/* Problem URL: https://codeforces.com/gym/104555/problem/G */ #include #include #include using namespace std; using namespace __gnu_pbds; template > using ordered_set = tree; #define V vector #define rmin(a, b) a = min(a, b) #define rmax(a, b) a = max(a, b) #define rep(i, lim) for (int i = 0; i < (lim); i++) #define nrep(i, s, lim) for (int i = s; i < (lim); i++) #define repv(i, v) for (auto &i : (v)) #define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; } #define sortv(v) sort(v.begin(), v.end()) #define all(v) (v).begin(), (v).end() using vi = vector; using vvi = vector; using vvvi = vector; using vvvvi = vector; using ll = long long; using vl = vector; using vvl = vector; using vvvl = vector; using vvvvl = vector; #define sq(x) ((x)*(ll)(x)) struct pt { // ponto int x, y; pt(int x_ = 0, int y_ = 0) : x(x_), y(y_) {} bool operator < (const pt p) const { if (x != p.x) return x < p.x; return y < p.y; } bool operator == (const pt p) const { return x == p.x and y == p.y; } pt operator + (const pt p) const { return pt(x+p.x, y+p.y); } pt operator - (const pt p) const { return pt(x-p.x, y-p.y); } pt operator * (const int c) const { return pt(x*c, y*c); } ll operator * (const pt p) const { return x*(ll)p.x + y*(ll)p.y; } ll operator ^ (const pt p) const { return x*(ll)p.y - y*(ll)p.x; } friend istream& operator >> (istream& in, pt& p) { return in >> p.x >> p.y; } }; struct line { // reta pt p, q; line() {} line(pt p_, pt q_) : p(p_), q(q_) {} friend istream& operator >> (istream& in, line& r) { return in >> r.p >> r.q; } }; // PONTO & VETOR ll dist2(pt p, pt q) { // quadrado da distancia return sq(p.x - q.x) + sq(p.y - q.y); } ll sarea2(pt p, pt q, pt r) { // 2 * area com sinal return (q-p)^(r-q); } bool col(pt p, pt q, pt r) { // se p, q e r sao colin. return sarea2(p, q, r) == 0; } bool ccw(pt p, pt q, pt r) { // se p, q, r sao ccw return sarea2(p, q, r) > 0; } int quad(pt p) { // quadrante de um ponto return (p.x<0)^3*(p.y<0); } bool compare_angle(pt p, pt q) { // retorna se ang(p) < ang(q) if (quad(p) != quad(q)) return quad(p) < quad(q); return ccw(q, pt(0, 0), p); } pt rotate90(pt p) { // rotaciona 90 graus return pt(-p.y, p.x); } // RETA bool isinseg(pt p, line r) { // se p pertence ao seg de r pt a = r.p - p, b = r.q - p; return (a ^ b) == 0 and (a * b) <= 0; } bool interseg(line r, line s) { // se o seg de r intersecta o seg de s if (isinseg(r.p, s) or isinseg(r.q, s) or isinseg(s.p, r) or isinseg(s.q, r)) return 1; return ccw(r.p, r.q, s.p) != ccw(r.p, r.q, s.q) and ccw(s.p, s.q, r.p) != ccw(s.p, s.q, r.q); } int segpoints(line r) { // numero de pontos inteiros no segmento return 1 + __gcd(abs(r.p.x - r.q.x), abs(r.p.y - r.q.y)); } double get_t(pt v, line r) { // retorna t tal que t*v pertence a reta r return (r.p^r.q) / (double) ((r.p-r.q)^v); } // POLIGONO // quadrado da distancia entre os retangulos a e b (lados paralelos aos eixos) // assume que ta representado (inferior esquerdo, superior direito) ll dist2_rect(pair a, pair b) { int hor = 0, vert = 0; if (a.second.x < b.first.x) hor = b.first.x - a.second.x; else if (b.second.x < a.first.x) hor = a.first.x - b.second.x; if (a.second.y < b.first.y) vert = b.first.y - a.second.y; else if (b.second.y < a.first.y) vert = a.first.y - b.second.y; return sq(hor) + sq(vert); } ll polarea2(vector v) { // 2 * area do poligono ll ret = 0; for (int i = 0; i < v.size(); i++) ret += sarea2(pt(0, 0), v[i], v[(i + 1) % v.size()]); return abs(ret); } // se o ponto ta dentro do poligono: retorna 0 se ta fora, // 1 se ta no interior e 2 se ta na borda int inpol(vector& v, pt p) { // O(n) int qt = 0; for (int i = 0; i < v.size(); i++) { if (p == v[i]) return 2; int j = (i+1)%v.size(); if (p.y == v[i].y and p.y == v[j].y) { if ((v[i]-p)*(v[j]-p) <= 0) return 2; continue; } bool baixo = v[i].y < p.y; if (baixo == (v[j].y < p.y)) continue; auto t = (p-v[i])^(v[j]-v[i]); if (!t) return 2; if (baixo == (t > 0)) qt += baixo ? 1 : -1; } return qt != 0; } vector convex_hull(vector v) { // convex hull - O(n log(n)) sort(v.begin(), v.end()); v.erase(unique(v.begin(), v.end()), v.end()); if (v.size() <= 1) return v; vector l, u; for (int i = 0; i < v.size(); i++) { while (l.size() > 1 and !ccw(l.end()[-2], l.end()[-1], v[i])) l.pop_back(); l.push_back(v[i]); } for (int i = v.size() - 1; i >= 0; i--) { while (u.size() > 1 and !ccw(u.end()[-2], u.end()[-1], v[i])) u.pop_back(); u.push_back(v[i]); } l.pop_back(); u.pop_back(); for (pt i : u) l.push_back(i); return l; } ll interior_points(vector v) { // pontos inteiros dentro de um poligono simples ll b = 0; for (int i = 0; i < v.size(); i++) b += segpoints(line(v[i], v[(i+1)%v.size()])) - 1; return (polarea2(v) - b) / 2 + 1; } struct convex_pol { vector pol; // nao pode ter ponto colinear no convex hull convex_pol() {} convex_pol(vector v) : pol(convex_hull(v)) {} // se o ponto ta dentro do hull - O(log(n)) bool is_inside(pt p) { if (pol.size() == 0) return false; if (pol.size() == 1) return p == pol[0]; int l = 1, r = pol.size(); while (l < r) { int m = (l+r)/2; if (ccw(p, pol[0], pol[m])) l = m+1; else r = m; } if (l == 1) return isinseg(p, line(pol[0], pol[1])); if (l == pol.size()) return false; return !ccw(p, pol[l], pol[l-1]); } // ponto extremo em relacao a cmp(p, q) = p mais extremo q // (copiado de https://github.com/gustavoM32/caderno-zika) int extreme(const function& cmp) { int n = pol.size(); auto extr = [&](int i, bool& cur_dir) { cur_dir = cmp(pol[(i+1)%n], pol[i]); return !cur_dir and !cmp(pol[(i+n-1)%n], pol[i]); }; bool last_dir, cur_dir; if (extr(0, last_dir)) return 0; int l = 0, r = n; while (l+1 < r) { int m = (l+r)/2; if (extr(m, cur_dir)) return m; bool rel_dir = cmp(pol[m], pol[l]); if ((!last_dir and cur_dir) or (last_dir == cur_dir and rel_dir == cur_dir)) { l = m; last_dir = cur_dir; } else r = m; } return l; } int max_dot(pt v) { return extreme([&](pt p, pt q) { return p*v > q*v; }); } pair tangents(pt p) { auto L = [&](pt q, pt r) { return ccw(p, r, q); }; auto R = [&](pt q, pt r) { return ccw(p, q, r); }; return {extreme(L), extreme(R)}; } }; template auto operator<<(ostream &os, const vector &vec)->ostream& { os << vec[0]; for (size_t i = 1; i < vec.size(); i++) { os << ' ' << vec[i]; } os << '\n'; return os; } template auto operator>>(istream &is, vector &vec)->istream& { for (auto &i : vec) { is >> i; } return is; } template auto operator<<(ostream &os, const vector> &vec)->ostream& { for (auto &i : vec) { os << i[0]; for (size_t j = 1; j < i.size(); j++) { os << ' ' << i[j]; } os << '\n'; } return os; } template auto operator>>(istream &is, vector> &vec)->istream& { for (auto &i : vec) { for (auto &j : i) { is >> j; } } return is; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int n; cin >> n; map var; V points(n); rep(i, n) { cin >> points[i].x >> points[i].y; var[{points[i].x, points[i].y}] = i + 1; } convex_pol conv(points); set ans; repv(i, points) { if (inpol(conv.pol, i) == 2) { ans.insert(var[i]); } } repv(i, ans) { cout << i << ' '; } cout << '\n'; }