#ifdef DEBUG
  #define _GLIBCXX_DEBUG
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr ); signal( SIGABRT , &AlertAbort )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , DEBUG_VALUE )
  #define CERR( ... ) 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
  #define ASSERT( A , MIN , MAX ) CERR( "ASSERTチェック： " , ( MIN ) , ( ( MIN ) <= A ? "<=" : ">" ) , A , ( A <= ( MAX ) ? "<=" : ">" ) , ( MAX ) ); assert( ( MIN ) <= A && A <= ( MAX ) )
  #define AUTO_CHECK int auto_checked; AutoCheck( auto_checked ); if( auto_checked == 3 ){ Jikken(); return 0; } else if( auto_checked == 4 ){ Debug(); return 0; } else if( auto_checked != 0 ){ return 0; };
#else
  #pragma GCC optimize ( "O3" )
  #pragma GCC optimize ( "unroll-loops" )
  #pragma GCC target ( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" )
  #define UNTIE ios_base::sync_with_stdio( false ); cin.tie( nullptr )
  #define DEXPR( LL , BOUND , VALUE , DEBUG_VALUE ) CEXPR( LL , BOUND , VALUE )
  #define CERR( ... ) 
  #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"
  #define ASSERT( A , MIN , MAX ) assert( ( MIN ) <= A && A <= ( MAX ) )
  #define AUTO_CHECK
#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 RANDOM_TEST
#if defined( DEBUG ) && defined( RANDOM_TEST )
  ll GetRand( const ll& Rand_min , const ll& Rand_max );
  #define SET_ASSERT( A , MIN , MAX ) CERR( #A , " = " , ( A = GetRand( MIN , MAX ) ) )
  #define CIN( LL , ... ) LL __VA_ARGS__; static_assert( false )
  #define CIN_A( LL , A , N ) LL A[N]; static_assert( false )
  #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = bound_T; static_assert( bound_T > 1 )
  #define RETURN( ANSWER ) if( ( ANSWER ) == guchoku ){ CERR( ANSWER , "==" , guchoku ); goto END_MAIN; } else { CERR( ANSWER , "!=" , guchoku ); return 0; }
#else
  #define SET_ASSERT( A , MIN , MAX ) cin >> A; ASSERT( A , MIN , MAX )
  #define CIN( LL , ... ) LL __VA_ARGS__; VariadicCin( cin , __VA_ARGS__ )
  #define CIN_A( LL , A , N ) LL A[N]; FOR( VARIABLE_FOR_CIN_A , 0 , N ){ cin >> A[VARIABLE_FOR_CIN_A]; }
  #define TEST_CASE_NUM( BOUND ) DEXPR( int , bound_T , BOUND , min( BOUND , 100 ) ); int T = 1; if constexpr( bound_T > 1 ){ SET_ASSERT( T , 1 , bound_T ); }
  #define RETURN( ANSWER ) COUT( ANSWER ); QUIT
#endif
#define ATT __attribute__( ( target( "sse4.2,fma,avx2,popcnt,lzcnt,bmi2" ) ) )
#define TYPE_OF( VAR ) decay_t<decltype( VAR )>
#define CEXPR( LL , BOUND , VALUE ) constexpr LL BOUND = VALUE
#define CIN_ASSERT( A , MIN , MAX ) TYPE_OF( MAX ) A; SET_ASSERT( A , MIN , MAX )
#define GETLINE_SEPARATE( SEPARATOR , ... ) string __VA_ARGS__; VariadicGetline( cin , SEPARATOR , __VA_ARGS__ )
#define GETLINE( ... ) GETLINE_SEPARATE( " " , ... )
#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 QUIT goto END_MAIN
#define START_MAIN REPEAT( T ){ { if constexpr( bound_T > 1 ){ CERR( "testcase " , VARIABLE_FOR_REPEAT_T , ":" ); }
#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 FINISH_MAIN QUIT; } END_MAIN: CERR( "" ); }

// 入出力用関数
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... ); }

// 算術用関数
template <typename T> inline T Residue( const T& a , const T& p ){ return a >= 0 ? a % p : p - 1 - ( ( - ( a + 1 ) ) % p ); }
inline ll MIN( const ll& a , const ll& b ){ return min( a , b ); }
inline ull MIN( const ull& a , const ull& b ){ return min( a , b ); }
inline ll MAX( const ll& a , const ll& b ){ return max( a , b ); }
inline ull MAX( const ull& a , const ull& b ){ return max( a , b ); }

#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 ); }

// データ構造用関数
template <typename T> inline T add( const T& t0 , const T& t1 ) { return t0 + t1; }
template <typename T> inline T xor_add( 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 add_inv( const T& t ) { return -t; }
template <typename T> inline T id( const T& v ) { return v; }

// グリッド問題用関数
int H , W , H_minus , W_minus , HW;
vector<vector<bool> > non_wall;
inline pair<int,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<pair<int,ll> > ( &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_type> list<path_type> E( const int& i );
template <typename path_type> vector<list<path_type> > e;

// デバッグ用関数
#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& auto_checked );
  void Jikken();
  void Debug();
#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。



template <int V_max>
class ZeroOneBreadthFirstSearch_Body
{

protected:
  int m_V;
  int m_init;
  list<int> m_next;
  int m_found[V_max];
  int m_prev[V_max];
  int m_weight[V_max];
  
public:
  inline ZeroOneBreadthFirstSearch_Body( const int& V );
  inline ZeroOneBreadthFirstSearch_Body( const int& V , const int& init );

  // m_foundとm_prevとm_weightを初期化
  inline void Reset( const int& init );
  // m_foundとm_prevとm_weightを非初期化
  inline void Shift( const int& init );

  inline const int& size() const;
  inline const int& init() const;
  inline int& found( const int& i );
  inline const int& prev( const int& i ) const;
  inline const int& weight( const int& i ) const;

  int Next();

  // Next()の反復でm_initから到達可能な頂点を全探索。
  // 計算量O((m_initの連結成分)+(m_initの連結成分におけるEのサイズの合計))
  inline void SetWeight();

  // Next()の反復でinitからgoalまでの最短経路を探索。
  // 計算量O((initの連結成分)+(m_initの連結成分におけるEのサイズの合計))
  inline const int& Solve( const int& init , const int& goal );

private:
  virtual list<pair<int,bool> > e( const int& t ) = 0;

};

template <int V_max,list<pair<int,bool> > E(const int&)>
class ZeroOneBreadthFirstSearch :
  public ZeroOneBreadthFirstSearch_Body<V_max>
{
  
public:
  template<typename... Args> inline ZeroOneBreadthFirstSearch( const Args&... args );

private:
  inline list<pair<int,bool> > e( const int& t );

};

template <int V_max> inline ZeroOneBreadthFirstSearch_Body<V_max>::ZeroOneBreadthFirstSearch_Body( const int& V ) : m_V( V ) , m_init() , m_next() , m_found() , m_prev() , m_weight() { assert( m_V <= V_max ); for( int i = 0 ; i < m_V ; i++ ){ m_prev[i] = m_weight[i] -1; } }
template <int V_max> inline ZeroOneBreadthFirstSearch_Body<V_max>::ZeroOneBreadthFirstSearch_Body( const int& V , const int& init ) : ZeroOneBreadthFirstSearch_Body( V ) { m_init = init; m_next.push_back( m_init ); m_found[m_init] = true; }
template <int V_max,list<pair<int,bool> > E(const int&)> template <typename... Args> inline ZeroOneBreadthFirstSearch<V_max,E>::ZeroOneBreadthFirstSearch( const Args&... args ) : ZeroOneBreadthFirstSearch_Body<V_max>( args... ) {}

template <int V_max> inline void ZeroOneBreadthFirstSearch_Body<V_max>::Reset( const int& init ) { m_init = init; assert( m_init < m_V ); m_next.clear(); m_next.push_back( m_init ); for( int i = 0 ; i < m_V ; i++ ){ m_found[i] = i == m_init; m_prev[i] = m_weight[i] = -1; } }
template <int V_max> inline void ZeroOneBreadthFirstSearch_Body<V_max>::Shift( const int& init ) { m_init = init; assert( m_init < m_V ); m_next.clear(); if( ! m_found[m_init] ){ m_next.push_back( m_init ); m_found[m_init] = true; } }

template <int V_max> inline const int& ZeroOneBreadthFirstSearch_Body<V_max>::size() const { return m_V; }
template <int V_max> inline const int& ZeroOneBreadthFirstSearch_Body<V_max>::init() const { return m_init; }
template <int V_max> inline int& ZeroOneBreadthFirstSearch_Body<V_max>::found( const int& i ) { assert( i < m_V ); return m_found[i]; }
template <int V_max> inline const int& ZeroOneBreadthFirstSearch_Body<V_max>::prev( const int& i ) const { assert( i < m_V ); return m_prev[i]; }
template <int V_max> inline const int& ZeroOneBreadthFirstSearch_Body<V_max>::weight( const int& i ) const { assert( i < m_V ); return m_weight[i]; }

template <int V_max>
int ZeroOneBreadthFirstSearch_Body<V_max>::Next()
{

  if( m_next.empty() ){

    return -1;

  }

  const int i_curr = m_next.front();

  if( m_weight[i_curr] == -1 ){

    m_weight[i_curr] = 0;
    
  }
  
  m_next.pop_front();
  auto edge = e( i_curr );

  while( ! edge.empty() ){

    const auto& [i,weighted] = edge.front();
    int& found_i = m_found[i];

    if( weighted ){

      if( found_i < 1 ){

	m_next.push_back( i );
	m_prev[i] = i_curr;
	m_weight[i] = m_weight[i_curr] + 1;
	found_i = 1;

      }

    } else {
      
      if( found_i < 2 ){

	m_next.push_front( i );
	m_prev[i] = i_curr;
	m_weight[i] = m_weight[i_curr];
	found_i = 2;

      }

    }

    edge.pop_front();

  }

  return i_curr;

}

template <int V_max> inline void ZeroOneBreadthFirstSearch_Body<V_max>::SetWeight() { while( Next() != -1 ){} }
template <int V_max> inline const int& ZeroOneBreadthFirstSearch_Body<V_max>::Solve( const int& init , const int& goal ) { Reset( init ); assert( goal < m_V ); int i = Next(); while( i != -1 && i != goal ){ i = Next(); } return m_weight[goal]; }

template <int V_max,list<pair<int,bool> > E(const int&)> inline list<pair<int,bool> > ZeroOneBreadthFirstSearch<V_max,E>::e( const int& t ) { return E( t ); }


// AAA ライブラリは以上に挿入する。

vector<vector<int> > i_max;
template <typename path_type> list<path_type> E( const int& i )
{
  list<path_type> answer{};
  // list<path_type> answer = e<path_type>[i];
  // VVV 入力によらない処理は以下に挿入する。
  auto [x,y] = EnumHW( i );
  if( y > 0 ){
    int& x_max = i_max[min(x+1,H-1)][y-1];
    if( x_max != -1 ){
      answer.push_back( { EnumHW_inv( x_max , y - 1 ) , false } );
      if( y > 1 ){
	int& x_next = i_max[min(x+1,H-1)][y-2];
	if( x_next != -1 ){
	  answer.push_back( { EnumHW_inv( x_next , y - 2 ) , x_next - x_max > 1 + ( x - x_max ) / 2 } );
	}
      }
      int& x_next = i_max[min(x+1,H-1)][y];
      if( x_next != -1 ){
	answer.push_back( { EnumHW_inv( x_next , y ) , x_next - x_max > 1 + ( x - x_max ) / 2 } );
      }
    }
  }
  if( y < W - 1 ){
    int& x_max = i_max[min(x+1,H-1)][y+1];
    if( x_max != -1 ){
      answer.push_back( { EnumHW_inv( x_max , y + 1 ) , false } );
      if( y < W - 2 ){
	int& x_next = i_max[min(x+1,H-1)][y+2];
	if( x_next != -1 ){
	  answer.push_back( { EnumHW_inv( x_next , y + 2 ) , x_next - x_max > 1 + ( x - x_max ) / 2 } );
	}
      }
      int& x_next = i_max[min(x+1,H-1)][y];
      if( x_next != -1 ){
	answer.push_back( { EnumHW_inv( x_next , y ) , x_next - x_max > 1 + ( x - x_max ) / 2 } );
      }
    }
  }
  // AAA 入力によらない処理は以上に挿入する。
  return answer;
}

ll Guchoku( int N , int M , int K )
{
  ll answer = N + M + K;
  return answer;
}

ll Answer( ll N , ll M , ll K )
{
  ll answer = N + M + K;
  return answer;
}

int main()
{
  UNTIE;
  AUTO_CHECK;
  // START_WATCH;
  TEST_CASE_NUM( 1 );
  START_MAIN;
  // Jikken();

  // // 大きな素数
  // CEXPR( ll , P , 998244353 );
  // // CEXPR( ll , P , 1000000007 ); // Mod<P>を使う時はP2に変更。

  // // データ構造使用畤のNの上限
  // DEXPR( int , bound_N , 100000 , 100 ); // 0が5個
  // // CEXPR( int , bound_N , 1000000000 ); // 0が9個
  // // CEXPR( ll , bound_N , 1000000000000000000 ); // 0が18個

  // // データ構造使用畤のMの上限
  // // CEXPR( TYPE_OF( bound_N ) , bound_M , bound_N );
  // DEXPR( int , bound_M , 100000 , 100 ); // 0が5個
  // // CEXPR( int , bound_M , 1000000000 ); // 0が9個
  // // CEXPR( ll , bound_M , 1000000000000000000 ); // 0が18個

  // // 数
  // CIN( ll , N );
  // CIN( ll , M );
  // CIN( ll , N , M , K );
  // // CIN_ASSERT( N , 1 , bound_N ); // ランダムテスト用。上限のデフォルト値は10^5。
  // // CIN_ASSERT( M , 1 , bound_M ); // ランダムテスト用。上限のデフォルト値は10^5。

  // // 文字列
  // CIN( string , S );
  // CIN( string , T );

  // // 配列
  // CIN_A( ll , A , N );
  // // CIN_A( ll , B , N );
  // // ll A[N];
  // // ll B[N];
  // // ll A[bound_N]; // 関数（コンストラクタ）の引数に使う。長さのデフォルト値は10^5。
  // // ll B[bound_N]; // 関数（コンストラクタ）の引数に使う。長さのデフォルト値は10^5。
  // // FOR( i , 0 , N ){
  // //   cin >> A[i] >> B[i];
  // // }

  // // 順列
  // int P[N];
  // int P_inv[N];
  // FOR( i , 0 , N ){
  //   cin >> P[i];
  //   P_inv[--P[i]] = i;
  // }
  
  // // グラフ
  // FOR( j , 0 , M ){
  //   CIN_ASSERT( uj , 1 , N );
  //   CIN_ASSERT( vj , 1 , N );
  //   uj--;
  //   vj--;
  //   e<int>[uj].push_back( vj );
  //   e<int>[vj].push_back( uj );
  //   // CIN( ll , wj );
  //   // e<path>[uj].push_back( { vj , wj } );
  //   // e<path>[vj].push_back( { uj , wj } );
  // }

  // // 座標圧縮や単一クエリタイプなどのための入力格納
  // T3<ll> data[M];
  // FOR( j , 0 , M ){
  //   CIN( ll , x , y , z );
  //   data[j] = { x , y , z };
  // }

  // // 一般のクエリ
  // CIN( int , Q );
  // // DEXPR( int , bound_Q , 100000 , 100 ); // 基本不要。
  // // CIN_ASSERT( Q , 1 , bound_Q ); // 基本不要。
  // // T3<int> query[Q];
  // // T2<int> query[Q];
  // FOR( q , 0 , Q ){
  //   CIN( int , type );
  //   if( type == 1 ){
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   } else if( type == 2 ){
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   } else {
  //     CIN( int , x , y );
  //     // query[q] = { type , x , y };
  //   }
  //   // CIN( int , x , y );
  //   // // query[q] = { x , y };
  // }
  // // sort( query , query + Q );
  // // FOR( q , 0 , Q ){
  // //   auto& [x,y] = query[q];
  // //   // auto& [type,x,y] = query[q];
  // // }
  
  // データ構造や壁配列使用畤のH,Wの上限
  DEXPR( int , bound_H , 2000 , 20 );
  // DEXPR( int , bound_H , 100000 , 10 ); // 0が5個
  // CEXPR( int , bound_H , 1000000000 ); // 0が9個
  CEXPR( int , bound_W , bound_H );
  static_assert( ll( bound_H ) * bound_W < ll( 1 ) << 31 );
  CEXPR( int , bound_HW , bound_H * bound_W );
  // CEXPR( int , bound_HW , 100000 ); // 0が5個
  // CEXPR( int , bound_HW , 1000000 ); // 0が6個

  // グリッド
  cin >> H >> W;
  // SET_ASSERT( H , 1 , bound_H ); // ランダムテスト用。上限のデフォルト値は10^3。
  // SET_ASSERT( W , 1 , bound_W ); // ランダムテスト用。上限のデフォルト値は10^3。
  H_minus = H - 1;
  W_minus = W - 1;
  HW = H * W;
  // assert( HW <= bound_HW ); // 基本不要。上限のデフォルト値は10^6。
  CIN( int , sx );
  CIN( int , sy );
  CIN( int , gx );
  CIN( int , gy );
  sx--;
  sy--;
  gx--;
  gy--;
  string S[H];
  FOR( i , 0 , H ){
    cin >> S[i];
    // SetEdgeOnGrid( S[i] , i , e<int> );
    SetWallOnGrid( S[i] , i , non_wall );
  }
  // {h,w}へデコード: EnumHW( v )
  // {h,w}をコード: EnumHW_inv( h , w );
  // (i,j)->(k,h)の方向番号を取得: DirectionNumberOnGrid( i , j , k , h );
  // v->wの方向番号を取得: DirectionNumberOnGrid( v , w );
  // 方向番号の反転U<->D、R<->L: ReverseDirectionNumberOnGrid( n );

  i_max.resize( H );
  FOR( i , 0 , H ){
    i_max[i].resize( W );
  }
  FOR( j , 0 , W ){
    int temp = -1;
    FOR( i , 0 , H ){
      non_wall[i][j] ? temp = i : temp;
      i_max[i][j] = temp;
    }
  }
  ZeroOneBreadthFirstSearch<bound_HW,E<pair<int,bool> > > zobfs( HW );
  // // TLに準じる乱択や全探索。デフォルトの猶予は100.0[ms]。
  // CEXPR( double , TL , 2000.0 );
  // while( CHECK_WATCH( TL ) ){

  // }

  // // デバッグ用の愚直解
  // auto guchoku = Guchoku<ll>( N , M , K );

  // ll answer = 0;
  // // MP answer{};
  // FOR( i , 0 , N ){
  //   answer += A[i];
  // }
  // RETURN( answer );
  // // COUT( answer );
  // // COUT_A( A , N );
  RETURN( zobfs.Solve( EnumHW_inv( sx , sy ) , EnumHW_inv( gx , gy ) ) );

  FINISH_MAIN;
}


void Jikken()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  //   	COUT( N , M , K , ":" , Guchoku( N , M , K ) );
  //     }
  //   }
  //   // cout << Guchoku( N ) << ",\n"[N==bound];
  // }
}

void Debug()
{
  // CEXPR( int , bound , 10 );
  // FOREQ( N , 0 , bound ){
  //   FOREQ( M , 0 , bound ){
  //     FOREQ( K , 0 , bound ){
  // 	auto guchoku = Guchoku( N , M , K );
  // 	auto answer = Answer( N , M , K );
  // 	bool match = guchoku == answer;
  //   	COUT( N , M , K , ":" , guchoku , match ? "==" : "!=" , answer );
  // 	if( !match ){
  // 	  return;
  // 	}
  //     }
  //   }
  //   // auto guchoku = Guchoku( N );
  //   // auto answer = Answer( N );
  //   // bool match = guchoku == answer;
  //   // COUT( N , ":" , guchoku , match ? "==" : "!=" , answer );
  //   // if( !match ){
  //   //   return;
  //   // }
  // }
}