// 入力制約／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( int , bound , 1e5 );
  GETLINE_COUNT( NMK_str , 3 , ' ' );
  STOI( NMK_str , N , 2 , bound );
  int bound_M = int( min( ll( bound ) , ll( N ) * ( N - 1 ) / 2 ) );
  STOI( NMK_str , M , N - 1 , bound_M );
  STOI( NMK_str , K , 1 , bound );
  vector<T2<ll>> XY( N + 1 );
  Set<T2<ll>> points{};
  FOREQ( i , 0 , N ){
    GETLINE_COUNT( XYi_str , 2 , ' ' );
    STOI( XYi_str , Xi , -bound , bound );
    STOI( XYi_str , Yi , -bound , bound );
    assert( points.count( XY[i] = { Xi , Yi } ) == 0 );
    points.insert( XY[i] );
  }
  vector<T2<ll>> AB( K );
  FOR( k , 0 , K ){
    GETLINE_COUNT( ABk_str , 2 , ' ' );
    STOI( ABk_str , Ak , -bound , bound );
    STOI( ABk_str , Bk , -bound , bound );
    assert( points.count( AB[k] = { Ak , Bk } ) == 0 );
    points.insert( AB[k] );
  }
  CEXPR( ll , V , 1e18 );
  GETLINE_COUNT( V_str , 1 , ' ' );
  STOI( V_str , V_same , V , V );
  vector<vector<int>> e( N ); 
  Set<T2<ll>> edges{};
  REPEAT( M ){
    GETLINE_COUNT( STj_str , 2 , ' ' );
    STOI( STj_str , Sj , 1 , N );
    STOI( STj_str , Tj , 1 , N );
    assert( edges.count( { Sj , Tj } ) == 0 );
    assert( edges.count( { Tj , Sj } ) == 0 );
    edges.insert( { Sj , Tj } );
    Sj--; Tj--;
    e[Sj].push_back( Tj );
    e[Tj].push_back( Sj );
  }
  Graph graph{ N , Get( e ) };
  BreadthFirstSearch bfs{ graph , -1 };
  auto [colour,cc] = bfs.GetConnectedComponent();
  assert( cc == 1 );
  double d = 1e18;
  FOREQ( i , 1 , N ){
    d = min( d , L2_Distance( XY[0] , XY[i] ) );
  }
  auto d2 = [&]( const T2<ll>& u , const T2<ll>& v ){ return L22_Distance( u , v ); };
  auto ann = TwoDimensionalAllNearestNeighbour( d2 , AB , XY );
  CERR( ann );
  double answer = 0;
  FOR( k , 0 , K ){
    double temp = L2_Distance( XY[0] , AB[k] );
    RUN( ann[k] , i ){
      temp = min( temp , d + L2_Distance( XY[i] , AB[k] ) );
    }
    answer += temp;
    CERR( temp );
  }
  SET_PRECISION( 6 );
  RETURN( answer * 2 );
}
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。redefinitionを避けるため圧縮元はincludeしない。

// 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

#define DC_OF_CPOINT(POINT)IN CO U& POINT()CO NE
#define DC_OF_POINT(POINT)IN U& POINT()NE
#define DF_OF_CPOINT(POINT)TE <TY U> IN CO U& VirtualPointedSet<U>::POINT()CO NE{RE Point();}
#define DF_OF_POINT(POINT)TE <TY U> IN U& VirtualPointedSet<U>::POINT()NE{RE Point();}
TE <TY U>CL UnderlyingSet{PU:US type = U;};TE <TY U>CL VirtualPointedSet:VI PU UnderlyingSet<U>{PU:VI CO U& Point()CO NE = 0;VI U& Point()NE = 0;DC_OF_CPOINT(Unit);DC_OF_CPOINT(Zero);DC_OF_CPOINT(One);DC_OF_CPOINT(Infty);DC_OF_POINT(init);DC_OF_POINT(root);};TE <TY U>CL PointedSet:VI PU VirtualPointedSet<U>{PU:U m_b_U;IN PointedSet(U b_u = U());IN CO U& Point()CO NE;IN U& Point()NE;};TE <TY U>CL VirtualNSet:VI PU UnderlyingSet<U>{PU:VI U Transfer(CO U& u)= 0;IN U Inverse(CO U& u);};TE <TY U,TY F_U>CL AbstractNSet:VI PU VirtualNSet<U>{PU:F_U m_f_U;IN AbstractNSet(F_U f_U);IN AbstractNSet<U,F_U>& OP=(CO AbstractNSet&)NE;IN U Transfer(CO U& u);};TE <TY U>CL VirtualMagma:VI PU UnderlyingSet<U>{PU:VI U Product(U u0,CO U& u1)= 0;IN U Sum(U u0,CO U& u1);};TE <TY U = ll>CL AdditiveMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U = ll>CL MultiplicativeMagma:VI PU VirtualMagma<U>{PU:IN U Product(U u0,CO U& u1);};TE <TY U,TY M_U>CL AbstractMagma:VI PU VirtualMagma<U>{PU:M_U m_m_U;IN AbstractMagma(M_U m_U);IN AbstractMagma<U,M_U>& OP=(CO AbstractMagma<U,M_U>&)NE;IN U Product(U u0,CO U& u1);};
TE <TY U> IN PointedSet<U>::PointedSet(U b_U):m_b_U(MO(b_U)){}TE <TY U> IN CO U& PointedSet<U>::Point()CO NE{RE m_b_U;}TE <TY U> IN U& PointedSet<U>::Point()NE{RE m_b_U;}DF_OF_CPOINT(Unit);DF_OF_CPOINT(Zero);DF_OF_CPOINT(One);DF_OF_CPOINT(Infty);DF_OF_POINT(init);DF_OF_POINT(root);TE <TY U,TY F_U> IN AbstractNSet<U,F_U>::AbstractNSet(F_U f_U):m_f_U(MO(f_U)){ST_AS(is_invocable_r_v<U,F_U,U>);}TE <TY U,TY F_U> IN AbstractNSet<U,F_U>& AbstractNSet<U,F_U>::operator=(CO AbstractNSet<U,F_U>&)NE{RE *TH;}TE <TY U,TY F_U> IN U AbstractNSet<U,F_U>::Transfer(CO U& u){RE m_f_U(u);}TE <TY U> IN U VirtualNSet<U>::Inverse(CO U& u){RE Transfer(u);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>::AbstractMagma(M_U m_U):m_m_U(MO(m_U)){ST_AS(is_invocable_r_v<U,M_U,U,U>);}TE <TY U,TY M_U> IN AbstractMagma<U,M_U>& AbstractMagma<U,M_U>::OP=(CO AbstractMagma<U,M_U>&)NE{RE *TH;}TE <TY U> IN U AdditiveMagma<U>::Product(U u0,CO U& u1){RE MO(u0 += u1);}TE <TY U> IN U MultiplicativeMagma<U>::Product(U u0,CO U& u1){RE MO(u0 *= u1);}TE <TY U,TY M_U> IN U AbstractMagma<U,M_U>::Product(U u0,CO U& u1){RE m_m_U(MO(u0),u1);}TE <TY U> IN U VirtualMagma<U>::Sum(U u0,CO U& u1){RE Product(MO(u0),u1);}

TE <TY U>CL VirtualMonoid:VI PU VirtualMagma<U>,VI PU VirtualPointedSet<U>{};TE <TY U = ll>CL AdditiveMonoid:VI PU VirtualMonoid<U>,PU AdditiveMagma<U>,PU PointedSet<U>{};TE <TY U = ll>CL MultiplicativeMonoid:VI PU VirtualMonoid<U>,PU MultiplicativeMagma<U>,PU PointedSet<U>{PU:IN MultiplicativeMonoid(U e_U);};TE <TY U,TY M_U>CL AbstractMonoid:VI PU VirtualMonoid<U>,PU AbstractMagma<U,M_U>,PU PointedSet<U>{PU:IN AbstractMonoid(M_U m_U,U e_U);};
TE <TY U> IN MultiplicativeMonoid<U>::MultiplicativeMonoid(U e_U):PointedSet<U>(MO(e_U)){}TE <TY U,TY M_U> IN AbstractMonoid<U,M_U>::AbstractMonoid(M_U m_U,U e_U):AbstractMagma<U,M_U>(MO(m_U)),PointedSet<U>(MO(e_U)){}

TE <TY U>CL VirtualGroup:VI PU VirtualMonoid<U>,VI PU VirtualPointedSet<U>,VI PU VirtualNSet<U>{};TE <TY U = ll>CL AdditiveGroup:VI PU VirtualGroup<U>,PU AdditiveMonoid<U>{PU:IN U Transfer(CO U& u);};TE <TY U,TY M_U,TY I_U>CL AbstractGroup:VI PU VirtualGroup<U>,PU AbstractMonoid<U,M_U>,PU AbstractNSet<U,I_U>{PU:IN AbstractGroup(M_U m_U,U e_U,I_U i_U);};
TE <TY U,TY M_U,TY I_U> IN AbstractGroup<U,M_U,I_U>::AbstractGroup(M_U m_U,U e_U,I_U i_U):AbstractMonoid<U,M_U>(MO(m_U),MO(e_U)),AbstractNSet<U,I_U>(MO(i_U)){}TE <TY U> IN U AdditiveGroup<U>::Transfer(CO U& u){RE -u;}

TE <TY T,TY R1,TY R2,TY E>CL VirtualGraph:VI PU UnderlyingSet<T>{PU:VI R1 Enumeration(CRI i)= 0;IN R2 Enumeration_inv(CO T& t);TE <TY PATH> IN R2 Enumeration_inv(CO PATH& p);IN VO Reset();VI CRI SZ()CO NE = 0;VI E& edge()NE = 0;VI ret_t<E,T> Edge(CO T& t)= 0;TE <TY PATH> IN ret_t<E,T> Edge(CO PATH& p);ST IN CO T& Vertex(CO T& t)NE;TE <TY PATH> ST IN CO T& Vertex(CO PATH& e)NE;VI R2 Enumeration_inv_Body(CO T& t)= 0;};TE <TY T,TY R1,TY R2,TY E>CL EdgeImplimentation:VI PU VirtualGraph<T,R1,R2,E>{PU:int m_SZ;E m_edge;IN EdgeImplimentation(CRI SZ,E edge);IN CRI SZ()CO NE;IN E& edge()NE;IN ret_t<E,T> Edge(CO T& t);};TE <TY E>CL Graph:PU EdgeImplimentation<int,CRI,CRI,E>{PU:IN Graph(CRI SZ,E edge);IN CRI Enumeration(CRI i);TE <TY F> IN Graph<F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CRI t);};TE <TY T,TY Enum_T,TY Enum_T_inv,TY E>CL EnumerationGraph:PU EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>{PU:Enum_T m_enum_T;Enum_T_inv m_enum_T_inv;IN EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge);IN ret_t<Enum_T,int> Enumeration(CRI i);TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> GetGraph(F edge)CO;IN ret_t<Enum_T_inv,T> Enumeration_inv_Body(CO T& t);};TE <TY Enum_T,TY Enum_T_inv,TY E> EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge)-> EnumerationGraph<decldecay_t(declval<Enum_T>()(0)),Enum_T,Enum_T_inv,E>;TE <TY T,TY E>CL MemorisationGraph:PU EdgeImplimentation<T,T,CRI,E>{PU:int m_LE;VE<T> m_memory;Map<T,int> m_memory_inv;IN MemorisationGraph(CRI SZ,CO T& dummy,E edge);IN T Enumeration(CRI i);IN VO Reset();TE <TY F> IN MemorisationGraph<T,F> GetGraph(F edge)CO;IN CRI Enumeration_inv_Body(CO T& t);};
TE <TY T,TY R1,TY R2,TY E> IN EdgeImplimentation<T,R1,R2,E>::EdgeImplimentation(CRI SZ,E edge):m_SZ(SZ),m_edge(MO(edge)){ST_AS(is_COructible_v<T,R1> && is_COructible_v<int,R2> && is_invocable_v<E,T>);}TE <TY E> IN Graph<E>::Graph(CRI SZ,E edge):EdgeImplimentation<int,CRI,CRI,E>(SZ,MO(edge)){}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN EnumerationGraph<T,Enum_T,Enum_T_inv,E>::EnumerationGraph(CRI SZ,Enum_T enum_T,Enum_T_inv enum_T_inv,E edge):EdgeImplimentation<T,ret_t<Enum_T,int>,ret_t<Enum_T_inv,T>,E>(SZ,MO(edge)),m_enum_T(MO(enum_T)),m_enum_T_inv(MO(enum_T_inv)){}TE <TY T,TY E> IN MemorisationGraph<T,E>::MemorisationGraph(CRI SZ,CO T& dummy,E edge):EdgeImplimentation<T,T,CRI,E>(SZ,MO(edge)),m_LE(),m_memory(),m_memory_inv(){ST_AS(is_invocable_v<E,T>);}TE <TY E> IN CRI Graph<E>::Enumeration(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T,int> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration(CRI i){RE m_enum_T(i);}TE <TY T,TY E> IN T MemorisationGraph<T,E>::Enumeration(CRI i){AS(0 <= i && i < m_LE);RE m_memory[i];}TE <TY T,TY R1,TY R2,TY E> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO T& t){RE Enumeration_inv_Body(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN R2 VirtualGraph<T,R1,R2,E>::Enumeration_inv(CO PATH& p){RE Enumeration_inv_Body(get<0>(p));}TE <TY E> IN CRI Graph<E>::Enumeration_inv_Body(CRI i){RE i;}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> IN ret_t<Enum_T_inv,T> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::Enumeration_inv_Body(CO T& t){RE m_enum_T_inv(t);}TE <TY T,TY E> IN CRI MemorisationGraph<T,E>::Enumeration_inv_Body(CO T& t){if(m_memory_inv.count(t)== 0){AS(m_LE < TH->SZ());m_memory.push_back(t);RE m_memory_inv[t]= m_LE++;}RE m_memory_inv[t];}TE <TY T,TY R1,TY R2,TY E> VO VirtualGraph<T,R1,R2,E>::Reset(){}TE <TY T,TY E> IN VO MemorisationGraph<T,E>::Reset(){m_LE = 0;m_memory.clear();m_memory_inv.clear();}TE <TY T,TY R1,TY R2,TY E> IN CRI EdgeImplimentation<T,R1,R2,E>::SZ()CO NE{RE m_SZ;}TE <TY T,TY R1,TY R2,TY E> IN E& EdgeImplimentation<T,R1,R2,E>::edge()NE{RE m_edge;}TE <TY T,TY R1,TY R2,TY E> IN ret_t<E,T> EdgeImplimentation<T,R1,R2,E>::Edge(CO T& t){RE m_edge(t);}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN ret_t<E,T> VirtualGraph<T,R1,R2,E>::Edge(CO PATH& p){RE Edge(get<0>(p));}TE <TY E> TE <TY F> IN Graph<F> Graph<E>::GetGraph(F edge)CO{RE Graph<F>(TH->SZ(),MO(edge));}TE <TY T,TY Enum_T,TY Enum_T_inv,TY E> TE <TY F> IN EnumerationGraph<T,Enum_T,Enum_T_inv,F> EnumerationGraph<T,Enum_T,Enum_T_inv,E>::GetGraph(F edge)CO{RE EnumerationGraph<T,Enum_T,Enum_T_inv,F>(TH->SZ(),m_enum_T,m_enum_T_inv,MO(edge));}TE <TY T,TY E> TE <TY F> IN MemorisationGraph<T,F> MemorisationGraph<T,E>::GetGraph(F edge)CO{RE MemorisationGraph<T,F>(TH->SZ(),MO(edge));}TE <TY T,TY R1,TY R2,TY E> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO T& t)NE{RE t;}TE <TY T,TY R1,TY R2,TY E> TE <TY PATH> IN CO T& VirtualGraph<T,R1,R2,E>::Vertex(CO PATH& e)NE{RE Vertex(get<0>(e));}

TE <TY T,TY GRAPH>CL VirtualBreadthFirstSearch{PU:GRAPH& m_G;T m_not_found;bool m_initialised;LI<T> m_next;VE<bool> m_found;VE<T> m_prev;IN VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found);TE <TY Arg> IN VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found,Arg&& init);IN VO Initialise();IN VO Initialise(CO T& init);IN VO Initialise(LI<T> inits);IN VO Shift(CO T& init);IN VO Shift(LI<T> inits);IN CRI SZ()CO NE;IN VE<bool>::reference found(CO T& t);IN CO T& prev(CO T& t);IN T Next();TE <TY U = T> auto GetDistance()-> enable_if_t<is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,Map<T,int>>;TE <TY U = T> auto GetDistance()-> enable_if_t<!is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,VE<int>>;pair<VE<int>,int> GetConnectedComponent();VE<T> GetNodeEnumeration();VE<T> GetReversedNodeEnumeration();VI VO Push(LI<T>& next,CO T& t)= 0;TE <TY PATH> IN VO Push(LI<T>& next,CO PATH& p);};
TE <TY T,TY GRAPH> IN VirtualBreadthFirstSearch<T,GRAPH>::VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found):m_G(G),m_not_found(not_found),m_initialised(false),m_next(),m_found(),m_prev(){ST_AS(is_same_v<inner_t<GRAPH>,T>);}TE <TY T,TY GRAPH> TE <TY Arg> IN VirtualBreadthFirstSearch<T,GRAPH>::VirtualBreadthFirstSearch(GRAPH& G,CO T& not_found,Arg&& init):VirtualBreadthFirstSearch<T,GRAPH>(G,not_found){Initialise(forward<Arg>(init));}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(){m_initialised = true;CRI V = SZ();m_next.clear();m_found = VE<bool>(V);m_prev = VE<T>(V,m_not_found);}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(CO T& init){auto&& i = m_G.Enumeration_inv(init);AS(0 <= i && i < SZ());Initialise();m_next.push_back(init);m_found[i]= true;}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Initialise(LI<T> inits){Initialise();m_next = MO(inits);CRI V = SZ();for(auto& u:m_next){auto&& i = m_G.Enumeration_inv(u);AS(0 <= i && i < V);m_found[i]= true;}}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Shift(CO T& init){if(m_initialised){CRI V = SZ();auto&& i = m_G.Enumeration_inv(init);AS(0 <= i && i < V);m_next.clear();if(! m_found[i]){m_next.push_back(init);m_found[i]= true;}}else{Initialise(init);}}TE <TY T,TY GRAPH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Shift(LI<T> inits){if(m_initialised){m_next.clear();CRI V = SZ();for(auto& u:m_next){auto&& i = m_G.Enumeration_inv(u);AS(0 <= i && i < V);if(! m_found[i]){m_next.push_back(u);m_found[i]= true;}}}else{Initialise(MO(inits));}}TE <TY T,TY GRAPH> IN CRI VirtualBreadthFirstSearch<T,GRAPH>::SZ()CO NE{RE m_G.SZ();}TE <TY T,TY GRAPH> IN VE<bool>::reference VirtualBreadthFirstSearch<T,GRAPH>::found(CO T& t){auto&& i = m_G.Enumeration_inv(t);AS(0 <= i && i < SZ());if(!m_initialised){Initialise();}RE m_found[i];}TE <TY T,TY GRAPH> IN CO T& VirtualBreadthFirstSearch<T,GRAPH>::prev(CO T& t){auto&& i = m_G.Enumeration_inv(t);AS(0 <= i && i < SZ());if(!m_initialised){Initialise();}RE m_prev[i];}TE <TY T,TY GRAPH> IN T VirtualBreadthFirstSearch<T,GRAPH>::Next(){if(m_next.empty()){RE m_not_found;}CO T t_curr = m_next.front();m_next.pop_front();for(auto& t:m_G.Edge(t_curr)){auto&& i = m_G.Enumeration_inv(t);auto&& found_i = m_found[i];if(! found_i){Push(m_next,t);m_prev[i]= t_curr;found_i = true;}}RE t_curr;}TE <TY T,TY GRAPH> TE <TY U>auto VirtualBreadthFirstSearch<T,GRAPH>::GetDistance()-> enable_if_t<is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,Map<T,int>>{Map<T,int> AN{};for(auto IT = m_next.BE(),EN = m_next.EN();IT != EN;IT++){AN[*IT]= 0;}T t;WH((t = Next())!= m_not_found){if(AN.count(t)== 0){AN[t]= AN[m_prev[m_G.Enumeration_inv(t)]]+ 1;}}RE AN;}TE <TY T,TY GRAPH> TE <TY U>auto VirtualBreadthFirstSearch<T,GRAPH>::GetDistance()-> enable_if_t<!is_same_v<GRAPH,MemorisationGraph<U,decldecay_t(declval<GRAPH>().edge())>>,VE<int>>{VE AN(SZ(),-1);for(auto IT = m_next.BE(),EN = m_next.EN();IT != EN;IT++){AN[m_G.Enumeration_inv(*IT)]= 0;}T t;WH((t = Next())!= m_not_found){auto&& i = m_G.Enumeration_inv(t);int& AN_i = AN[i];AN_i == -1?AN_i = AN[m_G.Enumeration_inv(m_prev[i])]+ 1:AN_i;}RE AN;}TE <TY T,TY GRAPH>pair<VE<int>,int> VirtualBreadthFirstSearch<T,GRAPH>::GetConnectedComponent(){ST_AS(!is_same_v<GRAPH,MemorisationGraph<T,decldecay_t(m_G.edge())>>);CRI V = SZ();VE cc_num(V,-1);int count = 0;for(int i = 0;i < V;i++){if(cc_num[i]== -1){Shift(m_G.Enumeration(i));T t = Next();if(t != m_not_found){WH(t != m_not_found){cc_num[m_G.Enumeration_inv(t)]= count;t = Next();}count++;}}}RE{MO(cc_num),MO(count)};}TE <TY T,TY GRAPH>VE<T> VirtualBreadthFirstSearch<T,GRAPH>::GetNodeEnumeration(){VE<T> AN{};T t = Next();WH(t != m_not_found){AN.push_back(t);t = Next();}RE AN;}TE <TY T,TY GRAPH>VE<T> VirtualBreadthFirstSearch<T,GRAPH>::GetReversedNodeEnumeration(){VE<T> AN{};VE<T> next{};T t;bool searched;WH(!(searched =(t = Next())== m_not_found)|| !next.empty()){WH(!next.empty()&&(searched || next.back()!= m_prev[m_G.Enumeration_inv(t)])){AN.push_back(next.back());next.pop_back();}if(!searched){next.push_back(t);}}RE AN;}TE <TY T,TY GRAPH> TE <TY PATH> IN VO VirtualBreadthFirstSearch<T,GRAPH>::Push(LI<T>& next,CO PATH& p){Push(next,get<0>(p));}

TE <TY T,TY GRAPH>CL BreadthFirstSearch:PU VirtualBreadthFirstSearch<T,GRAPH>{PU:TE <TY...Args> IN BreadthFirstSearch(GRAPH& G,CO T& not_found,Args&&... args);IN VO Push(LI<T>& next,CO T& t);};
TE <TY T,TY GRAPH> TE <TY...Args> IN BreadthFirstSearch<T,GRAPH>::BreadthFirstSearch(GRAPH& G,CO T& not_found,Args&&... args):VirtualBreadthFirstSearch<T,GRAPH>(G,not_found,forward<Args>(args)...){}TE <TY T,TY GRAPH> IN VO BreadthFirstSearch<T,GRAPH>::Push(LI<T>& next,CO T& t){next.push_back(t);}

TE <TY INT> IN INT L22(CO INT& x,CO INT& y){RE x * x + y * y;}TE <TY INT> IN INT L22(CO pair<INT,INT>& v){RE L22(v.first,v.second);}TE <TY INT> IN INT L22_Distance(CO INT& x0,CO INT& y0,CO INT& x1,CO INT& y1){RE L22(x0 - x1,y0 - y1);}TE <TY INT> IN INT L22_Distance(CO pair<INT,INT>& v0,CO pair<INT,INT>& v1){RE L22(v0 - v1);}TE <TY INT> IN double L2(CO INT& x,CO INT& y){RE sqrt(L22(x,y));}TE <TY INT> IN double L2(CO pair<INT,INT>& v){RE sqrt(L22(v));}TE <TY INT> IN double L2_Distance(CO INT& x0,CO INT& y0,CO INT& x1,CO INT& y1){RE sqrt(L22_Distance(x0,y0,x1,y1));}TE <TY INT> IN double L2_Distance(CO pair<INT,INT>& v0,CO pair<INT,INT>& v1){RE sqrt(L22_Distance(v0,v1));}


template <typename Dist2 , typename INT>
vector<vector<int>> TwoDimensionalAllNearestNeighbour( const Dist2& d2 , const vector<pair<INT,INT>>& S , const vector<pair<INT,INT>>& T )
{

  const int S_size = S.size();

  if( S_size == 0 ){

    return {};

  }

  const int T_size = T.size();
  assert( T_size > 0 );

  if( T_size == 1 ){

    return vector( S_size , vector<int>{ 0 } );

  }
  
  auto [x_min,y_min] = T[0];
  auto [x_max,y_max] = T[0];

  for( int j = 1 ; j < T_size ; j++ ){

    auto& [x,y] = T[j];
    x_min = min( x_min , x ); x_max = max( x , x_max ); 
    y_min = min( y_min , y ); y_max = max( y , y_max );

  }

  using Block = tuple<INT,INT,INT,INT,vector<int>>;
  vector<vector<pair<bool,int>>> neighbours( S_size , { { true , 0 } } );
  vector<bool> updatable( S_size , true );
  vector<Block> divisible_block = { { x_min , x_max , y_min , y_max , vector<int>( T_size ) } };

  for( int j = 0 ; j < T_size ; j++ ){

    get<4>( divisible_block[0] )[j] = j;

  }

  vector<Block> indivisible_block = {};

  // 最悪O(T_size)回のループ、良いケースではO(log T_size)回のループ
  while( !divisible_block.empty() ){

    const int divisible_block_size = divisible_block.size();
    vector<Block> next_divisible_block{};
    vector<vector<pair<bool,int>>> Partition( divisible_block_size );

    // 分割可能ブロックの分割の計算
    // 合計O(T_size)
    for( int num = 0 ; num < divisible_block_size ; num++ ){

      auto& [x_min,x_max,y_min,y_max,t] = divisible_block[num];
      const INT x_sum = x_min + x_max , x_mid = ( x_sum < 0 ? x_sum - 1 : x_sum ) / 2;
      const INT y_sum = y_min + y_max , y_mid = ( y_sum < 0 ? y_sum - 1 : y_sum ) / 2;
      Block block_sub[2][2]{};

      for( auto& j : t ){

        auto& [x,y] = T[j];
        auto& [x_min_sub,x_max_sub,y_min_sub,y_max_sub,t_sub] = block_sub[x <= x_mid ? 0 : 1][y <= y_mid ? 0 : 1];

        if( t_sub.empty() ){

          x_min_sub = x_max_sub = x; y_min_sub = y_max_sub = y;

        } else {

          x_min_sub = min( x_min_sub , x ); x_max_sub = max( x , x_max_sub );
          y_min_sub = min( y_min_sub , y ); y_max_sub = max( y , y_max_sub );

        }

        t_sub.push_back( j );
      
      }

      for( int num_x = 0 ; num_x <= 1 ; num_x++ ){

        for( int num_y = 0 ; num_y <= 1 ; num_y++ ){

          Block& block_xy = block_sub[num_x][num_y];
          const int t_size = get<4>( block_xy ).size();

          if( t_size != 0 ){

            if( t_size == 1 ){

              Partition[num].push_back( { false , indivisible_block.size() } );
              indivisible_block.push_back( move( block_xy ) );

            } else {

              Partition[num].push_back( { true , next_divisible_block.size() } );
              next_divisible_block.push_back( move( block_xy ) );

            }

          }

        }

      }

    }

    divisible_block = move( next_divisible_block );

    // 近傍の再計算
    // 合計O(近傍数総和)
    for( int i = 0 ; i < S_size ; i++ ){

      if( updatable[i] ){
        
        updatable[i] = false;
        vector<pair<bool,int>> neighbour_partition{};

        for( auto& coord : neighbours[i] ){

          auto& [divisible,num] = coord;
          
          if( divisible ){

            for( auto& coord_sub : Partition[num] ){

              neighbour_partition.push_back( coord_sub );

            }

          } else {

            neighbour_partition.push_back( coord );

          }

        }

        auto& [x,y] = S[i];
        
        auto d2_max = [&]( const pair<bool,int>& coord ){

          auto& [divisible,num] = coord;
          auto& [x_min,x_max,y_min,y_max,t] = ( divisible ? divisible_block : indivisible_block )[num];
          return d2( { 0 , 0 } , { max( abs( x - x_min ) , abs( x_max - x ) ) , max( abs( y - y_min ) , abs( y_max - y ) ) } );

        };
        
        auto d2_min = [&]( const pair<bool,int>& coord ){

          auto& [divisible,num] = coord;
          auto& [x_min,x_max,y_min,y_max,t] = ( divisible ? divisible_block : indivisible_block )[num];
          return d2( S[i] , { x < x_min ? x_min : x_max < x ? x_max : x , y < y_min ? y_min : y_max < y ? y_max : y } );

        };

        const int neighbour_partition_size = neighbour_partition.size();
        assert( neighbour_partition_size > 0 );
        
        decltype( d2({0,0},{0,0}) ) d2_max_min = d2_max( neighbour_partition[0] );

        for( int num = 1 ; num < neighbour_partition_size ; num++ ){

          d2_max_min = min( d2_max_min , d2_max( neighbour_partition[num] ) );

        }

        neighbours[i].clear();

        for( int num = 0 ; num < neighbour_partition_size ; num++ ){

          if( d2_min( neighbour_partition[num] ) <= d2_max_min ){

            updatable[i] = updatable[i] || neighbour_partition[num].first;
            neighbours[i].push_back( move( neighbour_partition[num] ) );

          }

        }
      
      }

    }

  }

  vector<vector<int>> answer( S_size );
  // 最近点の計算
  // 合計O(最近接数の総和)
  for( int i = 0 ; i < S_size ; i++ ){

    for( auto& [divisible,num] : neighbours[i] ){

      assert( !divisible );
      auto& [x_min,x_max,y_min,y_max,t] = indivisible_block[num];
      assert( t.size() == 1 && x_min == x_max && x_min == T[t[0]].first && y_min == y_max && y_min == T[t[0]].second );
      answer[i].push_back( t[0] );

    }

  }

  return answer;

}

// 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 COUT( ... ) VariadicCout( cout << "出力：" , __VA_ARGS__ ) << endl
  #define COUTNS( ... ) VariadicCoutNonSep( cout , __VA_ARGS__ ) << flush
  #define CERR( ... ) VariadicCout( cerr , __VA_ARGS__ ) << endl
  #define CERRNS( ... ) VariadicCout( cerr , __VA_ARGS__ ) << flush
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout << "出力："  , A , N ) << endl
  #define CERR_A( A , N ) OUTPUT_ARRAY( cerr , A , N ) << 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 COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << ENDL
  #define COUTNS( ... ) VariadicCoutNonSep( cout , __VA_ARGS__ )
  #define CERR( ... ) 
  #define CERRNS( ... ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << ENDL
  #define CERR_A( A , N ) 
#endif
#ifdef REACTIVE
  #ifdef DEBUG
    #define RSET( A , ... ) A = __VA_ARGS__
  #else
    #define RSET( A , ... ) cin >> A
  #endif
  #define RCIN( LL , A , ... ) LL A; RSET( A , __VA_ARGS__ )
  #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 , ... ) vector<LL> __VA_ARGS__; SET_A( I , N , __VA_ARGS__ )
  #define CIN_AA( LL , I0 , N0 , I1 , N1 , VAR ) vector<vector<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>;


/* VVV 常設ライブラリの非圧縮版は以下に挿入する。*/
// Random
ll GetRand( const int& Rand_min , const int& Rand_max ) { assert( Rand_min <= Rand_max ); ll answer = time( NULL ); return answer * rand() % ( Rand_max + 1 - Rand_min ) + Rand_min; }

// Set
#define DECLARATION_OF_HASH( ... )				\
  struct hash<__VA_ARGS__>					\
  {								\
								\
    inline size_t operator()( const __VA_ARGS__& n ) const;	\
								\
  };								\

class is_ordered
{

private:
  is_ordered() = delete;
  template <typename T> static constexpr auto Check( const T& t ) -> decltype( t < t , true_type() );
  static constexpr false_type Check( ... );

public:
  template <typename T> static constexpr const bool value = is_same_v< decltype( Check( declval<T>() ) ) , true_type >;

};

template <typename T>
using Set = conditional_t<is_constructible_v<unordered_set<T>>,unordered_set<T>,conditional_t<is_ordered::value<T>,set<T>,void>>;

// Tuple
#define DECLARATION_OF_ARITHMETIC_FOR_TUPLE( OPR )			\
  template <typename T , typename U , template <typename...> typename V> inline auto operator OPR ## =( V<T,U>& t0 , const V<T,U>& t1 ) -> decltype( ( get<0>( t0 ) , t0 ) )&; \
  template <typename T , typename U , typename V> inline tuple<T,U,V>& operator OPR ## =( tuple<T,U,V>& t0 , const tuple<T,U,V>& t1 ); \
  template <typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator OPR ## =( tuple<T,U,V,W>& t0 , const tuple<T,U,V,W>& t1 ); \
  template <typename ARG , typename T , typename U , template <typename...> typename V> inline auto operator OPR ## =( V<T,U>& t0 , const ARG& t1 ) -> decltype( ( get<0>( t0 ) , t0 ) )&; \
  template <typename ARG , typename T , typename U , typename V> inline tuple<T,U,V>& operator OPR ## =( tuple<T,U,V>& t0 , const ARG& t1 ); \
  template <typename ARG , typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator OPR ## =( tuple<T,U,V,W>& t0 , const ARG& t1 ); \
  template <template <typename...> typename V , typename...ARGS , typename ARG> inline auto operator OPR( const V<ARGS...>& t0 , const ARG& t1 ) -> decldecay_t( ( get<0>( t0 ) , t0 ) ) \

#define DEFINITION_OF_ARITHMETIC_FOR_TUPLE( OPR )			\
  template <typename T , typename U , template <typename...> typename V> inline auto operator OPR ## =( V<T,U>& t0 , const V<T,U>& t1 ) -> decltype( ( get<0>( t0 ) , t0 ) )& { get<0>( t0 ) OPR ## = get<0>( t1 ); get<1>( t0 ) OPR ## = get<1>( t1 ); return t0; } \
  template <typename T , typename U , typename V> inline tuple<T,U,V>& operator OPR ## =( tuple<T,U,V>& t0 , const tuple<T,U,V>& t1 ) { get<0>( t0 ) OPR ## = get<0>( t1 ); get<1>( t0 ) OPR ## = get<1>( t1 ); get<2>( t0 ) OPR ## = get<2>( t1 ); return t0; } \
  template <typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator OPR ## =( tuple<T,U,V,W>& t0 , const tuple<T,U,V,W>& t1 ) { get<0>( t0 ) OPR ## = get<0>( t1 ); get<1>( t0 ) OPR ## = get<1>( t1 ); get<2>( t0 ) OPR ## = get<2>( t1 ); get<3>( t0 ) OPR ## = get<3>( t1 ); return t0; } \
  template <typename ARG , typename T , typename U , template <typename...> typename V> inline auto operator OPR ## =( V<T,U>& t0 , const ARG& t1 ) -> decltype( ( get<0>( t0 ) , t0 ) )& { get<0>( t0 ) OPR ## = t1; get<1>( t0 ) OPR ## = t1; return t0; } \
  template <typename ARG , typename T , typename U , typename V> inline tuple<T,U,V>& operator OPR ## =( tuple<T,U,V>& t0 , const ARG& t1 ) { get<0>( t0 ) OPR ## = t1; get<1>( t0 ) OPR ## = t1; get<2>( t0 ) OPR ## = t1; return t0; } \
  template <typename ARG , typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator OPR ## =( tuple<T,U,V,W>& t0 , const ARG& t1 ) { get<0>( t0 ) OPR ## = t1; get<1>( t0 ) OPR ## = t1; get<2>( t0 ) OPR ## = t1; get<3>( t0 ) OPR ## = t1; return t0; } \
  template <template <typename...> typename V , typename...ARGS , typename ARG> inline auto operator OPR( const V<ARGS...>& t0 , const ARG& t1 ) -> decldecay_t( ( get<0>( t0 ) , t0 ) ) { auto t = t0; return move( t OPR ## = t1 ); } \

#define DECLARATION_OF_INCREMENT_FOR_TUPLE( INCR )			\
  template <typename T , typename U , template <typename...> typename V> inline auto operator INCR( V<T,U>& t ) -> decltype( ( get<0>( t ) , t ) )&; \
  template <typename T , typename U , typename V> inline tuple<T,U,V>& operator INCR ( tuple<T,U,V>& t ); \
  template <typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator INCR ( tuple<T,U,V,W>& t ); \

#define DEFINITION_OF_INCREMENT_FOR_TUPLE( INCR )			\
  template <typename T , typename U , template <typename...> typename V> inline auto operator INCR( V<T,U>& t ) -> decltype( ( get<0>( t ) , t ) )& { INCR get<0>( t ); INCR get<1>( t ); return t; } \
  template <typename T , typename U , typename V> inline tuple<T,U,V>& operator INCR ( tuple<T,U,V>& t ) { INCR get<0>( t ); INCR get<1>( t ); INCR get<2>( t ); return t; } \
  template <typename T , typename U , typename V , typename W> inline tuple<T,U,V,W>& operator INCR ( tuple<T,U,V,W>& t ) { INCR get<0>( t ); INCR get<1>( t ); INCR get<2>( t ); INCR get<3>( t ); return t; }	\

DEFINITION_OF_ARITHMETIC_FOR_TUPLE( + );
DEFINITION_OF_ARITHMETIC_FOR_TUPLE( - );
DEFINITION_OF_ARITHMETIC_FOR_TUPLE( * );
DEFINITION_OF_ARITHMETIC_FOR_TUPLE( / );
DEFINITION_OF_ARITHMETIC_FOR_TUPLE( % );

DEFINITION_OF_INCREMENT_FOR_TUPLE( ++ );
DEFINITION_OF_INCREMENT_FOR_TUPLE( -- );

template <class Traits , typename T> inline basic_istream<char,Traits>& operator>>( basic_istream<char,Traits>& is , tuple<T>& arg ){ return is >> get<0>( arg ); }
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> inline basic_ostream<char,Traits>& operator<<( basic_ostream<char,Traits>& os , const tuple<T>& arg ) { return os << get<0>( 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_HASH_FOR_TUPLE( PAIR )				\
  template <typename T , typename U> inline size_t hash<PAIR<T,U>>::operator()( const PAIR<T,U>& n ) const { static const size_t seed = ( GetRand( 1e3 , 1e8 ) << 1 ) | 1; static const hash<T> h0; static const hash<U> h1; return ( h0( get<0>( n ) ) * seed ) ^ h1( get<1>( n ) ); } \

template <typename T> DECLARATION_OF_HASH( tuple<T> );
template <typename T , typename U> DECLARATION_OF_HASH( pair<T,U> );
template <typename T , typename U> DECLARATION_OF_HASH( tuple<T,U> );
template <typename T , typename U , typename V> DECLARATION_OF_HASH( tuple<T,U,V> );
template <typename T , typename U , typename V , typename W> DECLARATION_OF_HASH( tuple<T,U,V,W> );

template <typename T> inline size_t hash<tuple<T>>::operator()( const tuple<T>& n ) const { static const hash<T> h; return h(get<0>( n ) ); }
DEFINITION_OF_HASH_FOR_TUPLE( pair );
DEFINITION_OF_HASH_FOR_TUPLE( tuple );
template <typename T , typename U , typename V> inline size_t hash<tuple<T,U,V>>::operator()( const tuple<T,U,V>& n ) const { static const size_t seed = ( GetRand( 1e3 , 1e8 ) << 1 ) | 1; static const hash<pair<T,U>> h01; static const hash<V> h2; return ( h01( { get<0>( n ) , get<1>( n ) } ) * seed ) ^ h2( get<2>( n ) ); }
template <typename T , typename U , typename V , typename W> inline size_t hash<tuple<T,U,V,W>>::operator()( const tuple<T,U,V,W>& n ) const { static const size_t seed = ( GetRand( 1e3 , 1e8 ) << 1 ) | 1; static const hash<pair<T,U>> h01; static const hash<pair<V,W>> h23; return ( h01( { get<0>( n ) , get<1>( n ) } ) * seed ) ^ h23( { get<2>( n ) , get<3>( n ) } ); }

// Vector
#define DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , OPR )			\
  template <typename T> inline V<T>& operator OPR ## = ( V<T>& a , const T& t ); \
  template <typename T> inline V<T>& operator OPR ## = ( V<T>& a0 , const V<T>& a1 ); \
  template <typename T , typename U> inline V<T> operator OPR( V<T> a , const U& u ); \

#define DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , OPR )			\
  template <typename T> inline V<T>& operator OPR ## = ( V<T>& a , const T& t ) { for( auto& s : a ){ s OPR ## = t; } return a; } \
  template <typename T> inline V<T>& operator OPR ## = ( V<T>& a0 , const V<T>& a1 ) { assert( a0.size() <= a1.size() ); auto itr0 = a0.begin() , end0 = a0.end(); auto itr1 = a1.begin(); while( itr0 != end0 ){ *( itr0++ ) OPR ## = *( itr1++ ); } return a0; } \
  template <typename T , typename U> inline V<T> operator OPR( V<T> a , const U& u ) { return move( a OPR ## = u ); } \

#define DECLARATION_OF_INCREMENT_FOR_VECTOR( V , INCR )		\
  template <typename T> inline V<T>& operator INCR( V<T>& a );	\

#define DEFINITION_OF_INCREMENT_FOR_VECTOR( V , INCR )			\
  template <typename T> inline V<T>& operator INCR( V<T>& a ) { for( auto& i : a ){ INCR i; } return a; } \

#define DECLARATION_OF_ARITHMETICS_FOR_VECTOR( V )			\
  DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , + );			\
  DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , - );			\
  DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , * );			\
  DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , / );			\
  DECLARATION_OF_ARITHMETIC_FOR_VECTOR( V , % );			\
  DECLARATION_OF_INCREMENT_FOR_VECTOR( V , ++ );			\
  DECLARATION_OF_INCREMENT_FOR_VECTOR( V , -- );			\
  template <typename T> inline V<T> operator*( const T& scalar , V<T> v ) \

#define DEFINITION_OF_ARITHMETICS_FOR_VECTOR( V )			\
  DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , + );				\
  DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , - );				\
  DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , * );				\
  DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , / );				\
  DEFINITION_OF_ARITHMETIC_FOR_VECTOR( V , % );				\
  DEFINITION_OF_INCREMENT_FOR_VECTOR( V , ++ );				\
  DEFINITION_OF_INCREMENT_FOR_VECTOR( V , -- );				\
  template <typename T> inline V<T> operator*( const T& scalar , V<T> v ) { for( auto& t : v ){ t *= scalar; } return move( v ); } \

DEFINITION_OF_ARITHMETICS_FOR_VECTOR( vector );
DEFINITION_OF_ARITHMETICS_FOR_VECTOR( list );

template <typename V> inline auto Get( V& a ) { return [&]( const int& i = 0 ) -> const decldecay_t( a[0] )& { return a[i]; }; }
template <typename T = int> inline vector<T> id( const int& size ) { vector<T> answer( size ); for( int i = 0 ; i < size ; i++ ){ answer[i] = i; } return answer; }

template <typename T> inline void Sort( vector<T>& a , const bool& reversed ) { if( reversed ){ static auto comp = []( const T& t0 , const T& t1 ) { return t1 < t0; }; sort( a.begin() , a.end() , comp ); } else { sort( a.begin() , a.end() ); } }

template <typename T> inline vector<int> IndexSort( const vector<T>& a , const bool& reversed ) { auto index = id<int>( a.size() ); if( reversed ){ sort( index.begin() , index.end() , [&]( const int& i , const int& j ) { return a[j] < a[i]; } ); } else { sort( index.begin() , index.end() , [&]( const int& i , const int& j ) { return a[i] < a[j]; } ); } return index; }

#define DECLARATION_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 )
#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... ); }

// Map
#define DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , OPR )			\
  template <typename T , typename U> inline MAP<T,U>& operator OPR ## = ( MAP<T,U>& a , const pair<T,U>& v ); \
  template <typename T , typename U> inline MAP<T,U>& operator OPR ## = ( MAP<T,U>& a0 , const MAP<T,U>& a1 ); \
  template <typename T , typename U , typename ARG> inline MAP<T,U> operator OPR( MAP<T,U> a , const ARG& arg ); \

#define DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , OPR )			\
  template <typename T , typename U> inline MAP<T,U>& operator OPR ## = ( MAP<T,U>& a , const pair<T,U>& v ) { a[v.first] OPR ## = v.second; return a; } \
  template <typename T , typename U> inline MAP<T,U>& operator OPR ## = ( MAP<T,U>& a0 , const MAP<T,U>& a1 ) { for( auto& [t,u] : a1 ){ a0[t] OPR ## = u; } return a0; } \
  template <typename T , typename U , typename ARG> inline MAP<T,U> operator OPR( MAP<T,U> a , const ARG& arg ) { return move( a OPR ## = arg ); } \

#define DECLARATION_OF_ARITHMETICS_FOR_MAP( MAP )	\
  DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , + );		\
  DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , - );		\
  DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , * );		\
  DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , / );		\
  DECLARATION_OF_ARITHMETIC_FOR_MAP( MAP , % );		\

#define DEFINITION_OF_ARITHMETICS_FOR_MAP( MAP ) \
  DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , + );	\
  DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , - );	\
  DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , * );	\
  DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , / );	\
  DEFINITION_OF_ARITHMETIC_FOR_MAP( MAP , % );	\

template <typename T , typename U>
using Map = conditional_t<is_constructible_v<unordered_map<T,int>>,unordered_map<T,U>,conditional_t<is_ordered::value<T>,map<T,U>,void>>;

DEFINITION_OF_ARITHMETICS_FOR_MAP( map );
DEFINITION_OF_ARITHMETICS_FOR_MAP( unordered_map );

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

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

template <class Traits , typename ARRAY> inline basic_ostream<char,Traits>& CoutArray( basic_ostream<char,Traits>& os , const int& i_start , const int& i_ulim , ARRAY&& a ) { for( int i = i_start ; i < i_ulim ; i++ ){ ( i == i_start ? os : ( os << " " ) ) << a[i]; } return os; }
/* AAA 常設ライブラリの非圧縮版は以上に挿入する。*/

// 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( VARIABLE_NUMBER == 0 ? size == 0 : count + 1 == VARIABLE_NUMBER ); }
// 余計な入力の有無を確認
#if defined( DEBUG ) || defined( REACTIVE )
  #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
// MIN <= N <= MAXを満たすNをSから構築
#define STOI( S , N , MIN , MAX ) decldecay_t( MAX ) N = 0; decldecay_t( MAX ) BOUND ## N = max( decldecay_t( MAX )( abs( MIN ) ) , abs( MAX ) ); { 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 ## N / 10 ? true : N == BOUND ## N / 10 && VARIABLE_FOR_DIGIT_FOR_GETLINE <= BOUND ## N % 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 ++; } ASSERT( N , MIN , MAX ); }
#define STOI_A( S , I , N , A , MIN , MAX ) vector<decldecay_t( MAX )> A( N + I ); FOR( VARIABLE_FOR_STOI_A , 0 , N ){ STOI( S , A ##_VARIABLE_FOR_STOI_A , MIN , MAX ); 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