#line 1 "library/Template/template.hpp" #include using namespace std; #define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++) #define ALL(v) (v).begin(),(v).end() #define UNIQUE(v) sort(ALL(v)),(v).erase(unique(ALL(v)),(v).end()) #define SZ(v) (int)v.size() #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(v,x) int(lower_bound(ALL(v),(x))-(v).begin()) #define UB(v,x) int(upper_bound(ALL(v),(x))-(v).begin()) using ll=long long int; using ull=unsigned long long; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; templateinline bool chmax(T& a,T b){if(ainline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} templateT ceil(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?(x+y-1)/y:x/y);} templateT floor(T x,U y){assert(y!=0); if(y<0)x=-x,y=-y; return (x>0?x/y:(x-y+1)/y);} templateint popcnt(T x){return __builtin_popcountll(x);} templateint topbit(T x){return (x==0?-1:63-__builtin_clzll(x));} templateint lowbit(T x){return (x==0?-1:__builtin_ctzll(x));} #line 2 "library/Utility/fastio.hpp" #include class FastIO{ static constexpr int L=1<<16; char rdbuf[L]; int rdLeft=0,rdRight=0; inline void reload(){ int len=rdRight-rdLeft; memmove(rdbuf,rdbuf+rdLeft,len); rdLeft=0,rdRight=len; rdRight+=fread(rdbuf+len,1,L-len,stdin); } inline bool skip(){ for(;;){ while(rdLeft!=rdRight and rdbuf[rdLeft]<=' ')rdLeft++; if(rdLeft==rdRight){ reload(); if(rdLeft==rdRight)return false; } else break; } return true; } template::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdLeft=rdRight)reload(); x=0; while(rdbuf[rdLeft]>='0' and rdLeft::value,int> =0>inline bool _read(T& x){ if(!skip())return false; if(rdLeft+20>=rdRight)reload(); bool neg=false; if(rdbuf[rdLeft]=='-'){ neg=true; rdLeft++; } x=0; while(rdbuf[rdLeft]>='0' and rdbuf[rdLeft]<='9' and rdLeft='0' and rdbuf[rdLeft]<='9' and rdLeft=rdRight)reload(); x=rdbuf[rdLeft++]; return true; } inline bool _read(string& x){ if(!skip())return false; for(;;){ int pos=rdLeft; while(pos' ')pos++; x.append(rdbuf+rdLeft,pos-rdLeft); if(rdLeft==pos)break; rdLeft=pos; if(rdLeft==rdRight)reload(); else break; } return true; } templateinline bool _read(vector& v){ for(auto& x:v){ if(!_read(x))return false; } return true; } char wtbuf[L],tmp[50]; int wtRight=0; inline void _write(const char& x){ if(wtRight>L-32)flush(); wtbuf[wtRight++]=x; } inline void _write(const string& x){ for(auto& c:x)_write(c); } template::value,int> =0>inline void _write(T x){ if(wtRight>L-32)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); if (__builtin_expect(x == std::numeric_limits::min(), 0)) { switch (sizeof(x)) { case 2: _write("32768"); return; case 4: _write("2147483648"); return; case 8: _write("9223372036854775808"); return; } } x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__int128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } else if(x<0){ _write('-'); x=-x; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(__uint128_t x){ if(wtRight>L-40)flush(); if(x==0){ _write('0'); return; } int pos=0; while(x!=0){ tmp[pos++]=char((x%10)|48); x/=10; } rep(i,0,pos)wtbuf[wtRight+i]=tmp[pos-1-i]; wtRight+=pos; } inline void _write(double x){ ostringstream oss; oss << fixed << setprecision(15) << double(x); string s = oss.str(); _write(s); } templateinline void _write(const vector& v){ rep(i,0,v.size()){ if(i)_write(' '); _write(v[i]); } } public: FastIO(){} ~FastIO(){flush();} inline void read(){} template inline void read(Head& head,Tail&... tail){ assert(_read(head)); read(tail...); } templateinline void write(){if(ln)_write('\n');} template inline void write(const Head& head,const Tail&... tail){ _write(head); write(tail...); if(space)_write(' '); } inline void flush(){ fwrite(wtbuf,1,wtRight,stdout); wtRight=0; } }; /** * @brief Fast IO */ #line 3 "sol.cpp" #include using fr = boost::multiprecision::cpp_rational; FastIO io; int main() { auto yes = [&] { io.write("Yes"); exit(0); }; auto no = [&] { io.write("No"); exit(0); }; int n; io.read(n); vector a(n), b(n), c(n), d(n); io.read(a, b, c, d); using P = pair; vector ord1(n), ord2(n); iota(ALL(ord1), 0); iota(ALL(ord2), 0); sort(ALL(ord1), [&](int i, int j) { return fr(b[i], a[i]) < fr(b[j], a[j]); }); sort(ALL(ord2), [&](int i, int j) { return fr(d[i], c[i]) < fr(d[j], c[j]); }); vector

L({{fr(0), fr(0)}}), U = L; for (auto &i : ord1) { fr x = L.back().first + fr(a[i]); fr y = L.back().second + fr(b[i]); L.push_back({x, y}); } for (auto &i : ord2) { fr x = U.back().first + fr(c[i]); fr y = U.back().second + fr(d[i]); U.push_back({x, y}); } rep(i, 0, SZ(U)) { rep(j, 0, SZ(L) - 1) { P pq = {L[j + 1].first - L[j].first, L[j + 1].second - L[j].second}; P pr = {U[i].first - L[j].first, U[i].second - L[j].second}; if (pq.first * pr.second - pq.second * pr.first < fr(0)) no(); } } if (ord1 == ord2) yes(); cerr << "CP3" << '\n'; fr x, y; rep(i, 0, n - 1) { auto [xi2, yi2] = L[i + 2]; fr direct = (yi2 - y) / (xi2 - x); fr mx; rep(i, 0, SZ(U)) { if (x < U[i].first and U[i].first < xi2) { fr slope=(U[i].second - y) / (U[i].first - x); if(mx==0 or mx>slope)mx=slope; } } if (mx == fr(0) or direct <= mx) yes(); // pass auto [xi1, yi1] = L[i + 1]; fr nslope = (yi2 - yi1) / (xi2 - xi1); if (mx == nslope) { x = xi1, y = yi1; continue; } fr nx = (mx * x - nslope * xi1 - y + yi1) / (mx - nslope); fr ny = mx * (nx - x) + y; x = nx, y = ny; cerr << i << '\n'; } no(); return 0; }