#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" using namespace std; #include<bits/stdc++.h> #line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp" namespace noya2 { template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &p){ os << p.first << " " << p.second; return os; } template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &p){ is >> p.first >> p.second; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &v){ int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; } void in() {} template <typename T, class... U> void in(T &t, U &...u){ cin >> t; in(u...); } void out() { cout << "\n"; } template <typename T, class... U, char sep = ' '> void out(const T &t, const U &...u){ cout << t; if (sizeof...(u)) cout << sep; out(u...); } template<typename T> void out(const vector<vector<T>> &vv){ int s = (int)vv.size(); for (int i = 0; i < s; i++) out(vv[i]); } struct IoSetup { IoSetup(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetup_noya2; } // namespace noya2 #line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp" namespace noya2{ const int iinf = 1'000'000'007; const long long linf = 2'000'000'000'000'000'000LL; const long long mod998 = 998244353; const long long mod107 = 1000000007; const long double pi = 3.14159265358979323; const vector<int> dx = {0,1,0,-1,1,1,-1,-1}; const vector<int> dy = {1,0,-1,0,1,-1,-1,1}; const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const string alp = "abcdefghijklmnopqrstuvwxyz"; const string NUM = "0123456789"; void yes(){ cout << "Yes\n"; } void no(){ cout << "No\n"; } void YES(){ cout << "YES\n"; } void NO(){ cout << "NO\n"; } void yn(bool t){ t ? yes() : no(); } void YN(bool t){ t ? YES() : NO(); } } // namespace noya2 #line 2 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" #line 6 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp" namespace noya2{ unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){ if (a == 0 || b == 0) return a + b; int n = __builtin_ctzll(a); a >>= n; int m = __builtin_ctzll(b); b >>= m; while (a != b) { int mm = __builtin_ctzll(a - b); bool f = a > b; unsigned long long c = f ? a : b; b = f ? b : a; a = (c - b) >> mm; } return a << std::min(n, m); } template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(std::abs(a),std::abs(b))); } long long sqrt_fast(long long n) { if (n <= 0) return 0; long long x = sqrt(n); while ((x + 1) * (x + 1) <= n) x++; while (x * x > n) x--; return x; } template<typename T> T floor_div(const T n, const T d) { assert(d != 0); return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0); } template<typename T> T ceil_div(const T n, const T d) { assert(d != 0); return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0); } template<typename T> void uniq(std::vector<T> &v){ std::sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()); } template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; } } // namespace noya2 #line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp" #define rep(i,n) for (int i = 0; i < (int)(n); i++) #define repp(i,m,n) for (int i = (m); i < (int)(n); i++) #define reb(i,n) for (int i = (int)(n-1); i >= 0; i--) #define all(v) (v).begin(),(v).end() using ll = long long; using ld = long double; using uint = unsigned int; using ull = unsigned long long; using pii = pair<int,int>; using pll = pair<ll,ll>; using pil = pair<int,ll>; using pli = pair<ll,int>; namespace noya2{ /* ~ (. _________ . /) */ } using namespace noya2; #line 2 "c.cpp" namespace geometry2d { template<class Rat> requires std::constructible_from<Rat, int> && std::totally_ordered<Rat> constexpr int sign(const Rat &x){ const Rat Rat0 = Rat(0); return (x < Rat0 ? -1 : x > Rat0 ? 1 : 0); } template<class Rat> struct point { Rat x, y; point () {} point (Rat _x, Rat _y) : x(_x), y(_y) {} point &operator+=(const point &r){ x += r.x; y += r.y; return *this; } point &operator-=(const point &r){ x -= r.x; y -= r.y; return *this; } point operator+() const { return *this; } point operator-() const { x = -x; y = -y; return *this; } point &operator*=(const Rat &a){ x *= a; y *= a; return *this; } point &operator/=(const Rat &a){ x /= a; y /= a; return *this; } friend point operator+(const point& lhs, const point& rhs){ return point(lhs) += rhs; } friend point operator-(const point& lhs, const point& rhs){ return point(lhs) -= rhs; } friend point operator*(const point& lhs, const Rat& a){ return point(lhs) *= a; } friend point operator*(const Rat& a, const point& rhs){ return point(rhs) *= a; } friend point operator/(const point& lhs, const Rat& a){ return point(lhs) /= a; } auto operator<=>(const point&) const = default; friend std::ostream &operator<<(std::ostream &os, const point& p){ return os << p.x << ' ' << p.y; } friend std::istream &operator>>(std::istream &is, point &a){ Rat _x, _y; is >> _x >> _y; a = point(_x, _y); return (is); } friend Rat norm(const point &a) { return a.x*a.x + a.y*a.y; } friend Rat dot(const point &a, const point &b){ return a.x*b.x + a.y*b.y; } friend Rat cross(const point &a, const point &b){ return a.x*b.y - a.y*b.x; } friend int quadrant_atan2(const point &a){ // not origin point // ceil ( atan2(y,x) / (pi/2) ) int signx = sign(a.x); int signy = sign(a.y); if (signx <= 0 && signy < 0) return -1; if (signx > 0 && signy <= 0) return 0; if (signx >= 0 && signy > 0) return 1; if (signx < 0 && signy >= 0) return 2; // origin point x == 0 && y == 0 return 0; } friend int ccw(const point &a, point b, point c){ b -= a; c -= a; int signcr = sign(cross(b, c)); if (signcr > 0){ // ccw // c // a --> b return 1; } if (signcr < 0){ // cw // a --> b // c return -1; } if (sign(dot(b, c)) < 0){ // c a --> b return 2; } if (norm(b) < norm(c)){ // a --> b c return -2; } // a - c -> b return 0; } friend point rot90(const point &a){ return point(-a.y, a.x); } }; template<class Rat> using vec = point<Rat>; template<class Rat> struct arg_less { constexpr bool operator()(const point<Rat> &l, const point<Rat> &r){ int lq = quadrant_atan2(l); int rq = quadrant_atan2(r); if (lq == rq){ return sign(cross(l,r)) > 0; } return lq < rq; } }; template<class Rat> void arg_sort(std::vector<point<Rat>> &a){ sort(a.begin(), a.end(), arg_less<Rat>{}); } template<class Point> std::vector<int> upper_convex_hull_index(const std::vector<Point> &a){ if (a.empty()) return {}; std::vector<int> ids(a.size()); iota(ids.begin(), ids.end(), 0); std::sort(ids.begin(), ids.end(), [&](int l, int r){ return a[l] < a[r]; }); std::vector<int> st(a.size()); int ptr = 0; for (int i : ids){ if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) ptr--; while (ptr >= 2){ int c = st[ptr-1]; int p = st[ptr-2]; if (sign(cross(a[i] - a[c], a[c] - a[p])) > 0){ break; } ptr--; } st[ptr++] = i; } st.resize(ptr); return st; } template<class Point> std::vector<int> lower_convex_hull_index(const std::vector<Point> &a){ if (a.empty()) return {}; std::vector<int> ids(a.size()); iota(ids.begin(), ids.end(), 0); std::sort(ids.begin(), ids.end(), [&](int l, int r){ return a[l] < a[r]; }); std::vector<int> st(a.size()); int ptr = 0; for (int i : ids){ if (ptr >= 1 && a[st[ptr-1]].x == a[i].x) continue; while (ptr >= 2){ int c = st[ptr-1]; int p = st[ptr-2]; if (sign(cross(a[c] - a[p], a[i] - a[c])) > 0){ break; } ptr--; } st[ptr++] = i; } st.resize(ptr); return st; } template<class Point> std::vector<int> convex_hull_index(const std::vector<Point> &a){ if (a.empty()) return {}; auto upper = upper_convex_hull_index(a); auto lower = lower_convex_hull_index(a); if (upper.size() == 1u){ // lower.size() == 1u if (a[upper.front()] == a[lower.front()]){ return {upper.front()}; } return {lower.front(), upper.front()}; } if (a[upper.back()] == a[lower.back()]){ lower.pop_back(); } lower.insert(lower.end(), upper.rbegin(), upper.rend()); if (a[upper.front()] == a[lower.front()]) lower.pop_back(); return lower; } template<class Rat> struct line { point<Rat> end0, end1; line (const point<Rat> &_end0, const point<Rat> &_end1) : end0(_end0), end1(_end1) { assert(end0 != end1); } auto operator<=>(const line &) const = default; bool operator==(const line &that) const { return is_parallel(*this, that) && has_common_point(*this, that.end0); } vec<Rat> direction() const { return end1 - end0; } friend bool has_common_point(const line &a, const point<Rat> &b){ return sign(cross(a.direction(), b - a.end0)) == 0; } friend bool has_common_point(const line &a, const line &b){ return !is_parallel(a, b) || has_common_point(a, b.end0); } friend point<Rat> common_point(const line &a, const line &b){ // assert(has_common_point(a, b)); if (is_parallel(a, b)){ return a.end0; } return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction()); } friend point<Rat> projection(const line &a, const point<Rat> &b){ auto dir = a.direction(); return a.end0 + dir * (dot(dir, b - a.end0) / norm(dir)); } friend point<Rat> reflection(const line &a, const point<Rat> &b){ auto prj = projection(a, b); return prj + prj - b; } }; template<class Rat> struct segment { point<Rat> end0, end1; segment (const point<Rat> &_end0, const point<Rat> &_end1) : end0(_end0), end1(_end1) { assert(end0 != end1); } auto operator<=>(const segment &) const = default; bool operator==(const segment &that) const { return (end0 == that.end0 && end1 == that.end1) || (end1 == that.end0 && end0 == that.end1); } vec<Rat> direction() const { return end1 - end0; } friend bool has_common_point(const segment &a, const segment &b){ return ccw(a.end0, a.end1, b.end0) * ccw(a.end0, a.end1, b.end1) <= 0 && ccw(b.end0, b.end1, a.end0) * ccw(b.end0, b.end1, a.end1) <= 0; } friend bool has_common_point(const segment &a, const point<Rat> &b){ return ccw(a.end0, a.end1, b) == 0; } friend point<Rat> common_point(const segment &a, const segment &b){ // assert(has_common_point(a, b)); if (is_parallel(a, b)){ if (has_common_point(a, b.end0)){ return b.end0; } if (has_common_point(a, b.end1)){ return b.end1; } return a.end0; } return a.end0 + a.direction() * cross(b.end0 - a.end0, b.end1 - b.end0) / cross(a.direction(), b.direction()); } line<Rat> as_line() const { return line<Rat>(end0, end1); } }; template<class T> concept hasDirection = requires (T a){ a.direction(); }; template<hasDirection T, hasDirection U> bool is_parallel(const T &a, const U &b){ return sign(cross(a.direction(), b.direction())) == 0; } template<hasDirection T, hasDirection U> bool is_orthogonal(const T &a, const U &b){ return sign(dot(a.direction(), b.direction())) == 0; } template<class Rat> line<Rat> perpendicular_bisector(const point<Rat> &p1, const point<Rat> &p2){ auto ctr = (p1 + p2) / Rat{2}; auto dir = rot90(p2 - p1); return line<Rat>(ctr, ctr + dir); } } // namespace geometry2d #include <boost/rational.hpp> using rat = boost::rational<ll>; using vec = geometry2d::point<rat>; vec input(){ ll x, y; in(x,y); vec ret(rat(x,1),rat(y,1)); return ret; } void solve(){ int n; in(n); vector<vec> a(n); rep(i,n){ a[i] = input(); } a.emplace_back(a[0]); a.emplace_back(a[1]); rep(i,n){ vec p0 = a[i]; vec p1 = a[i+1]; vec p2 = a[i+2]; if (p0 == p1 || p1 == p2){ out(0); return ; } geometry2d::line l01(p0,p1); geometry2d::line l12(p1,p2); if (l01 == l12){ out(0); return ; } } rep(i,n) repp(j,i+1,n){ geometry2d::segment l0(a[i],a[i+1]); geometry2d::segment l1(a[j],a[j+1]); if (!has_common_point(l0,l1)) continue; { int same = 0; rep(p,2) rep(q,2){ if ((p == 0 ? l0.end0 : l0.end1) == (q == 0 ? l1.end0 : l1.end1)){ same++; } } if (same != 1){ out(0); return ; } } if (l0.end0 == l1.end1){ swap(l1.end0,l1.end1); } else if (l0.end1 == l1.end0){ swap(l0.end0,l0.end1); } else if (l0.end1 == l1.end1){ swap(l0.end0,l0.end1); swap(l1.end0,l1.end1); } assert(l0.end0 == l1.end0); if (has_common_point(l0,l1.end1)){ out(0); return ; } } a.pop_back(); a.pop_back(); auto comp = geometry2d::arg_less<rat>{}; rep(i,n){ vector<int> ids; rep(j,n){ if (a[i] == a[j]) continue; ids.emplace_back(j); } int sm = 0, bg = 0; int sz = ids.size(); rep(j,sz){ (comp(a[ids[j]]-a[i],a[ids[j == sz-1 ? 0 : j+1]]-a[i]) ? bg : sm)++; } if (sm <= 1 || bg <= 1){ out(1); return ; } } out(-1); } int main(){ int t = 1; //in(t); while (t--) { solve(); } }