結果
| 問題 | No.2180 Comprehensive Line Segments |
| ユーザー |
 hitonanode
|
| 提出日時 | 2023-01-06 22:20:50 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
WA
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 22,797 bytes |
| コンパイル時間 | 2,992 ms |
| コンパイル使用メモリ | 205,788 KB |
| 実行使用メモリ | 13,908 KB |
| 最終ジャッジ日時 | 2024-12-14 15:09:09 |
| 合計ジャッジ時間 | 5,573 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 23 WA * 2 |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
// Subset sum (fast zeta transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void subset_sum(std::vector<T> &f) {
const int sz = f.size(), n = __builtin_ctz(sz);
assert(__builtin_popcount(sz) == 1);
for (int d = 0; d < n; d++) {
for (int S = 0; S < 1 << n; S++)
if (S & (1 << d)) f[S] += f[S ^ (1 << d)];
}
}
// Inverse of subset sum (fast moebius transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void subset_sum_inv(std::vector<T> &g) {
const int sz = g.size(), n = __builtin_ctz(sz);
assert(__builtin_popcount(sz) == 1);
for (int d = 0; d < n; d++) {
for (int S = 0; S < 1 << n; S++)
if (S & (1 << d)) g[S] -= g[S ^ (1 << d)];
}
}
// Superset sum / its inverse (fast zeta/moebius transform)
// Complexity: O(N 2^N) for array of size 2^N
template <typename T> void superset_sum(std::vector<T> &f) {
const int sz = f.size(), n = __builtin_ctz(sz);
assert(__builtin_popcount(sz) == 1);
for (int d = 0; d < n; d++) {
for (int S = 0; S < 1 << n; S++)
if (!(S & (1 << d))) f[S] += f[S | (1 << d)];
}
}
template <typename T> void superset_sum_inv(std::vector<T> &g) {
const int sz = g.size(), n = __builtin_ctz(sz);
assert(__builtin_popcount(sz) == 1);
for (int d = 0; d < n; d++) {
for (int S = 0; S < 1 << n; S++)
if (!(S & (1 << d))) g[S] -= g[S | (1 << d)];
}
}
template <typename T> std::vector<std::vector<T>> build_zeta_(int D, const std::vector<T> &f) {
int n = f.size();
std::vector<std::vector<T>> ret(D, std::vector<T>(n));
for (int i = 0; i < n; i++) ret[__builtin_popcount(i)][i] += f[i];
for (auto &vec : ret) subset_sum(vec);
return ret;
}
template <typename T>
std::vector<T> get_moebius_of_prod_(const std::vector<std::vector<T>> &mat1,
const std::vector<std::vector<T>> &mat2) {
int D = mat1.size(), n = mat1[0].size();
std::vector<std::vector<int>> pc2i(D);
for (int i = 0; i < n; i++) pc2i[__builtin_popcount(i)].push_back(i);
std::vector<T> tmp, ret(mat1[0].size());
for (int d = 0; d < D; d++) {
tmp.assign(mat1[d].size(), 0);
for (int e = 0; e <= d; e++) {
for (int i = 0; i < int(tmp.size()); i++) tmp[i] += mat1[e][i] * mat2[d - e][i];
}
subset_sum_inv(tmp);
for (auto i : pc2i[d]) ret[i] = tmp[i];
}
return ret;
};
// Subset convolution
// h[S] = \sum_T f[T] * g[S - T]
// Complexity: O(N^2 2^N) for arrays of size 2^N
template <typename T> std::vector<T> subset_convolution(std::vector<T> f, std::vector<T> g) {
const int sz = f.size(), m = __builtin_ctz(sz) + 1;
assert(__builtin_popcount(sz) == 1 and f.size() == g.size());
auto ff = build_zeta_(m, f), fg = build_zeta_(m, g);
return get_moebius_of_prod_(ff, fg);
}
// https://hos-lyric.hatenablog.com/entry/2021/01/14/201231
template <class T, class Function> void subset_func(std::vector<T> &f, const Function &func) {
const int sz = f.size(), m = __builtin_ctz(sz) + 1;
assert(__builtin_popcount(sz) == 1);
auto ff = build_zeta_(m, f);
std::vector<T> p(m);
for (int i = 0; i < sz; i++) {
for (int d = 0; d < m; d++) p[d] = ff[d][i];
func(p);
for (int d = 0; d < m; d++) ff[d][i] = p[d];
}
for (auto &vec : ff) subset_sum_inv(vec);
for (int i = 0; i < sz; i++) f[i] = ff[__builtin_popcount(i)][i];
}
// log(f(x)) for f(x), f(0) == 1
// Requires inv()
template <class T> void poly_log(std::vector<T> &f) {
assert(f.at(0) == T(1));
static std::vector<T> invs{0};
const int m = f.size();
std::vector<T> finv(m);
for (int d = 0; d < m; d++) {
finv[d] = (d == 0);
if (int(invs.size()) <= d) invs.push_back(T(d).inv());
for (int e = 0; e < d; e++) finv[d] -= finv[e] * f[d - e];
}
std::vector<T> ret(m);
for (int d = 1; d < m; d++) {
for (int e = 0; d + e < m; e++) ret[d + e] += f[d] * d * finv[e] * invs[d + e];
}
f = ret;
}
// log(f(S)) for set function f(S), f(0) == 1
// Requires inv()
// Complexity: O(n^2 2^n)
// https://atcoder.jp/contests/abc213/tasks/abc213_g
template <class T> void subset_log(std::vector<T> &f) { subset_func(f, poly_log<T>); }
// exp(f(S)) for set function f(S), f(0) == 0
// Complexity: O(n^2 2^n)
// https://codeforces.com/blog/entry/92183
template <class T> void subset_exp(std::vector<T> &f) {
const int sz = f.size(), m = __builtin_ctz(sz);
assert(sz == 1 << m);
assert(f.at(0) == 0);
std::vector<T> ret{T(1)};
ret.reserve(sz);
for (int d = 0; d < m; d++) {
auto c = subset_convolution({f.begin() + (1 << d), f.begin() + (1 << (d + 1))}, ret);
ret.insert(ret.end(), c.begin(), c.end());
}
f = ret;
}
// sqrt(f(x)), f(x) == 1
// Requires inv of 2
// Compelxity: O(n^2)
template <class T> void poly_sqrt(std::vector<T> &f) {
assert(f.at(0) == T(1));
const int m = f.size();
static const auto inv2 = T(2).inv();
for (int d = 1; d < m; d++) {
if (~(d & 1)) f[d] -= f[d / 2] * f[d / 2];
f[d] *= inv2;
for (int e = 1; e < d - e; e++) f[d] -= f[e] * f[d - e];
}
}
// sqrt(f(S)) for set function f(S), f(0) == 1
// Requires inv()
// https://atcoder.jp/contests/xmascon20/tasks/xmascon20_h
template <class T> void subset_sqrt(std::vector<T> &f) { subset_func(f, poly_sqrt<T>); }
// exp(f(S)) for set function f(S), f(0) == 0
template <class T> void poly_exp(std::vector<T> &P) {
const int m = P.size();
assert(m and P[0] == 0);
std::vector<T> Q(m), logQ(m), Qinv(m);
Q[0] = Qinv[0] = T(1);
static std::vector<T> invs{0};
auto set_invlog = [&](int d) {
Qinv[d] = 0;
for (int e = 0; e < d; e++) Qinv[d] -= Qinv[e] * Q[d - e];
while (d >= int(invs.size())) {
int sz = invs.size();
invs.push_back(T(sz).inv());
}
logQ[d] = 0;
for (int e = 1; e <= d; e++) logQ[d] += Q[e] * e * Qinv[d - e];
logQ[d] *= invs[d];
};
for (int d = 1; d < m; d++) {
Q[d] += P[d] - logQ[d];
set_invlog(d);
assert(logQ[d] == P[d]);
if (d + 1 < m) set_invlog(d + 1);
}
P = Q;
}
// f(S)^k for set function f(S)
// Requires inv()
template <class T> void subset_pow(std::vector<T> &f, long long k) {
auto poly_pow = [&](std::vector<T> &f) {
const int m = f.size();
if (k == 0) f[0] = 1, std::fill(f.begin() + 1, f.end(), T(0));
if (k <= 1) return;
int nzero = 0;
while (nzero < int(f.size()) and f[nzero] == T(0)) nzero++;
int rem = std::max<long long>((long long)f.size() - nzero * k, 0LL);
if (rem == 0) {
std::fill(f.begin(), f.end(), 0);
return;
}
f.erase(f.begin(), f.begin() + nzero);
f.resize(rem);
const T f0 = f.at(0), f0inv = f0.inv(), f0pow = f0.pow(k);
for (auto &x : f) x *= f0inv;
poly_log(f);
for (auto &x : f) x *= k;
poly_exp(f);
for (auto &x : f) x *= f0pow;
f.resize(rem, 0);
f.insert(f.begin(), m - int(f.size()), T(0));
};
subset_func(f, poly_pow);
}
#include <algorithm>
#include <cassert>
#include <cmath>
#include <complex>
#include <iostream>
#include <tuple>
#include <utility>
#include <vector>
template <typename T_P> struct Point2d {
static T_P EPS;
static void set_eps(T_P e) { EPS = e; }
T_P x, y;
Point2d() : x(0), y(0) {}
Point2d(T_P x, T_P y) : x(x), y(y) {}
Point2d(const std::pair<T_P, T_P> &p) : x(p.first), y(p.second) {}
Point2d(const std::complex<T_P> &p) : x(p.real()), y(p.imag()) {}
std::complex<T_P> to_complex() const noexcept { return {x, y}; }
Point2d operator+(const Point2d &p) const noexcept { return Point2d(x + p.x, y + p.y); }
Point2d operator-(const Point2d &p) const noexcept { return Point2d(x - p.x, y - p.y); }
Point2d operator*(const Point2d &p) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x * p.x - y * p.y, x * p.y + y * p.x);
}
Point2d operator*(T_P d) const noexcept { return Point2d(x * d, y * d); }
Point2d operator/(T_P d) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x / d, y / d);
}
Point2d inv() const {
static_assert(std::is_floating_point<T_P>::value == true);
return conj() / norm2();
}
Point2d operator/(const Point2d &p) const { return (*this) * p.inv(); }
bool operator<(const Point2d &r) const noexcept { return x != r.x ? x < r.x : y < r.y; }
bool operator==(const Point2d &r) const noexcept { return x == r.x and y == r.y; }
bool operator!=(const Point2d &r) const noexcept { return !((*this) == r); }
T_P dot(Point2d p) const noexcept { return x * p.x + y * p.y; }
T_P det(Point2d p) const noexcept { return x * p.y - y * p.x; }
T_P absdet(Point2d p) const noexcept { return std::abs(det(p)); }
T_P norm() const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return std::sqrt(x * x + y * y);
}
T_P norm2() const noexcept { return x * x + y * y; }
T_P arg() const noexcept { return std::atan2(y, x); }
// rotate point/vector by rad
Point2d rotate(T_P rad) const noexcept {
static_assert(std::is_floating_point<T_P>::value == true);
return Point2d(x * std::cos(rad) - y * std::sin(rad), x * std::sin(rad) + y * std::cos(rad));
}
Point2d normalized() const {
static_assert(std::is_floating_point<T_P>::value == true);
return (*this) / this->norm();
}
Point2d conj() const noexcept { return Point2d(x, -y); }
template <class IStream> friend IStream &operator>>(IStream &is, Point2d &p) {
T_P x, y;
is >> x >> y;
p = Point2d(x, y);
return is;
}
template <class OStream> friend OStream &operator<<(OStream &os, const Point2d &p) {
return os << '(' << p.x << ',' << p.y << ')';
}
};
template <> double Point2d<double>::EPS = 1e-9;
template <> long double Point2d<long double>::EPS = 1e-12;
template <> long long Point2d<long long>::EPS = 0;
template <typename T_P>
int ccw(const Point2d<T_P> &a, const Point2d<T_P> &b, const Point2d<T_P> &c) {
// a->b->cの曲がり方
Point2d<T_P> v1 = b - a;
Point2d<T_P> v2 = c - a;
if (v1.det(v2) > Point2d<T_P>::EPS) return 1; // 左折
if (v1.det(v2) < -Point2d<T_P>::EPS) return -1; // 右折
if (v1.dot(v2) < -Point2d<T_P>::EPS) return 2; // c-a-b
if (v1.norm() < v2.norm()) return -2; // a-b-c
return 0; // a-c-b
}
// Convex hull （凸包）
// return: IDs of vertices used for convex hull, counterclockwise
// include_boundary: If true, interior angle pi is allowed
template <typename T_P>
std::vector<int> convex_hull(const std::vector<Point2d<T_P>> &ps, bool include_boundary = false) {
int n = ps.size();
if (n <= 1) return std::vector<int>(n, 0);
std::vector<std::pair<Point2d<T_P>, int>> points(n);
for (size_t i = 0; i < ps.size(); i++) points[i] = std::make_pair(ps[i], i);
std::sort(points.begin(), points.end());
int k = 0;
std::vector<std::pair<Point2d<T_P>, int>> qs(2 * n);
auto ccw_check = [&](int c) { return include_boundary ? (c == -1) : (c <= 0); };
for (int i = 0; i < n; i++) {
while (k > 1 and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
qs[k++] = points[i];
}
for (int i = n - 2, t = k; i >= 0; i--) {
while (k > t and ccw_check(ccw(qs[k - 2].first, qs[k - 1].first, points[i].first))) k--;
qs[k++] = points[i];
}
std::vector<int> ret(k - 1);
for (int i = 0; i < k - 1; i++) ret[i] = qs[i].second;
return ret;
}
#include <optional>
// Solve r1 + t1 * v1 == r2 + t2 * v2
template <typename T_P, typename std::enable_if<std::is_floating_point<T_P>::value>::type * = nullptr>
std::optional<Point2d<T_P>> lines_crosspoint(Point2d<T_P> r1, Point2d<T_P> v1, Point2d<T_P> r2, Point2d<T_P> v2) {
static_assert(std::is_floating_point<T_P>::value == true);
if (abs(v2.det(v1)) <= Point2d<T_P>::EPS) return nullopt;
return r1 + v1 * (v2.det(r2 - r1) / v2.det(v1));
}
// Whether two segments s1t1 & s2t2 intersect or not (endpoints not included)
// Google Code Jam 2013 Round 3 - Rural Planning
// Google Code Jam 2021 Round 3 - Fence Design
template <typename T>
bool intersect_open_segments(Point2d<T> s1, Point2d<T> t1, Point2d<T> s2, Point2d<T> t2) {
if (s1 == t1 or s2 == t2) return false; // Not segment but point
int nbad = 0;
for (int t = 0; t < 2; t++) {
Point2d<T> v1 = t1 - s1, v2 = t2 - s2;
T den = v2.det(v1);
if (den == 0) {
if (s1.det(v1) == s2.det(v1)) {
auto L1 = s1.dot(v1), R1 = t1.dot(v1);
auto L2 = s2.dot(v1), R2 = t2.dot(v1);
if (L1 > R1) std::swap(L1, R1);
if (L2 > R2) std::swap(L2, R2);
if (L1 > L2) std::swap(L1, L2), std::swap(R1, R2);
return R1 > L2;
} else {
return false;
}
} else {
auto num = v2.det(s2 - s1);
if ((0 < num and num < den) or (den < num and num < 0)) nbad++;
}
std::swap(s1, s2);
std::swap(t1, t2);
}
return nbad == 2;
}
int main() {
int N;
cin >> N;
if (N == 1) {
puts("1");
return 0;
}
using Pti = Point2d<int>;
using Pt = Point2d<double>;
vector<Pti> Pi(N);
vector<Pt> P(N);
REP(i, N) {
int x, y;
cin >> x >> y;
P.at(i) = Pt(x, y);
Pi.at(i) = Pti(x, y);
}
// cin >> P;
dbg(P);
vector masks(N, vector<int>(N));
vector<pair<Pt, Pt>> lines;
REP(i, N) {
auto c = P.at(i);
REP(j, i) {
auto dr = P.at(j) - P.at(i);
lines.emplace_back(c, dr);
}
}
vector<Pt> pts{P.begin(), P.end()};
for (auto [c0, dr0] : lines) {
for (auto [c1, dr1] : lines) {
auto cp = lines_crosspoint(c0, dr0, c1, dr1);
if (cp.has_value()) pts.push_back(cp.value());
}
}
for (auto &p : pts) {
p.x = llround(p.x * 1e9) / 1e9;
p.y = llround(p.y * 1e9) / 1e9;
}
pts = sort_unique(pts);
const int V = pts.size();
using BS = bitset<(1 << 12)>;
vector<BS> dp(V);
REP(i, V) dp.at(i).set(0);
vector mask(V, vector<int>(V));
vector<vector<pint>> graph_to(V);
REP(i, V) REP(j, V) {
const auto &from = pts.at(i);
const auto &to = pts.at(j);
REP(k, N) {
auto p = P.at(k);
bool match = false;
if ((from - p).norm2() < 1e-5 or (to - p).norm2() < 1e-5) match = true;
if ((from - p).norm2() < (to - from).norm2() and (to - p).norm2() < (to - from).norm2() and abs((to - from).det(p - from)) < 1e-5) match = true;
if (match) mask[i][j] |= 1 << k;
}
int v = __builtin_popcount(mask[i][j]);
if (v >= 2) graph_to.at(i).emplace_back(j, mask[i][j]);
}
FOR(d, 1, 6) {
dbg(d);
auto dpnxt = dp;
REP(i, V) {
for (auto [j, madd] : graph_to.at(i)) {
// REP(j, V) {
// int madd = mask.at(i).at(j);
for (int s = dp.at(i)._Find_first(); s < 1 << N; s = dp.at(i)._Find_next(s)) {
dpnxt.at(j)[s | madd] = 1;
}
}
}
dp = dpnxt;
for (auto v : dp) {
if (v[(1 << N) - 1]) {
cout << d << endl;
return 0;
}
}
}
puts("6");
}