& arg , ARGS&... args ) { return VariadicGetline( getline( is , arg , separator ) , separator , args... ); }

template <class Traits , typename Arg> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg& arg ) { return os << arg; }
template <class Traits , typename Arg1 , typename Arg2 , typename... ARGS> inline basic_ostream<char,Traits>& VariadicCout( basic_ostream<char,Traits>& os , const Arg1& arg1 , const Arg2& arg2 , const ARGS&... args ) { return VariadicCout( os << arg1 << " " , arg2 , args... ); }

// デバッグ用
#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

// 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[i] == 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
  #ifdef USE_GETLINE
    #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 )
  #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 )
  #endif
#endif
// |N| <= BOUNDを満たすNをSから構築
#define STOI( S , N , BOUND ) decldecay_t( 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 ++; } }
#define STOI_A( S , I , N , A , BOUND ) vector<decldecay_t( BOUND )> A( N + I ); FOR( VARIABLE_FOR_STOI_A , 0 , N ){ STOI( S , A ##_VARIABLE_FOR_STOI_A , BOUND ); A[VARIABLE_FOR_STOI_A + I] = A ##_VARIABLE_FOR_STOI_A; }
// 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 ++; } }

#define INCLUDE_LIBRARY
#include __FILE__

#endif // INCLUDE_LIBRARY

#endif // INCLUDE_MAIN