#include using namespace std; typedef long long ll; typedef pair< int, int > pii; typedef vector< int > vi; typedef vector< vi > vvi; typedef vector< ll > vl; typedef vector< vl > vvl; typedef vector< pii > vp; typedef vector< vp > vvp; typedef vector< string > vs; typedef vector< double > vd; typedef vector< vd > vvd; template< class T1, class T2 > int upmin( T1 &x, T2 v ){ if( x > v ){ x = v; return 1; } return 0; } template< class T1, class T2 > int upmax( T1 &x, T2 v ){ if( x < v ){ x = v; return 1; } return 0; } const int INF = 0x3f3f3f3f; int N; vi X, Y; void init(){ cin >> N; X = Y = vi( N ); for( int i = 0; i < N; ++i ) cin >> X[ i ] >> Y[ i ]; } struct dsu{ vi fa; dsu( int sz ){ fa = vi( sz ); for( int i = 0; i < sz; ++i ) fa[ i ] = i; } int find( int x ){ return fa[ x ] == x ? x : fa[ x ] = find( fa[ x ] ); } int merge( int a, int b ){ int x = find( a ); int y = find( b ); if( x == y ) return 0; fa[ x ] = y; return 1; } }; map< int, vi > group; int eu_dis2( int a, int b, int x, int y ){ int dx = a - x; int dy = b - y; return dx * dx + dy * dy; } double eu_dis( int a, int b, int x, int y ){ double dx = a - x; double dy = b - y; return sqrt( dx * dx + dy * dy ); } void preprocess(){ map< pii, vi > box; for( int i = 0; i < N; ++i ) box[ make_pair( ( X[ i ] + 10000 ) /10, ( Y[ i ] + 10000 ) / 10 ) ].emplace_back( i ); dsu *uf = new dsu( N ); for( auto it = box.begin(); it != box.end(); ++it ){ for( int i = 0; i < ( it->second ).size(); ++i ) for( int j = i + 1; j < ( it->second ).size(); ++j ) if( eu_dis2( X[ ( it->second )[ i ] ], Y[ ( it->second )[ i ] ], X[ ( it->second )[ j ] ], Y[ ( it->second )[ j ] ] ) <= 100 ) uf->merge( ( it->second )[ i ], ( it->second )[ j ] ); static const int dx[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; static const int dy[] = { 1, 0, -1, 0, 1, -1, 1, -1 }; for( int di = 0; di < 8; ++di ){ pii key = make_pair( ( it->first ).first + dx[ di ], ( it->first ).second + dy[ di ] ); if( not box.count( key ) ) continue; auto &cur = it->second; auto &adj = box[ key ]; for( auto &u : cur ) for( auto &v : adj ) if( eu_dis2( X[ u ], Y[ u ], X[ v ], Y[ v ] ) <= 100 ) uf->merge( u, v ); } } for( int i = 0; i < N; ++i ) group[ uf->find( i ) ].emplace_back( i ); } void solve(){ double ans = N == 0 ? 1.0 : 2.0; for( auto it = group.begin(); it != group.end(); ++it ){ sort( ( it->second ).begin(), ( it->second ).end(), [ & ]( int i, int j ){ return X[ i ] != X[ j ] ? X[ i ] < X[ j ] : Y[ i ] < Y[ j ]; } ); vector< int > stk; function< double ( double, double, double, double ) > cross = [ & ]( double x1, double y1, double x2, double y2 ){ return x1 * y2 - y1 * x2; }; for( int i = 0; i < ( it->second ).size(); ++i ){ while( stk.size() >= 2 ){ int s = stk.size(); double dx1 = X[ stk[ s - 1 ] ] - X[ stk[ s - 2 ] ]; double dy1 = Y[ stk[ s - 1 ] ] - Y[ stk[ s - 2 ] ]; double dx2 = X[ ( it->second )[ i ] ] - X[ stk[ s - 2 ] ]; double dy2 = Y[ ( it->second )[ i ] ] - Y[ stk[ s - 2 ] ]; if( cross( dx1, dy1, dx2, dy2 ) <= 0.0 ) stk.pop_back(); else break; } stk.emplace_back( ( it->second )[ i ] ); } int h = stk.size(); for( int i = ( int ) ( it->second ).size() - 2; i >= 0; --i ){ while( stk.size() > h ){ int s = stk.size(); double dx1 = X[ stk[ s - 1 ] ] - X[ stk[ s - 2 ] ]; double dy1 = Y[ stk[ s - 1 ] ] - Y[ stk[ s - 2 ] ]; double dx2 = X[ ( it->second )[ i ] ] - X[ stk[ s - 2 ] ]; double dy2 = Y[ ( it->second )[ i ] ] - Y[ stk[ s - 2 ] ]; if( cross( dx1, dy1, dx2, dy2 ) <= 0.0 ) stk.pop_back(); else break; } stk.emplace_back( ( it->second )[ i ] ); } stk.pop_back(); // start h = stk.size(); for( int i = 0; i < h; ++i ) stk.emplace_back( stk[ i ] ); for( int i = 0, j = 1; i < h; ++i ){ while( eu_dis2( X[ stk[ i ] ], Y[ stk[ i ] ], X[ stk[ j ] ], Y[ stk[ j ] ] ) <= eu_dis2( X[ stk[ i ] ], Y[ stk[ i ] ], X[ stk[ j + 1 ] ], Y[ stk[ j + 1 ] ] ) ) ++j, assert( j < stk.size() ); upmax( ans, 2.0 + eu_dis( X[ stk[ i ] ], Y[ stk[ i ] ], X[ stk[ j ] ], Y[ stk[ j ] ] ) ); } } cout << fixed << setprecision( 8 ) << ans << endl; } signed main(){ ios::sync_with_stdio( 0 ); init(); preprocess(); solve(); return 0; }