#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define REPEAT_MAIN( BOUND ) START_MAIN; signal( SIGABRT , &AlertAbort ); AutoCheck( exec_mode ); if( exec_mode == debug_mode || exec_mode == library_search_mode ){ return 0; } else if( exec_mode == experiment_mode ){ Experiment(); return 0; } else if( exec_mode == small_test_mode ){ SmallTest(); return 0; }; DEXPR( int , bound_test_case_num , BOUND , min( BOUND , 100 ) ); int test_case_num = 1; if( exec_mode == solve_mode ){ if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } } else if( exec_mode == random_test_mode ){ CERR( "ランダムテストを行う回数を指定してください。" ); cin >> test_case_num; } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) if( exec_mode == solve_mode ){ cin >> A; ASSERT( A , MIN , MAX ); } else if( exec_mode == random_test_mode ){ CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) ); } else { assert( false ); }
  #define SOLVE_ONLY static_assert( __FUNCTION__[0] == 'S' )
  #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 REPEAT_MAIN( BOUND ) START_MAIN; CEXPR( int , bound_test_case_num , BOUND ); int test_case_num = 1; if constexpr( bound_test_case_num > 1 ){ SET_ASSERT( test_case_num , 1 , bound_test_case_num ); } FINISH_MAIN
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX )
  #define SOLVE_ONLY 
  #define CERR( ... ) 
  #define COUT( ... ) VariadicCout( cout , __VA_ARGS__ ) << "\n"
  #define CERR_A( A , N ) 
  #define COUT_A( A , N ) OUTPUT_ARRAY( cout , A , N ) << "\n"
  #define CERR_ITR( A ) 
  #define COUT_ITR( A ) OUTPUT_ITR( cout , A ) << "\n"
#endif
#include <bits/stdc++.h>
using namespace std;
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>;
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define START_MAIN int main(){ ios_base::sync_with_stdio( false ); cin.tie( nullptr )
#define FINISH_MAIN REPEAT( test_case_num ){ if constexpr( bound_test_case_num > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_test_case_num , ":" ); } Solve(); CERR( "" ); } }
#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 TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN( LL , ... ) SOLVE_ONLY; LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define SET_A( A , N ) SOLVE_ONLY; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
#define CIN_A( LL , A , N ) LL A[N]; SET_A( A , N );
#define GETLINE_SEPARATE( SEPARATOR , ... ) SOLVE_ONLY; string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) SOLVE_ONLY; GETLINE_SEPARATE( '\n' , __VA_ARGS__ )
#define FOR( VAR , INITIAL , FINAL_PLUS_ONE ) for( TYPE_OF( FINAL_PLUS_ONE ) VAR = INITIAL ; VAR < FINAL_PLUS_ONE ; VAR ++ )
#define FOREQ( VAR , INITIAL , FINAL ) for( TYPE_OF( FINAL ) VAR = INITIAL ; VAR <= FINAL ; VAR ++ )
#define FOREQINV( VAR , INITIAL , FINAL ) for( TYPE_OF( INITIAL ) VAR = INITIAL ; VAR >= FINAL ; VAR -- )
#define 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( ... ) SOLVE_ONLY; COUT( __VA_ARGS__ ); return
#define COMPARE( ... ) auto naive = Naive( __VA_ARGS__ ); auto answer = Answer( __VA_ARGS__ ); bool match = naive == answer; COUT( #__VA_ARGS__ , ":" , naive , match ? "==" : "!=" , answer ); if( !match ){ return; }

// 入出力用
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>& 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... ); }

// 算術用
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }

#define POWER( ANSWER , ARGUMENT , EXPONENT )				\
  static_assert( ! is_same<TYPE_OF( ARGUMENT ),int>::value && ! is_same<TYPE_OF( ARGUMENT ),uint>::value ); \
  TYPE_OF( ARGUMENT ) ANSWER{ 1 };					\
  {									\
    TYPE_OF( ARGUMENT ) ARGUMENT_FOR_SQUARE_FOR_POWER = ( ARGUMENT );	\
    TYPE_OF( EXPONENT ) EXPONENT_FOR_SQUARE_FOR_POWER = ( EXPONENT );	\
    while( EXPONENT_FOR_SQUARE_FOR_POWER != 0 ){			\
      if( EXPONENT_FOR_SQUARE_FOR_POWER % 2 == 1 ){			\
	ANSWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;			\
      }									\
      ARGUMENT_FOR_SQUARE_FOR_POWER *= ARGUMENT_FOR_SQUARE_FOR_POWER;	\
      EXPONENT_FOR_SQUARE_FOR_POWER /= 2;				\
    }									\
  }									\

#define POWER_MOD( ANSWER , ARGUMENT , EXPONENT , MODULO )		\
  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;				\
    }									\
  }									\

#define FACTORIAL_MOD( ANSWER , ANSWER_INV , INVERSE , MAX_INDEX , CONSTEXPR_LENGTH , MODULO ) \
  static ll ANSWER[CONSTEXPR_LENGTH];					\
  static ll ANSWER_INV[CONSTEXPR_LENGTH];				\
  static ll INVERSE[CONSTEXPR_LENGTH];					\
  {									\
    ll VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1;				\
    ANSWER[0] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL;			\
    FOREQ( i , 1 , MAX_INDEX ){						\
      ANSWER[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= i ) %= ( MODULO ); \
    }									\
    ANSWER_INV[0] = ANSWER_INV[1] = INVERSE[1] = VARIABLE_FOR_PRODUCT_FOR_FACTORIAL = 1; \
    FOREQ( i , 2 , MAX_INDEX ){						\
      ANSWER_INV[i] = ( VARIABLE_FOR_PRODUCT_FOR_FACTORIAL *= INVERSE[i] = ( MODULO ) - ( ( ( ( MODULO ) / i ) * INVERSE[ ( MODULO ) % i ] ) % ( MODULO ) ) ) %= ( MODULO ); \
    }									\
  }									\

// 二分探索テンプレート
// EXPRESSIONがANSWERの広義単調関数の時、EXPRESSION >= TARGETの整数解を格納。
#define BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , DESIRED_INEQUALITY , TARGET , INEQUALITY_FOR_CHECK , UPDATE_U , UPDATE_L , UPDATE_ANSWER ) \
  static_assert( ! is_same<TYPE_OF( TARGET ),uint>::value && ! is_same<TYPE_OF( TARGET ),ull>::value ); \
  ll ANSWER = MINIMUM;							\
  if( MINIMUM <= MAXIMUM ){						\
    ll VARIABLE_FOR_BINARY_SEARCH_L = MINIMUM;				\
    ll VARIABLE_FOR_BINARY_SEARCH_U = MAXIMUM;				\
    ANSWER = ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2; \
    ll VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH;			\
    while( VARIABLE_FOR_BINARY_SEARCH_L != VARIABLE_FOR_BINARY_SEARCH_U ){ \
      VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH = ( EXPRESSION ) - ( TARGET ); \
      CERR( "二分探索中：" , VARIABLE_FOR_BINARY_SEARCH_L , "<=" , ANSWER , "<=" , VARIABLE_FOR_BINARY_SEARCH_U , ":" , EXPRESSION , "-" , TARGET , "=" , VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH ); \
      if( VARIABLE_FOR_DIFFERENCE_FOR_BINARY_SEARCH INEQUALITY_FOR_CHECK 0 ){	\
	VARIABLE_FOR_BINARY_SEARCH_U = UPDATE_U;			\
      } else {								\
	VARIABLE_FOR_BINARY_SEARCH_L = UPDATE_L;			\
      }									\
      ANSWER = UPDATE_ANSWER;						\
    }									\
    CERR( "二分探索終了：" , VARIABLE_FOR_BINARY_SEARCH_L , "<=" , ANSWER , "<=" , VARIABLE_FOR_BINARY_SEARCH_U , ":" , EXPRESSION , ( EXPRESSION > TARGET ? ">" : EXPRESSION < TARGET ? "<" : "=" ) , TARGET ); \
    if( EXPRESSION DESIRED_INEQUALITY TARGET ){				\
      CERR( "二分探索成功" );						\
    } else {								\
      CERR( "二分探索失敗" );						\
      ANSWER = MAXIMUM + 1;						\
    }									\
  } else {								\
    CERR( "二分探索失敗： " , MINIMUM , ">" , MAXIMUM );		\
    ANSWER = MAXIMUM + 1;						\
  }									\

// 単調増加の時にEXPRESSION >= TARGETの最小解を格納。
#define BS1( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , >= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調増加の時にEXPRESSION <= TARGETの最大解を格納。
#define BS2( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , > , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION >= TARGETの最大解を格納。
#define BS3( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , >= , TARGET , < , ANSWER - 1 , ANSWER , ( VARIABLE_FOR_BINARY_SEARCH_L + 1 + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// 単調減少の時にEXPRESSION <= TARGETの最小解を格納。
#define BS4( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , TARGET )		\
  BS( ANSWER , MINIMUM , MAXIMUM , EXPRESSION , <= , TARGET , <= , ANSWER , ANSWER + 1 , ( VARIABLE_FOR_BINARY_SEARCH_L + VARIABLE_FOR_BINARY_SEARCH_U ) / 2 ) \

// t以下の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLeq( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.upper_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t未満の値が存在すればその最大値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MaximumLt( set<T>& S , const T& t ) { const auto end = S.end(); if( S.empty() ){ return end; } auto itr = S.lower_bound( t ); return itr == end ? S.find( *( S.rbegin() ) ) : itr == S.begin() ? end : --itr; }
// t以上の値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGeq( set<T>& S , const T& t ) { return S.lower_bound( t ); }
// tより大きい値が存在すればその最小値のiterator、存在しなければend()を返す。
template <typename T> inline typename set<T>::iterator MinimumGt( set<T>& S , const T& t ) { return S.upper_bound( t ); }

// データ構造用
template <typename T> inline T Add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T XorAdd( const T& t0 , const T& t1 ){ return t0 ^ t1; }
template <typename T> inline T Multiply( const T& t0 , const T& t1 ) { return t0 * t1; }
template <typename T> inline const T& Zero() { static const T z = 0; return z; }
template <typename T> inline const T& One() { static const T o = 1; return o; }\
template <typename T> inline T AddInv( const T& t ) { return -t; }
template <typename T> inline T Id( const T& v ) { return v; }
template <typename T> inline T Min( const T& a , const T& b ){ return a < b ? a : b; }
template <typename T> inline T Max( const T& a , const T& b ){ return a < b ? b : a; }

// グリッド問題用
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline T2<int> EnumHW( const int& v ) { return { v / W , v % W }; }
inline int EnumHW_inv( const int& h , const int& w ) { return h * W + w; }
const string direction[4] = {"U","R","D","L"};
// (i,j)->(k,h)の方向番号を取得
inline int DirectionNumberOnGrid( const int& i , const int& j , const int& k , const int& h ){return i<k?2:i>k?0:j<h?1:j>h?3:(assert(false),-1);}
// v->wの方向番号を取得
inline int DirectionNumberOnGrid( const int& v , const int& w ){auto [i,j]=EnumHW(v);auto [k,h]=EnumHW(w);return DirectionNumberOnGrid(i,j,k,h);}
// 方向番号の反転U<->D、R<->L
inline int ReverseDirectionNumberOnGrid( const int& n ){assert(0<=n&&n<4);return(n+2)%4;}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<int> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){int v = EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back(v);}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back(v);}if(j>0){e[EnumHW_inv(i,j-1)].push_back(v);}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back(v);}}}}
inline void SetEdgeOnGrid( const string& Si , const int& i , list<path> ( &e )[] , const char& walkable = '.' ){FOR(j,0,W){if(Si[j]==walkable){const int v=EnumHW_inv(i,j);if(i>0){e[EnumHW_inv(i-1,j)].push_back({v,1});}if(i+1<H){e[EnumHW_inv(i+1,j)].push_back({v,1});}if(j>0){e[EnumHW_inv(i,j-1)].push_back({v,1});}if(j+1<W){e[EnumHW_inv(i,j+1)].push_back({v,1});}}}}
inline void SetWallOnGrid( const string& Si , const int& i , vector<vector<bool> >& non_wall , const char& walkable = '.'  , const char& unwalkable = '#' ){non_wall.push_back(vector<bool>(W));auto& non_wall_i=non_wall[i];FOR(j,0,W){non_wall_i[j]=Si[j]==walkable?true:(assert(Si[j]==unwalkable),false);}}

// グラフ用関数
template <typename PATH> list<PATH> E( const int& i );
template <typename PATH> vector<list<PATH> > e;

// 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。" ); }
  void AutoCheck( int& exec_mode );
  inline void Solve();
  inline void Experiment();
  inline void SmallTest();
  inline void RandomTest();
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  int exec_mode;
  CEXPR( int , solve_mode , 0 );
  CEXPR( int , debug_mode , 1 );
  CEXPR( int , library_search_mode , 2 );
  CEXPR( int , experiment_mode , 3 );
  CEXPR( int , small_test_mode , 4 );
  CEXPR( int , random_test_mode , 5 );
#endif

// 圧縮用
#define TE template
#define TY typename
#define US using
#define ST static
#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 MO move
#define TH this
#define CRI CO int&
#define CRUI CO uint&
#define CRL CO ll&

/*

C-x 3 C-x o C-x C-fによるファイル操作用

BIT:
c:/Users/user/Documents/Programming/Mathematics/SetTheory/DirectProduct/AffineSpace/BIT/compress.txt

BFS:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/BreadthFirstSearch/compress.txt

DFS on Tree:
c:/Users/user/Documents/Programming/Mathematics/Geometry/Graph/DepththFirstSearch/Tree/compress.txt

Divisor:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Prime/Divisor/compress.txt

Mod:
c:/Users/user/Documents/Programming/Mathematics/Arithmetic/Mod/ConstexprModulo/compress.txt

Polynomial
c:/Users/user/Documents/Programming/Mathematics/Polynomial/compress.txt

*/

// VVV ライブラリは以下に挿入する。

// 入力の範囲内で要件
// (1) (T,A_T:T^2->T)がmeet半束（可換羃等半群）である。
//     （以下A_Tの定める等号つき半順序を<=と置く）
// (2) (T,m_T:T^2->T,e_T:1->T)がモノイドである。
// (3) m_TがA_T上分配的、つまり
//     - Tの任意の要素s,t,uに対しならば
//       - m_T(u,A_T(s,t)) = A_T(m_T(u,s),m_T(u,t)) 
//       - m_T(A_T(s,t),u) = A_T(m_T(s,u),m_T(t,u))
//     である。
// (4) dの値は<=に関してe_T()以上またはinftyである。
// (5) inftyが<=に関してe_T()以上の項size_max個以下のm_Tに関する積で表せない。
// が成り立つ場合にのみサポート。

// ただしinftyが<=から定まる場合、(3)は
// (3)' m_Tが<=に関する順序モノイド演算、つまり
//     - Tの任意の要素s,t,uに対しs<=tならば
//       - m_T(u,s) <= m_T(u,t) 
//       - m_T(s,u) <= m_T(t,u)
//     である。
// と同値であることに注意。

// O(size_max^3)で全経路の重み（edgeごとの重みのm_Tに関する積）の
// A_Tに関する下限（多変数化したA_Tへの適用値）を計算。
template <typename T , T m_T(const T&,const T&) , const T& e_T() , T A_T(const T&,const T&) , int size_max>
void FloydWarshall( const T ( &d )[size_max][size_max] , T ( &weight )[size_max][size_max] , const int& size , const T& infty )
{

  for( int i = 0 ; i < size ; i++ ){

    T ( &weight_i )[size_max] = weight[i];
    const T ( &d_i )[size_max] = d[i];
    
    for( int j = 0 ; j < size ; j++ ){

      weight_i[j] = d_i[j];

    }

  }

  for( int k = 0 ; k < size ; k++ ){

    T ( &weight_k )[size_max] = weight[k];

    for( int i = 0 ; i < size ; i++ ){

      T ( &weight_i )[size_max] = weight[i];
      const T& weight_ik = weight_i[k];
    
      if( weight_ik != infty ){
	
	for( int j = 0 ; j < size ; j++ ){

	  const T& weight_kj = weight_k[j];

	  if( weight_kj != infty ){

	    T& weight_ij = weight_i[j];
	    const T weight_curr = m_T( weight_ik , weight_kj );
	    weight_ij = weight_ij == infty ? weight_curr : A_T( weight_ij , weight_curr );

	  }

	}

      }

    }

  }

  return;

}


#define AREA_OF_TRIANGLE ( x1 - x0 ) * ( y2 - y0 ) - ( y1 - y0 ) * ( x2 - x0 )
#define CALL_AREA_OF_TRIANGLE Area( v0.first , v0.second , v1.first , v1.second , v2.first , v2.second )

// xy平面内の３点がなす三角形の符号つき面積
template <typename INT> inline ll Area( const INT& x0 , const INT& y0 , const INT& x1 , const INT& y1 , const INT& x2 , const INT& y2 );
inline double Area( const double& x0 , const double& y0 , const double& x1 , const double& y1 , const double& x2 , const double& y2 );
template <typename INT> inline ll Area( const pair<INT,INT>& v0 , const pair<INT,INT>& v1 , const pair<INT,INT>& v2 );
inline double Area( const pair<double,double>& v0 , const pair<double,double>& v1 , const pair<double,double>& v2 );

// xy平面内の２線分（１点に潰れている場合含む）の交差判定
// 返り値1：交差する
// 返り値0：交差しないが、接触するか線分が１点に潰れている
// 返り値-1：接触しないかつ線分が１点に潰れてもいない
template <typename INT> inline int Intersect( const INT& x0 , const INT& y0 , const INT& x1 , const INT& y1 , const INT& z0 , const INT& w0 , const INT& z1 , const INT& w1 );
inline int Intersect( const double& x0 , const double& y0 , const double& x1 , const double& y1 , const double& z0 , const double& w0 , const double& z1 , const double& w1 , const double& epsilon );
template <typename INT> inline int Intersect( const pair<INT,INT>& v0 , const pair<INT,INT>& v1 , const pair<INT,INT>& w0 , const pair<INT,INT>& w1 );
inline int Intersect( const pair<double,double>& v0 , const pair<double,double>& v1 , const pair<double,double>& w0 , const pair<double,double>& w1 , const double& epsilon );

inline ll Area_ll( const ll& x0 , const ll& y0 , const ll& x1 , const ll& y1 , const ll& x2 , const ll& y2 ) { return AREA_OF_TRIANGLE; }
template <typename INT> inline ll Area( const INT& x0 , const INT& y0 , const INT& x1 , const INT& y1 , const INT& x2 , const INT& y2 ) { return Area_ll( x0 ,y0 , x1 ,y1 , x2 ,y2 ); }
inline double Area( const double& x0 , const double& y0 , const double& x1 , const double& y1 , const double& x2 , const double& y2 ) { return AREA_OF_TRIANGLE; }
template <typename INT> inline ll Area( const pair<INT,INT>& v0 , const pair<INT,INT>& v1 , const pair<INT,INT>& v2 ) { return CALL_AREA_OF_TRIANGLE; }
inline double Area( const pair<double,double>& v0 , const pair<double,double>& v1 , const pair<double,double>& v2 ) { return CALL_AREA_OF_TRIANGLE; }

template <typename INT> inline int Intersect( const INT& x0 , const INT& y0 , const INT& x1 , const INT& y1 , const INT& z0 , const INT& w0 , const INT& z1 , const INT& w1 )
{

  static_assert( ! is_same<INT,double>::value );
  const ll sign0 = Area( x0 , y0 , x1 , y1 , z0 , w0 ) * Area( x0 , y0 , x1 , y1 , z1 , w1 );
  const ll sign1 = Area( z0 , w0 , z1 , w1 , x0 , y0 ) * Area( z0 , w0 , z1 , w1 , x1 , y1 );
  return ( sign0 < 0 && sign1 < 0 ) ? 1 : ( sign0 == 0 || sign1 == 0 ) ? 0 : -1;

}

inline int Intersect( const double& x0 , const double& y0 , const double& x1 , const double& y1 , const double& z0 , const double& w0 , const double& z1 , const double& w1 , const double& epsilon )
{

  const double sign0 = Area( x0 , y0 , x1 , y1 , z0 , w0 ) * Area( x0 , y0 , x1 , y1 , z1 , w1 );
  const double sign1 = Area( z0 , w0 , z1 , w1 , x0 , y0 ) * Area( z0 , w0 , z1 , w1 , x1 , y1 );
  return ( sign0 <= -epsilon && sign1 <= -epsilon ) ? 1 : ( ( -epsilon < sign0 && sign0 < epsilon ) || ( -epsilon < sign1 && sign1 < epsilon ) ) ? 0 : -1;

}

template <typename INT> inline int Intersect( const pair<INT,INT>& v0 , const pair<INT,INT>& v1 , const pair<INT,INT>& w0 , const pair<INT,INT>& w1 ) { return Intersect( v0.first , v0.second , v1.first , v1.second , w0.first , w0.second , w1.first , w1.second ); }

inline int Intersect( const pair<double,double>& v0 , const pair<double,double>& v1 , const pair<double,double>& w0 , const pair<double,double>& w1 , const double& epsilon ) { return Intersect( v0.first , v0.second , v1.first , v1.second , w0.first , w0.second , w1.first , w1.second , epsilon ); }

// AAA ライブラリは以上に挿入する。

void Solve()
{
  CEXPR( int , bound_N , 150 );
  CIN_ASSERT( N , 2 , bound_N );
  DEXPR( int , bound_M , 200000 , 100 ); // 0が5個
  CIN_ASSERT( M , 1 , bound_M );
  CEXPR( int , bound_xy , 10000 );
  pair<ll,ll> xy[bound_N * 2];
  int N2 = N * 2;
  FOR( i , 0 , N2 ){
    CIN_ASSERT( xi , -bound_xy , bound_xy );
    CIN_ASSERT( yi , -bound_xy , bound_xy );
    xy[i] = { xi , yi };
  }
  T2<int> ab[bound_M * 2];
  int M2 = M * 2;
  FOR( i , 0 , M2 ){
    CIN_ASSERT( ai , 1 , N );
    CIN_ASSERT( bi , 1 , 2 );
    ab[i] = { --ai , --bi };
  }
  double d[bound_N*2][bound_N*2];
  double infty = -1.0;
  FOR( i , 0 , N2 ){
    pair<ll,ll>& xyi = xy[i];
    double( &d_i )[bound_N*2] = d[i];
    FOR( j , i + 1 , N2 ){
      pair<ll,ll>& xyj = xy[j];
      pair<ll,ll> dij = { xyj.first - xyi.first , xyj.second - xyi.second };
      bool connected = true;
      FOR( k , 0 , N ){
	pair<ll,ll>& xyk0 = xy[2 * k];
	pair<ll,ll>& xyk1 = xy[2 * k + 1];
	if( Intersect( xyi ,xyj , xyk0 , xyk1 , 0.1 ) == 1 ){
	  connected = false;
	  break;
	}
      }
      d_i[j] = d[j][i] = connected ? sqrt( dij.first * dij.first + dij.second * dij.second ) : infty;
      CERR( i << "," << j << "," << d_i[j] );
    }
  }
  double weight[bound_N*2][bound_N*2];
  FloydWarshall<double,Add<double>,Zero<double>,Min<double>,bound_N*2>( d , weight , N * 2 , infty );
  SET_PRECISION( 6 );
  FOR( i , 0 , M ){
    T2<int>& ab_i0 = ab[2 * i];
    T2<int>& ab_i1 = ab[2 * i + 1];
    COUT( weight[2 * ab_i0.first + ab_i0.second][2 * ab_i1.first + ab_i1.second] );
  }
}

REPEAT_MAIN(1);