#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using namespace placeholders; using LL = long long; using ULL = unsigned long long; using VI = vector< int >; using VVI = vector< vector< int > >; using VS = vector< string >; using ISS = istringstream; using OSS = ostringstream; using PII = pair< int, int >; using VPII = vector< pair< int, int > >; template < typename T = int > using VT = vector< T >; template < typename T = int > using VVT = vector< vector< T > >; template < typename T = int > using LIM = numeric_limits< T >; template < typename T > inline istream& operator>>( istream &s, vector< T > &v ){ for ( T &t : v ) { s >> t; } return s; } template < typename T > inline ostream& operator<<( ostream &s, const vector< T > &v ){ for ( int i = 0; i < int( v.size() ); ++i ){ s << ( " " + !i ) << v[i]; } return s; } void in_impl(){}; template < typename T, typename... TS > void in_impl( T &head, TS &... tail ){ cin >> head; in_impl( tail ... ); } #define IN( T, ... ) T __VA_ARGS__; in_impl( __VA_ARGS__ ); template < typename T > struct getv_fmt; template <> struct getv_fmt< int >{ static constexpr const char *fmt = "%d"; }; template <> struct getv_fmt< long long >{ static constexpr const char *fmt = "%lld"; }; template < typename T > void getv( std::vector< T > &v ){ for_each( begin( v ), end( v ), []( T &a ){ scanf( getv_fmt< T >::fmt, &a ); } ); }; template < typename T > inline T fromString( const string &s ) { T res; istringstream iss( s ); iss >> res; return res; } template < typename T > inline string toString( const T &a ) { ostringstream oss; oss << a; return oss.str(); } #define NUMBERED( name, number ) NUMBERED2( name, number ) #define NUMBERED2( name, number ) name ## _ ## number #define REP1( n ) REP2( NUMBERED( REP_COUNTER, __LINE__ ), n ) #define REP2( i, n ) REP3( i, 0, n ) #define REP3( i, m, n ) for ( int i = ( int )( m ); i < ( int )( n ); ++i ) #define GET_REP( a, b, c, F, ... ) F #define REP( ... ) GET_REP( __VA_ARGS__, REP3, REP2, REP1 )( __VA_ARGS__ ) #define FOR( e, c ) for ( auto &&e : c ) #define ALL( c ) begin( c ), end( c ) #define AALL( a ) ( remove_all_extents< decltype( a ) >::type * )a, ( remove_all_extents< decltype( a ) >::type * )a + sizeof( a ) / sizeof( remove_all_extents< decltype( a ) >::type ) #define DRANGE( c, p ) begin( c ), begin( c ) + ( p ), end( c ) #define SZ( v ) ( (int)( v ).size() ) #define EXIST( c, e ) ( ( c ).find( e ) != ( c ).end() ) template < typename T > inline bool chmin( T &a, const T &b ){ if ( b < a ) { a = b; return true; } return false; } template < typename T > inline bool chmax( T &a, const T &b ){ if ( a < b ) { a = b; return true; } return false; } #define PB push_back #define EM emplace #define EB emplace_back #define BI back_inserter #define MP make_pair #define fst first #define snd second #define DUMP( x ) cerr << #x << " = " << ( x ) << endl #include using Point = complex< double >; constexpr double EPS = 1e-15; constexpr double PI = acos( -1 ); constexpr Point O( 0, 0 ); // 入力ストリームから実数二つをとって Point へ istream& operator>> ( istream &s, Point &a ) { double r, i; s >> r >> i; a = Point( r, i ); return s; } // 内積(ドット積) double dot( const Point &a, const Point &b ) { return a.real() * b.real() + a.imag() * b.imag(); } // 外積(クロス積) double cross( const Point &a, const Point &b ) { return a.real() * b.imag() - a.imag() * b.real(); } // 点 p が線分 ( q1, q2 ) に乗っているか // include : dot, cross bool intersectPS( const Point &p, const Point &q1, const Point &q2 ) { // 端点からの p へのベクトルの外積が 0 ⇔ 端点からのベクトルが並行 ⇔ 直線 ( q1, q2 ) に点 p が乗る // p から端点へのベクトルの内積が 0 以下 ⇔ 点 p が q1, q2 の内側にある return abs( cross( q1 - p, q2 - p ) ) <= EPS && dot( q1 - p, q2 - p ) <= EPS; } // 直線 ( p1, p2 ) と直線 ( q1, q2 ) の交点 // include : cross Point intersectionLL( const Point &p1, const Point &p2, const Point &q1, const Point &q2 ) { return p1 + ( p2 - p1 ) * ( cross( q2 - q1, q1 - p1 ) / cross( q2 - q1, p2 - p1 ) ); } // 線分 ( p1, p2 ) と線分 ( q1, q2 ) が交差するか // include : cross, intersectPS, intersectionLL bool intersectSS( const Point &p1, const Point &p2, const Point &q1, const Point &q2 ) { if ( abs( cross( p1 - p2, q1 - q2 ) ) <= EPS ) // 二直線が並行な場合 { // 片方の線分に他方の端点が乗るか return intersectPS( q1, p1, p2 ) || intersectPS( q2, p1, p2 ) || intersectPS( p1, q1, q2 ) || intersectPS( p2, q1, q2 ); } else { // 二直線の交点が両方の線分に乗るか Point r( intersectionLL( p1, p2, q1, q2 ) ); return intersectPS( r, p1, p2 ) && intersectPS( r, q1, q2 ); } } int num_of_intersect( const VT< Point > &ps, const VT< Point > &qs, const Point &a, const Point &b ) { const int N = SZ( ps ); int res = 0; const Point aa = a + ( b - a ) * 1000.; const Point bb = b + ( a - b ) * 1000.; REP( i, N ) { res += intersectSS( ps[i], qs[i], aa, bb ); } return res; } int main() { cin.tie( 0 ); ios::sync_with_stdio( false ); cout << setprecision( 12 ) << fixed; IN( int, N ); VT< Point > ps( N ), qs( N ); REP( i, N ) { cin >> ps[i] >> qs[i]; } int res = 0; REP( i, N ) { REP( j, i ) { chmax( res, num_of_intersect( ps, qs, ps[i], ps[j] ) ); chmax( res, num_of_intersect( ps, qs, ps[i], qs[j] ) ); chmax( res, num_of_intersect( ps, qs, qs[i], ps[j] ) ); chmax( res, num_of_intersect( ps, qs, qs[i], qs[j] ) ); } } cout << res << endl; return 0; }