#include #include using namespace std; using namespace atcoder; #define overload4(_1, _2, _3, _4, name, ...) name #define rep1(n) for(int i = 0; i < (int)(n); ++i) #define rep2(i, n) for(int i = 0; i < (int)(n); ++i) #define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i) #define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c)) #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i) #define ALL(a) a.begin(), a.end() #define Sort(a) sort(a.begin(), a.end()) #define RSort(a) sort(a.rbegin(), a.rend()) typedef long long int ll; typedef unsigned long long ul; typedef long double ld; typedef vector vi; typedef vector vll; typedef vector vc; typedef vector vst; typedef vector vd; typedef vector vld; typedef pair P; template long long sum(const T& a){ return accumulate(a.begin(), a.end(), 0LL); } template auto min(const T& a){ return *min_element(a.begin(), a.end()); } template auto max(const T& a){ return *max_element(a.begin(), a.end()); } const long long MINF = 0x7fffffffffff; const long long INF = 0x1fffffffffffffff; const long long MOD = 998244353; const long double EPS = 1e-9; const long double PI = acos(-1); template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template istream &operator>>(istream &is, pair &p){ is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p){ os << "(" << p.first << ", " << p.second << ")"; return os; } template istream &operator>>(istream &is, vector &v){ for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const vector &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; } template ostream &operator<<(ostream &os, const map &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; } template ostream &operator<<(ostream &os, const set &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, const multiset &st){ auto itr = st.begin(); for(int i = 0; i < (int)st.size(); ++i){ os << *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; } template ostream &operator<<(ostream &os, queue q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; } template ostream &operator<<(ostream &os, deque q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; } template ostream &operator<<(ostream &os, stack st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; } template ostream &operator<<(ostream &os, priority_queue pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; } template inline T vin(T& vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; } template inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; } template void in(T&... a){ (cin >> ... >> a); } void out(){ cout << '\n'; } template void out(const T& a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; } template void inGraph(vector>& G, U n, U m, bool directed = false){ G.resize(n); for(int i = 0; i < m; ++i){ int a, b; cin >> a >> b; a--, b--; G[a].push_back(b); if(!directed) G[b].push_back(a); } } namespace Geometry{ using T = long long; inline constexpr int type(T x, T y){ if(!x && !y) return 0; if(y < 0 || (y == 0 && x > 0)) return -1; return 1; } struct Point{ T x, y; Point(T X = 0, T Y = 0) : x(X), y(Y){} inline bool operator==(const Point &other) const { return ((x == other.x) && (y == other.y)); } inline bool operator!=(const Point &other) const { return ((x != other.x) || (y != other.y)); } inline bool operator<(const Point &other) const { int L = type(x, y), R = type(other.x, other.y); if(L != R) return L < R; if(x * other.y == other.x * y) return abs(x + y) < abs(other.x + other.y); return x * other.y > other.x * y; } inline bool operator>(const Point &other) const { int L = type(x, y), R = type(other.x, other.y); if(L != R) return L > R; if(x * other.y == other.x * y) return abs(x + y) > abs(other.x + other.y); return x * other.y < other.x * y; } inline Point operator+() const noexcept { return *this; } inline Point operator-() const noexcept { return Point(-x, -y); } inline Point operator+(const Point &p) const { return Point(x + p.x, y + p.y); } inline Point operator-(const Point &p) const { return Point(x - p.x, y - p.y); } inline Point &operator+=(const Point &p) { return x += p.x, y += p.y, *this; } inline Point &operator-=(const Point &p) { return x -= p.x, y -= p.y, *this; } inline T operator*(const Point &p) const { return x * p.x + y * p.y; } inline Point &operator*=(const T &k) { return x *= k, y *= k, *this; } inline Point operator*(const T &k) { return (*this *= k); } // floor inline Point &operator/=(const T &k) { return x /= k, y /= k, *this; } inline Point operator/(const T &k) { return (*this /= k); } friend inline ostream& operator<<(ostream& os, const Point& p) noexcept { return os << p.x << " " << p.y; } }; bool angle_eq(const Point &p, const Point &q){ int L = type(p.x, p.y), R = type(q.x, q.y); if(L != R) return false; return p.x * q.y == q.x * p.y; } T cross(const Point &p, const Point &q){ return p.x * q.y - p.y * q.x; } T dot(const Point &p, const Point &q){ return p.x * q.x + p.y * q.y; } // 2乗 T dist(const Point &p, const Point &q){ return (p.x - q.x) * (p.x - q.x) + (p.y - q.y) * (p.y - q.y); } // 2倍 T polygonArea(const vector &points){ const int n = points.size(); T res = 0; for(int i = 0; i < n - 1; i++){ res += cross(points[i], points[i + 1]); } res += cross(points[n - 1], points[0]); return res; } vector convexHull(vector points){ const int n = points.size(); if(n <= 2){ return points; } vector U, L, res; sort(points.begin(), points.end(), [](Point p, Point q){ return (p.x == q.x ? p.x < q.x : p.y < q.y); }); // lower for(int i = 0; i < n; i++){ int j = L.size(); // 傾きで左回りかをチェック while(j >= 2 && cross(L[j - 1] - L[j - 2], points[i] - L[j - 2]) <= 0){ L.pop_back(); j--; } L.push_back(points[i]); } // upper for(int i = n - 1; i >= 0; i--){ int j = U.size(); while(j >= 2 && cross(U[j - 1] - U[j - 2], points[i] - U[j - 2]) <= 0){ U.pop_back(); j--; } U.push_back(points[i]); } res = L; for(int i = 1; i < (int) U.size() - 1; i++){ res.push_back(U[i]); } return res; } // 点が領域外部: 0, 内部: 1, 境界上: 2 int inCcwConvex(Point p, const vector &points) { const int n = points.size(); T cr1 = cross(points[1] - points[0], p - points[0]); T cr2 = cross(points[n - 1] - points[0], p - points[0]); if(cr1 < 0 || 0 < cr2){ return 0; } int l = 1, r = n - 1; while(abs(r - l) > 1){ int mid = (l + r) / 2; if(cross(p - points[0], points[mid] - points[0]) >= 0){ r = mid; }else{ l = mid; } } T cr = cross(points[l] - p, points[r] - p); if(cr == 0){ return 2; }else if(cr > 0){ if(cr1 == 0 || cr2 == 0){ return 2; }else{ return 1; } }else{ return 0; } } } using namespace Geometry; struct fraction{ long long p, q; // long long or __int128_t fraction(long long P = 0, long long Q = 1): p(P), q(Q){ normalize(); } void normalize(){ long long g = __gcd(p, q); p /= g, q /= g; // if(q < 0) p *= -1, q *= -1; } inline bool operator==(const fraction &other) const { return p * other.q == other.p * q; } inline bool operator!=(const fraction &other) const { return p * other.q != other.p * q; } inline bool operator<(const fraction &other) const { return p * other.q < other.p * q; } inline bool operator<=(const fraction &other) const { return p * other.q <= other.p * q; } inline bool operator>(const fraction &other) const { return p * other.q > other.p * q; } inline bool operator>=(const fraction &other) const { return p * other.q >= other.p * q; } inline fraction operator+(const fraction &other) const { return fraction(p * other.q + q * other.p, q * other.q); } inline fraction operator-(const fraction &other) const { return fraction(p * other.q - q * other.p, q * other.q); } inline fraction operator*(const fraction &other) const { return fraction(p * other.p, q * other.q); } inline fraction operator/(const fraction &other) const { return fraction(p * other.q, q * other.p); } inline fraction& operator+=(const fraction& rhs) noexcept { *this = *this + rhs; return *this; } inline fraction& operator-=(const fraction& rhs) noexcept { *this = *this - rhs; return *this; } inline fraction& operator*=(const fraction& rhs) noexcept { *this = *this * rhs; return *this; } inline fraction& operator/=(const fraction& rhs) noexcept { *this = *this / rhs; return *this; } friend inline istream& operator>>(istream& is, fraction& x) noexcept { is >> x.p; x.q = 1; return is; } friend inline ostream& operator<<(ostream& os, const fraction& x) noexcept { return os << x.p << "/" << x.q; } }; ll n; vector p; void input(){ in(n); p.resize(n); rep(i, n){ ll x, y; in(x, y); p[i] = Point(x, y); } } void solve(){ ll ans = 0; rep(i, n){ vector q; rep(j, n){ if(i == j) continue; Point d = p[j] - p[i]; q.push_back(d); } Sort(q); ll check = 0; rep(j, n - 2){ if(angle_eq(q[j], q[j + 1])){ check = 1; break; } } if(check) ans++; } out(ans); } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20); input(); solve(); }