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#line 1 "main.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "library/my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'000'000'000; template <> constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) \ vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector<vector<vector<type>>> name( \ h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name( \ a, vector<vector<vector<type>>>( \ b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T, typename U> T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T, typename U> pair<T, T> divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { assert(!que.empty()); T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { assert(!que.empty()); T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "library/other/io.hpp" // based on yosupo's fastio #include <unistd.h> namespace fastio { #define FASTIO // クラスが read(), print() を持っているかを判定するメタ関数 struct has_write_impl { template <class T> static auto check(T &&x) -> decltype(x.write(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) { }; struct has_read_impl { template <class T> static auto check(T &&x) -> decltype(x.read(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {}; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template <class T, enable_if_t<is_same<T, string>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template <typename T, typename enable_if<has_read<T>::value>::type * = nullptr> inline bool read_single(T &x) { x.read(); return true; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template <class T> bool read_single(vector<T> &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template <class T, class U> bool read_single(pair<T, U> &p) { return (read_single(p.first) && read_single(p.second)); } template <size_t N = 0, typename T> void read_single_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); read_single(x); read_single_tuple<N + 1>(t); } } template <class... T> bool read_single(tuple<T...> &tpl) { read_single_tuple(tpl); return true; } void read() {} template <class H, class... T> void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char val) { if (pos == SIZE) flush(); line[pos++] = val; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template <typename T, typename enable_if<has_write<T>::value>::type * = nullptr> inline void write(T x) { x.write(); } template <class T> void write(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template <class T, class U> void write(const pair<T, U> val) { write(val.first); write(' '); write(val.second); } template <size_t N = 0, typename T> void write_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { write(' '); } const auto x = std::get<N>(t); write(x); write_tuple<N + 1>(t); } } template <class... T> bool write(tuple<T...> tpl) { write_tuple(tpl); return true; } template <class T, size_t S> void write(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if (val < 0) { negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if (negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward<Tail>(tail)...); } void read() {} template <class Head, class... Tail> void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } } // namespace fastio using fastio::print; using fastio::flush; using fastio::read; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 4 "main.cpp" #line 2 "library/mod/modint_common.hpp" struct has_mod_impl { template <class T> static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {}; template <typename mint> mint inv(int n) { static const int mod = mint::get_mod(); static vector<mint> dat = {0, 1}; assert(0 <= n); if (n >= mod) n %= mod; while (len(dat) <= n) { int k = len(dat); int q = (mod + k - 1) / k; dat.eb(dat[k * q - mod] * mint::raw(q)); } return dat[n]; } template <typename mint> mint fact(int n) { static const int mod = mint::get_mod(); assert(0 <= n && n < mod); static vector<mint> dat = {1, 1}; while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat))); return dat[n]; } template <typename mint> mint fact_inv(int n) { static vector<mint> dat = {1, 1}; if (n < 0) return mint(0); while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat))); return dat[n]; } template <class mint, class... Ts> mint fact_invs(Ts... xs) { return (mint(1) * ... * fact_inv<mint>(xs)); } template <typename mint, class Head, class... Tail> mint multinomial(Head &&head, Tail &&... tail) { return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...); } template <typename mint> mint C_dense(int n, int k) { static vvc<mint> C; static int H = 0, W = 0; auto calc = [&](int i, int j) -> mint { if (i == 0) return (j == 0 ? mint(1) : mint(0)); return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0); }; if (W <= k) { FOR(i, H) { C[i].resize(k + 1); FOR(j, W, k + 1) { C[i][j] = calc(i, j); } } W = k + 1; } if (H <= n) { C.resize(n + 1); FOR(i, H, n + 1) { C[i].resize(W); FOR(j, W) { C[i][j] = calc(i, j); } } H = n + 1; } return C[n][k]; } template <typename mint, bool large = false, bool dense = false> mint C(ll n, ll k) { assert(n >= 0); if (k < 0 || n < k) return 0; if constexpr (dense) return C_dense<mint>(n, k); if constexpr (!large) return multinomial<mint>(n, k, n - k); k = min(k, n - k); mint x(1); FOR(i, k) x *= mint(n - i); return x * fact_inv<mint>(k); } template <typename mint, bool large = false> mint C_inv(ll n, ll k) { assert(n >= 0); assert(0 <= k && k <= n); if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k); return mint(1) / C<mint, 1>(n, k); } // [x^d] (1-x) ^ {-n} の計算 template <typename mint, bool large = false, bool dense = false> mint C_negative(ll n, ll d) { assert(n >= 0); if (d < 0) return mint(0); if (n == 0) { return (d == 0 ? mint(1) : mint(0)); } return C<mint, large, dense>(n + d - 1, d); } #line 3 "library/mod/modint.hpp" template <int mod> struct modint { static constexpr u32 umod = u32(mod); static_assert(umod < u32(1) << 31); u32 val; static modint raw(u32 v) { modint x; x.val = v; return x; } constexpr modint() : val(0) {} constexpr modint(u32 x) : val(x % umod) {} constexpr modint(u64 x) : val(x % umod) {} constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){}; constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){}; bool operator<(const modint &other) const { return val < other.val; } modint &operator+=(const modint &p) { if ((val += p.val) >= umod) val -= umod; return *this; } modint &operator-=(const modint &p) { if ((val += umod - p.val) >= umod) val -= umod; return *this; } modint &operator*=(const modint &p) { val = u64(val) * p.val % umod; return *this; } modint &operator/=(const modint &p) { *this *= p.inverse(); return *this; } modint operator-() const { return modint::raw(val ? mod - val : u32(0)); } modint operator+(const modint &p) const { return modint(*this) += p; } modint operator-(const modint &p) const { return modint(*this) -= p; } modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } bool operator==(const modint &p) const { return val == p.val; } bool operator!=(const modint &p) const { return val != p.val; } modint inverse() const { int a = val, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } return modint(u); } modint pow(ll n) const { assert(n >= 0); modint ret(1), mul(val); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } #ifdef FASTIO void write() { fastio::printer.write(val); } void read() { fastio::scanner.read(val); val %= mod; } #endif static constexpr int get_mod() { return mod; } // (n, r), r は 1 の 2^n 乗根 static constexpr pair<int, int> ntt_info() { if (mod == 167772161) return {25, 17}; if (mod == 469762049) return {26, 30}; if (mod == 754974721) return {24, 362}; if (mod == 880803841) return {23, 211}; if (mod == 998244353) return {23, 31}; if (mod == 1045430273) return {20, 363}; if (mod == 1051721729) return {20, 330}; if (mod == 1053818881) return {20, 2789}; return {-1, -1}; } static constexpr bool can_ntt() { return ntt_info().fi != -1; } }; using modint107 = modint<1000000007>; using modint998 = modint<998244353>; #line 2 "library/geo/base.hpp" template <typename T> struct Point { T x, y; Point() : x(0), y(0) {} template <typename A, typename B> Point(A x, B y) : x(x), y(y) {} template <typename A, typename B> Point(pair<A, B> p) : x(p.fi), y(p.se) {} Point operator+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(Point other) { return x * other.x + y * other.y; } T det(Point other) { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral<T>::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } #ifdef FASTIO void read() { fastio::read(x), fastio::read(y); } void write() { fastio::printer.write(pair<T, T>({x, y})); } #endif }; // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template <typename T> int ccw(Point<T> A, Point<T> B, Point<T> C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template <typename REAL, typename T> REAL dist(Point<T> A, Point<T> B) { A = A - B; T p = A.dot(A); return sqrt(REAL(p)); } template <typename T> struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {} template <typename U> U eval(Point<U> P) { return a * P.x + b * P.y + c; } template <typename U> T eval(U x, U y) { return a * x + b * y + c; } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template <typename T> struct Segment { Point<T> A, B; Segment(Point<T> A, Point<T> B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {} bool contain(Point<T> C) { static_assert(is_integral<T>::value); T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line<T> to_Line() { return Line(A, B); } }; template <typename REAL> struct Circle { Point<REAL> O; REAL r; Circle(Point<REAL> O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template <typename T> bool contain(Point<T> p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; template <typename T> struct Polygon { vc<Point<T>> points; T a; template <typename A, typename B> Polygon(vc<pair<A, B>> pairs) { for (auto&& [a, b]: pairs) points.eb(Point<T>(a, b)); build(); } Polygon(vc<Point<T>> points) : points(points) { build(); } int size() { return len(points); } template <typename REAL> REAL area() { return a * 0.5; } template <enable_if_t<is_integral<T>::value, int> = 0> T area_2() { return a; } bool is_convex() { FOR(j, len(points)) { int i = (j == 0 ? len(points) - 1 : j - 1); int k = (j == len(points) - 1 ? 0 : j + 1); if ((points[j] - points[i]).det(points[k] - points[j]) < 0) return false; } return true; } private: void build() { a = 0; FOR(i, len(points)) { int j = (i + 1 == len(points) ? 0 : i + 1); a += points[i].det(points[j]); } if (a < 0) { a = -a; reverse(all(points)); } } }; #line 1 "library/geo/inside_polygon.hpp" // https://qoj.ac/problem/5443 // 線分上に頂点や辺が来ることは許容 template <typename T> bool inside_polygon(Segment<T> S, vc<Point<T>>& dat) { using P = Point<T>; int N = len(dat); int cnt = 0; P A = S.A, B = S.B; auto PREV = [&](int i) -> int { return (i == 0 ? N : i) - 1; }; auto NEXT = [&](int i) -> int { return (i == N - 1 ? 0 : i + 1); }; FOR(i, N) { P p = dat[i], q = dat[NEXT(i)], r = dat[PREV(i)]; int a = ccw(A, B, p); int b = ccw(A, B, q); int c = ccw(A, B, r); if (a * b == -1) { Segment pq(p, q); auto L = pq.to_Line(); T x = L.eval(A), y = L.eval(B); if (x < y) { x = -x, y = -y; } if (x <= 0) ++cnt; if (0 < x && x < x - y) return 0; } if (a == 0) { if (b != c && (b * c < 0 || ccw(p, q, r) > 0)) { T t = (p - A).dot(B - A), x = (B - A).dot(B - A); if (t <= 0) ++cnt; if (0 < t && t < x) return 0; } } } return cnt % 2 == 1; } #line 2 "library/geo/angle_sort.hpp" #line 4 "library/geo/angle_sort.hpp" // 偏角ソートに対する argsort template <typename T> vector<int> angle_sort(vector<Point<T>>& P) { vector<int> lower, origin, upper; const Point<T> O = {0, 0}; FOR(i, len(P)) { if (P[i] == O) origin.eb(i); elif ((P[i].y < 0) || (P[i].y == 0 && P[i].x > 0)) lower.eb(i); else upper.eb(i); } sort(all(lower), [&](auto& i, auto& j) { return P[i].det(P[j]) > 0; }); sort(all(upper), [&](auto& i, auto& j) { return P[i].det(P[j]) > 0; }); auto& I = lower; I.insert(I.end(), all(origin)); I.insert(I.end(), all(upper)); return I; } // 偏角ソートに対する argsort template <typename T> vector<int> angle_sort(vector<pair<T, T>>& P) { vc<Point<T>> tmp(len(P)); FOR(i, len(P)) tmp[i] = Point<T>(P[i]); return angle_sort<T>(tmp); } #line 2 "library/nt/primetable.hpp" template <typename T = int> vc<T> primetable(int LIM) { ++LIM; const int S = 32768; static int done = 2; static vc<T> primes = {2}, sieve(S + 1); if (done < LIM) { done = LIM; primes = {2}, sieve.assign(S + 1, 0); const int R = LIM / 2; primes.reserve(int(LIM / log(LIM) * 1.1)); vc<pair<int, int>> cp; for (int i = 3; i <= S; i += 2) { if (!sieve[i]) { cp.eb(i, i * i / 2); for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1; } } for (int L = 1; L <= R; L += S) { array<bool, S> block{}; for (auto& [p, idx]: cp) for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1; FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1); } } int k = LB(primes, LIM + 1); return {primes.begin(), primes.begin() + k}; } #line 3 "library/mod/powertable.hpp" // a^0, ..., a^N template <typename mint> vc<mint> powertable_1(mint a, ll N) { // table of a^i vc<mint> f(N + 1, 1); FOR(i, N) f[i + 1] = a * f[i]; return f; } // 0^e, ..., N^e template <typename mint> vc<mint> powertable_2(ll e, ll N) { auto primes = primetable(N); vc<mint> f(N + 1, 1); f[0] = mint(0).pow(e); for (auto&& p: primes) { if (p > N) break; mint xp = mint(p).pow(e); ll pp = p; while (pp <= N) { ll i = pp; while (i <= N) { f[i] *= xp; i += pp; } pp *= p; } } return f; } #line 10 "main.cpp" using P = Point<ll>; using mint = modint998; mint solve_QOJ5443(int N, vc<P> dat) { vv(bool, CAN, N, N); vv(int, CNT, N, N); FOR(a, N) FOR(b, N) { if (a == b) continue; P A = dat[a], B = dat[b]; Segment<ll> AB(A, B); vc<bool> ON(N); FOR(c, N) { if (AB.contain(dat[c])) ON[c] = 1; } CNT[a][b] = SUM<int>(ON) - 2; CAN[a][b] = inside_polygon(AB, dat); } FOR(a, N) FOR(b, N) assert(CAN[a][b] == CAN[b][a]); FOR(a, N) FOR(b, N) assert(CNT[a][b] == CNT[b][a]); mint ANS = 0; vc<mint> POW = powertable_1<mint>(2, N); // 凸包が線分 FOR(a, N) FOR(b, a) { if (CAN[a][b]) ANS += POW[CNT[a][b]]; } // angle sort vc<pi> edge; vc<P> dir; FOR(a, N) FOR(b, N) { if (CAN[a][b]) { edge.eb(a, b); dir.eb(dat[b] - dat[a]); } } auto I = angle_sort(dir); edge = rearrange(edge, I); dir = rearrange(dir, I); FOR(s, N) { // s スタート // [0][v]:1 回だけ進んだ // [1][v]:2 回以上進んだ vv(mint, dp, 2, N); // 同じ向きの線分での遷移をまとめて更新するようにする auto SAME = [&](int i, int j) -> bool { return (dir[i].det(dir[j]) == 0 && dir[i].dot(dir[j]) > 0); }; int L = 0; while (L < len(edge)) { int R = L; while (R < len(edge) && SAME(L, R)) ++R; vc<tuple<int, int, mint>> upd; FOR(e, L, R) { auto [frm, to] = edge[e]; mint cf = POW[CNT[frm][to]]; if (frm == s) { upd.eb(0, to, cf); } else { if (to != s) upd.eb(1, to, dp[0][frm] * cf); upd.eb(1, to, dp[1][frm] * cf); } } L = R; for (auto&& [a, b, c]: upd) dp[a][b] += c; } ANS += dp[1][s]; } return ANS; } void test_QOJ5443_1() { int N = 7; vc<P> dat(N); dat[0] = {0, 2}; dat[1] = {4, 0}; dat[2] = {4, 2}; dat[3] = {7, 5}; dat[4] = {5, 7}; dat[5] = {3, 5}; dat[6] = {0, 5}; mint ANS = solve_QOJ5443(N, dat); assert(ANS.val == 56); } void test_QOJ5443_2() { int N = 12; vc<P> dat(N); dat[0] = {0, 0}; dat[1] = {4, 0}; dat[2] = {4, 5}; dat[3] = {0, 5}; dat[4] = {0, 2}; dat[5] = {2, 2}; dat[6] = {2, 3}; dat[7] = {1, 3}; dat[8] = {1, 4}; dat[9] = {3, 4}; dat[10] = {3, 1}; dat[11] = {0, 1}; mint ANS = solve_QOJ5443(N, dat); assert(ANS.val == 51); } void solve() { LL(a, b); print(a + b); } signed main() { test_QOJ5443_1(); test_QOJ5443_2(); solve(); return 0; }
#line 1 "test/1_mytest/qoj5443.test.cpp" #line 1 "main.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/aplusb" #line 1 "library/my_template.hpp" #if defined(LOCAL) #include <my_template_compiled.hpp> #else #pragma GCC optimize("Ofast") #pragma GCC optimize("unroll-loops") #include <bits/stdc++.h> using namespace std; using ll = long long; using u32 = unsigned int; using u64 = unsigned long long; using i128 = __int128; using u128 = unsigned __int128; using f128 = __float128; template <class T> constexpr T infty = 0; template <> constexpr int infty<int> = 1'000'000'000; template <> constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2; template <> constexpr u32 infty<u32> = infty<int>; template <> constexpr u64 infty<u64> = infty<ll>; template <> constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>; template <> constexpr double infty<double> = infty<ll>; template <> constexpr long double infty<long double> = infty<ll>; using pi = pair<ll, ll>; using vi = vector<ll>; template <class T> using vc = vector<T>; template <class T> using vvc = vector<vc<T>>; template <class T> using vvvc = vector<vvc<T>>; template <class T> using vvvvc = vector<vvvc<T>>; template <class T> using vvvvvc = vector<vvvvc<T>>; template <class T> using pq = priority_queue<T>; template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; #define vv(type, name, h, ...) \ vector<vector<type>> name(h, vector<type>(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector<vector<vector<type>>> name( \ h, vector<vector<type>>(w, vector<type>(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector<vector<vector<vector<type>>>> name( \ a, vector<vector<vector<type>>>( \ b, vector<vector<type>>(c, vector<type>(__VA_ARGS__)))) // https://trap.jp/post/1224/ #define FOR1(a) for (ll _ = 0; _ < ll(a); ++_) #define FOR2(i, a) for (ll i = 0; i < ll(a); ++i) #define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i) #define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c)) #define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i) #define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i) #define overload4(a, b, c, d, e, ...) e #define overload3(a, b, c, d, ...) d #define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__) #define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__) #define FOR_subset(t, s) \ for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define all(x) x.begin(), x.end() #define len(x) ll(x.size()) #define elif else if #define eb emplace_back #define mp make_pair #define mt make_tuple #define fi first #define se second #define stoi stoll int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2) int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } // (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2) int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template <typename T, typename U> T ceil(T x, U y) { return (x > 0 ? (x + y - 1) / y : x / y); } template <typename T, typename U> T floor(T x, U y) { return (x > 0 ? x / y : (x - y + 1) / y); } template <typename T, typename U> pair<T, T> divmod(T x, U y) { T q = floor(x, y); return {q, x - q * y}; } template <typename T, typename U> T SUM(const vector<U> &A) { T sum = 0; for (auto &&a: A) sum += a; return sum; } #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define LB(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) \ sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit() template <typename T> T POP(deque<T> &que) { T a = que.front(); que.pop_front(); return a; } template <typename T> T POP(pq<T> &que) { T a = que.top(); que.pop(); return a; } template <typename T> T POP(pqg<T> &que) { assert(!que.empty()); T a = que.top(); que.pop(); return a; } template <typename T> T POP(vc<T> &que) { assert(!que.empty()); T a = que.back(); que.pop_back(); return a; } template <typename F> ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { auto x = (ng + ok) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return ok; } template <typename F> double binary_search_real(F check, double ok, double ng, int iter = 100) { FOR(iter) { double x = (ok + ng) / 2; tie(ok, ng) = (check(x) ? mp(x, ng) : mp(ok, x)); } return (ok + ng) / 2; } template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); } template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); } // ? は -1 vc<int> s_to_vi(const string &S, char first_char) { vc<int> A(S.size()); FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); } return A; } template <typename T, typename U> vector<T> cumsum(vector<U> &A, int off = 1) { int N = A.size(); vector<T> B(N + 1); FOR(i, N) { B[i + 1] = B[i] + A[i]; } if (off == 0) B.erase(B.begin()); return B; } // stable sort template <typename T> vector<int> argsort(const vector<T> &A) { vector<int> ids(len(A)); iota(all(ids), 0); sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); }); return ids; } // A[I[0]], A[I[1]], ... template <typename T> vc<T> rearrange(const vc<T> &A, const vc<int> &I) { vc<T> B(len(I)); FOR(i, len(I)) B[i] = A[I[i]]; return B; } #endif #line 1 "library/other/io.hpp" // based on yosupo's fastio #include <unistd.h> namespace fastio { #define FASTIO // クラスが read(), print() を持っているかを判定するメタ関数 struct has_write_impl { template <class T> static auto check(T &&x) -> decltype(x.write(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_write : public decltype(has_write_impl::check<T>(std::declval<T>())) { }; struct has_read_impl { template <class T> static auto check(T &&x) -> decltype(x.read(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_read : public decltype(has_read_impl::check<T>(std::declval<T>())) {}; struct Scanner { FILE *fp; char line[(1 << 15) + 1]; size_t st = 0, ed = 0; void reread() { memmove(line, line + st, ed - st); ed -= st; st = 0; ed += fread(line + ed, 1, (1 << 15) - ed, fp); line[ed] = '\0'; } bool succ() { while (true) { if (st == ed) { reread(); if (st == ed) return false; } while (st != ed && isspace(line[st])) st++; if (st != ed) break; } if (ed - st <= 50) { bool sep = false; for (size_t i = st; i < ed; i++) { if (isspace(line[i])) { sep = true; break; } } if (!sep) reread(); } return true; } template <class T, enable_if_t<is_same<T, string>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; while (true) { size_t sz = 0; while (st + sz < ed && !isspace(line[st + sz])) sz++; ref.append(line + st, sz); st += sz; if (!sz || st != ed) break; reread(); } return true; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> bool read_single(T &ref) { if (!succ()) return false; bool neg = false; if (line[st] == '-') { neg = true; st++; } ref = T(0); while (isdigit(line[st])) { ref = 10 * ref + (line[st++] & 0xf); } if (neg) ref = -ref; return true; } template <typename T, typename enable_if<has_read<T>::value>::type * = nullptr> inline bool read_single(T &x) { x.read(); return true; } bool read_single(double &ref) { string s; if (!read_single(s)) return false; ref = std::stod(s); return true; } bool read_single(char &ref) { string s; if (!read_single(s) || s.size() != 1) return false; ref = s[0]; return true; } template <class T> bool read_single(vector<T> &ref) { for (auto &d: ref) { if (!read_single(d)) return false; } return true; } template <class T, class U> bool read_single(pair<T, U> &p) { return (read_single(p.first) && read_single(p.second)); } template <size_t N = 0, typename T> void read_single_tuple(T &t) { if constexpr (N < std::tuple_size<T>::value) { auto &x = std::get<N>(t); read_single(x); read_single_tuple<N + 1>(t); } } template <class... T> bool read_single(tuple<T...> &tpl) { read_single_tuple(tpl); return true; } void read() {} template <class H, class... T> void read(H &h, T &... t) { bool f = read_single(h); assert(f); read(t...); } Scanner(FILE *fp) : fp(fp) {} }; struct Printer { Printer(FILE *_fp) : fp(_fp) {} ~Printer() { flush(); } static constexpr size_t SIZE = 1 << 15; FILE *fp; char line[SIZE], small[50]; size_t pos = 0; void flush() { fwrite(line, 1, pos, fp); pos = 0; } void write(const char val) { if (pos == SIZE) flush(); line[pos++] = val; } template <class T, enable_if_t<is_integral<T>::value, int> = 0> void write(T val) { if (pos > (1 << 15) - 50) flush(); if (val == 0) { write('0'); return; } if (val < 0) { write('-'); val = -val; // todo min } size_t len = 0; while (val) { small[len++] = char(0x30 | (val % 10)); val /= 10; } for (size_t i = 0; i < len; i++) { line[pos + i] = small[len - 1 - i]; } pos += len; } void write(const string s) { for (char c: s) write(c); } void write(const char *s) { size_t len = strlen(s); for (size_t i = 0; i < len; i++) write(s[i]); } void write(const double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } void write(const long double x) { ostringstream oss; oss << fixed << setprecision(15) << x; string s = oss.str(); write(s); } template <typename T, typename enable_if<has_write<T>::value>::type * = nullptr> inline void write(T x) { x.write(); } template <class T> void write(const vector<T> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } template <class T, class U> void write(const pair<T, U> val) { write(val.first); write(' '); write(val.second); } template <size_t N = 0, typename T> void write_tuple(const T t) { if constexpr (N < std::tuple_size<T>::value) { if constexpr (N > 0) { write(' '); } const auto x = std::get<N>(t); write(x); write_tuple<N + 1>(t); } } template <class... T> bool write(tuple<T...> tpl) { write_tuple(tpl); return true; } template <class T, size_t S> void write(const array<T, S> val) { auto n = val.size(); for (size_t i = 0; i < n; i++) { if (i) write(' '); write(val[i]); } } void write(i128 val) { string s; bool negative = 0; if (val < 0) { negative = 1; val = -val; } while (val) { s += '0' + int(val % 10); val /= 10; } if (negative) s += "-"; reverse(all(s)); if (len(s) == 0) s = "0"; write(s); } }; Scanner scanner = Scanner(stdin); Printer printer = Printer(stdout); void flush() { printer.flush(); } void print() { printer.write('\n'); } template <class Head, class... Tail> void print(Head &&head, Tail &&... tail) { printer.write(head); if (sizeof...(Tail)) printer.write(' '); print(forward<Tail>(tail)...); } void read() {} template <class Head, class... Tail> void read(Head &head, Tail &... tail) { scanner.read(head); read(tail...); } } // namespace fastio using fastio::print; using fastio::flush; using fastio::read; #define INT(...) \ int __VA_ARGS__; \ read(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ read(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ read(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ read(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ read(__VA_ARGS__) #define VEC(type, name, size) \ vector<type> name(size); \ read(name) #define VV(type, name, h, w) \ vector<vector<type>> name(h, vector<type>(w)); \ read(name) void YES(bool t = 1) { print(t ? "YES" : "NO"); } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { print(t ? "Yes" : "No"); } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { print(t ? "yes" : "no"); } void no(bool t = 1) { yes(!t); } #line 4 "main.cpp" #line 2 "library/mod/modint_common.hpp" struct has_mod_impl { template <class T> static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{}); template <class T> static auto check(...) -> std::false_type; }; template <class T> class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {}; template <typename mint> mint inv(int n) { static const int mod = mint::get_mod(); static vector<mint> dat = {0, 1}; assert(0 <= n); if (n >= mod) n %= mod; while (len(dat) <= n) { int k = len(dat); int q = (mod + k - 1) / k; dat.eb(dat[k * q - mod] * mint::raw(q)); } return dat[n]; } template <typename mint> mint fact(int n) { static const int mod = mint::get_mod(); assert(0 <= n && n < mod); static vector<mint> dat = {1, 1}; while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat))); return dat[n]; } template <typename mint> mint fact_inv(int n) { static vector<mint> dat = {1, 1}; if (n < 0) return mint(0); while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat))); return dat[n]; } template <class mint, class... Ts> mint fact_invs(Ts... xs) { return (mint(1) * ... * fact_inv<mint>(xs)); } template <typename mint, class Head, class... Tail> mint multinomial(Head &&head, Tail &&... tail) { return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...); } template <typename mint> mint C_dense(int n, int k) { static vvc<mint> C; static int H = 0, W = 0; auto calc = [&](int i, int j) -> mint { if (i == 0) return (j == 0 ? mint(1) : mint(0)); return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0); }; if (W <= k) { FOR(i, H) { C[i].resize(k + 1); FOR(j, W, k + 1) { C[i][j] = calc(i, j); } } W = k + 1; } if (H <= n) { C.resize(n + 1); FOR(i, H, n + 1) { C[i].resize(W); FOR(j, W) { C[i][j] = calc(i, j); } } H = n + 1; } return C[n][k]; } template <typename mint, bool large = false, bool dense = false> mint C(ll n, ll k) { assert(n >= 0); if (k < 0 || n < k) return 0; if constexpr (dense) return C_dense<mint>(n, k); if constexpr (!large) return multinomial<mint>(n, k, n - k); k = min(k, n - k); mint x(1); FOR(i, k) x *= mint(n - i); return x * fact_inv<mint>(k); } template <typename mint, bool large = false> mint C_inv(ll n, ll k) { assert(n >= 0); assert(0 <= k && k <= n); if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k); return mint(1) / C<mint, 1>(n, k); } // [x^d] (1-x) ^ {-n} の計算 template <typename mint, bool large = false, bool dense = false> mint C_negative(ll n, ll d) { assert(n >= 0); if (d < 0) return mint(0); if (n == 0) { return (d == 0 ? mint(1) : mint(0)); } return C<mint, large, dense>(n + d - 1, d); } #line 3 "library/mod/modint.hpp" template <int mod> struct modint { static constexpr u32 umod = u32(mod); static_assert(umod < u32(1) << 31); u32 val; static modint raw(u32 v) { modint x; x.val = v; return x; } constexpr modint() : val(0) {} constexpr modint(u32 x) : val(x % umod) {} constexpr modint(u64 x) : val(x % umod) {} constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){}; constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){}; bool operator<(const modint &other) const { return val < other.val; } modint &operator+=(const modint &p) { if ((val += p.val) >= umod) val -= umod; return *this; } modint &operator-=(const modint &p) { if ((val += umod - p.val) >= umod) val -= umod; return *this; } modint &operator*=(const modint &p) { val = u64(val) * p.val % umod; return *this; } modint &operator/=(const modint &p) { *this *= p.inverse(); return *this; } modint operator-() const { return modint::raw(val ? mod - val : u32(0)); } modint operator+(const modint &p) const { return modint(*this) += p; } modint operator-(const modint &p) const { return modint(*this) -= p; } modint operator*(const modint &p) const { return modint(*this) *= p; } modint operator/(const modint &p) const { return modint(*this) /= p; } bool operator==(const modint &p) const { return val == p.val; } bool operator!=(const modint &p) const { return val != p.val; } modint inverse() const { int a = val, b = mod, u = 1, v = 0, t; while (b > 0) { t = a / b; swap(a -= t * b, b), swap(u -= t * v, v); } return modint(u); } modint pow(ll n) const { assert(n >= 0); modint ret(1), mul(val); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } #ifdef FASTIO void write() { fastio::printer.write(val); } void read() { fastio::scanner.read(val); val %= mod; } #endif static constexpr int get_mod() { return mod; } // (n, r), r は 1 の 2^n 乗根 static constexpr pair<int, int> ntt_info() { if (mod == 167772161) return {25, 17}; if (mod == 469762049) return {26, 30}; if (mod == 754974721) return {24, 362}; if (mod == 880803841) return {23, 211}; if (mod == 998244353) return {23, 31}; if (mod == 1045430273) return {20, 363}; if (mod == 1051721729) return {20, 330}; if (mod == 1053818881) return {20, 2789}; return {-1, -1}; } static constexpr bool can_ntt() { return ntt_info().fi != -1; } }; using modint107 = modint<1000000007>; using modint998 = modint<998244353>; #line 2 "library/geo/base.hpp" template <typename T> struct Point { T x, y; Point() : x(0), y(0) {} template <typename A, typename B> Point(A x, B y) : x(x), y(y) {} template <typename A, typename B> Point(pair<A, B> p) : x(p.fi), y(p.se) {} Point operator+(Point p) const { return {x + p.x, y + p.y}; } Point operator-(Point p) const { return {x - p.x, y - p.y}; } bool operator==(Point p) const { return x == p.x && y == p.y; } bool operator!=(Point p) const { return x != p.x || y != p.y; } Point operator-() const { return {-x, -y}; } Point operator*(T t) const { return {x * t, y * t}; } bool operator<(Point p) const { if (x != p.x) return x < p.x; return y < p.y; } T dot(Point other) { return x * other.x + y * other.y; } T det(Point other) { return x * other.y - y * other.x; } double norm() { return sqrtl(x * x + y * y); } double angle() { return atan2(y, x); } Point rotate(double theta) { static_assert(!is_integral<T>::value); double c = cos(theta), s = sin(theta); return Point{c * x - s * y, s * x + c * y}; } #ifdef FASTIO void read() { fastio::read(x), fastio::read(y); } void write() { fastio::printer.write(pair<T, T>({x, y})); } #endif }; // A -> B -> C と進むときに、左に曲がるならば +1、右に曲がるならば -1 template <typename T> int ccw(Point<T> A, Point<T> B, Point<T> C) { T x = (B - A).det(C - A); if (x > 0) return 1; if (x < 0) return -1; return 0; } template <typename REAL, typename T> REAL dist(Point<T> A, Point<T> B) { A = A - B; T p = A.dot(A); return sqrt(REAL(p)); } template <typename T> struct Line { T a, b, c; Line(T a, T b, T c) : a(a), b(b), c(c) {} Line(Point<T> A, Point<T> B) { a = A.y - B.y, b = B.x - A.x, c = A.x * B.y - A.y * B.x; } Line(T x1, T y1, T x2, T y2) : Line(Point<T>(x1, y1), Point<T>(x2, y2)) {} template <typename U> U eval(Point<U> P) { return a * P.x + b * P.y + c; } template <typename U> T eval(U x, U y) { return a * x + b * y + c; } bool is_parallel(Line other) { return a * other.b - b * other.a == 0; } bool is_orthogonal(Line other) { return a * other.a + b * other.b == 0; } }; template <typename T> struct Segment { Point<T> A, B; Segment(Point<T> A, Point<T> B) : A(A), B(B) {} Segment(T x1, T y1, T x2, T y2) : Segment(Point<T>(x1, y1), Point<T>(x2, y2)) {} bool contain(Point<T> C) { static_assert(is_integral<T>::value); T det = (C - A).det(B - A); if (det != 0) return 0; return (C - A).dot(B - A) >= 0 && (C - B).dot(A - B) >= 0; } Line<T> to_Line() { return Line(A, B); } }; template <typename REAL> struct Circle { Point<REAL> O; REAL r; Circle(Point<REAL> O, REAL r) : O(O), r(r) {} Circle(REAL x, REAL y, REAL r) : O(x, y), r(r) {} template <typename T> bool contain(Point<T> p) { REAL dx = p.x - O.x, dy = p.y - O.y; return dx * dx + dy * dy <= r * r; } }; template <typename T> struct Polygon { vc<Point<T>> points; T a; template <typename A, typename B> Polygon(vc<pair<A, B>> pairs) { for (auto&& [a, b]: pairs) points.eb(Point<T>(a, b)); build(); } Polygon(vc<Point<T>> points) : points(points) { build(); } int size() { return len(points); } template <typename REAL> REAL area() { return a * 0.5; } template <enable_if_t<is_integral<T>::value, int> = 0> T area_2() { return a; } bool is_convex() { FOR(j, len(points)) { int i = (j == 0 ? len(points) - 1 : j - 1); int k = (j == len(points) - 1 ? 0 : j + 1); if ((points[j] - points[i]).det(points[k] - points[j]) < 0) return false; } return true; } private: void build() { a = 0; FOR(i, len(points)) { int j = (i + 1 == len(points) ? 0 : i + 1); a += points[i].det(points[j]); } if (a < 0) { a = -a; reverse(all(points)); } } }; #line 1 "library/geo/inside_polygon.hpp" // https://qoj.ac/problem/5443 // 線分上に頂点や辺が来ることは許容 template <typename T> bool inside_polygon(Segment<T> S, vc<Point<T>>& dat) { using P = Point<T>; int N = len(dat); int cnt = 0; P A = S.A, B = S.B; auto PREV = [&](int i) -> int { return (i == 0 ? N : i) - 1; }; auto NEXT = [&](int i) -> int { return (i == N - 1 ? 0 : i + 1); }; FOR(i, N) { P p = dat[i], q = dat[NEXT(i)], r = dat[PREV(i)]; int a = ccw(A, B, p); int b = ccw(A, B, q); int c = ccw(A, B, r); if (a * b == -1) { Segment pq(p, q); auto L = pq.to_Line(); T x = L.eval(A), y = L.eval(B); if (x < y) { x = -x, y = -y; } if (x <= 0) ++cnt; if (0 < x && x < x - y) return 0; } if (a == 0) { if (b != c && (b * c < 0 || ccw(p, q, r) > 0)) { T t = (p - A).dot(B - A), x = (B - A).dot(B - A); if (t <= 0) ++cnt; if (0 < t && t < x) return 0; } } } return cnt % 2 == 1; } #line 2 "library/geo/angle_sort.hpp" #line 4 "library/geo/angle_sort.hpp" // 偏角ソートに対する argsort template <typename T> vector<int> angle_sort(vector<Point<T>>& P) { vector<int> lower, origin, upper; const Point<T> O = {0, 0}; FOR(i, len(P)) { if (P[i] == O) origin.eb(i); elif ((P[i].y < 0) || (P[i].y == 0 && P[i].x > 0)) lower.eb(i); else upper.eb(i); } sort(all(lower), [&](auto& i, auto& j) { return P[i].det(P[j]) > 0; }); sort(all(upper), [&](auto& i, auto& j) { return P[i].det(P[j]) > 0; }); auto& I = lower; I.insert(I.end(), all(origin)); I.insert(I.end(), all(upper)); return I; } // 偏角ソートに対する argsort template <typename T> vector<int> angle_sort(vector<pair<T, T>>& P) { vc<Point<T>> tmp(len(P)); FOR(i, len(P)) tmp[i] = Point<T>(P[i]); return angle_sort<T>(tmp); } #line 2 "library/nt/primetable.hpp" template <typename T = int> vc<T> primetable(int LIM) { ++LIM; const int S = 32768; static int done = 2; static vc<T> primes = {2}, sieve(S + 1); if (done < LIM) { done = LIM; primes = {2}, sieve.assign(S + 1, 0); const int R = LIM / 2; primes.reserve(int(LIM / log(LIM) * 1.1)); vc<pair<int, int>> cp; for (int i = 3; i <= S; i += 2) { if (!sieve[i]) { cp.eb(i, i * i / 2); for (int j = i * i; j <= S; j += 2 * i) sieve[j] = 1; } } for (int L = 1; L <= R; L += S) { array<bool, S> block{}; for (auto& [p, idx]: cp) for (int i = idx; i < S + L; idx = (i += p)) block[i - L] = 1; FOR(i, min(S, R - L)) if (!block[i]) primes.eb((L + i) * 2 + 1); } } int k = LB(primes, LIM + 1); return {primes.begin(), primes.begin() + k}; } #line 3 "library/mod/powertable.hpp" // a^0, ..., a^N template <typename mint> vc<mint> powertable_1(mint a, ll N) { // table of a^i vc<mint> f(N + 1, 1); FOR(i, N) f[i + 1] = a * f[i]; return f; } // 0^e, ..., N^e template <typename mint> vc<mint> powertable_2(ll e, ll N) { auto primes = primetable(N); vc<mint> f(N + 1, 1); f[0] = mint(0).pow(e); for (auto&& p: primes) { if (p > N) break; mint xp = mint(p).pow(e); ll pp = p; while (pp <= N) { ll i = pp; while (i <= N) { f[i] *= xp; i += pp; } pp *= p; } } return f; } #line 10 "main.cpp" using P = Point<ll>; using mint = modint998; mint solve_QOJ5443(int N, vc<P> dat) { vv(bool, CAN, N, N); vv(int, CNT, N, N); FOR(a, N) FOR(b, N) { if (a == b) continue; P A = dat[a], B = dat[b]; Segment<ll> AB(A, B); vc<bool> ON(N); FOR(c, N) { if (AB.contain(dat[c])) ON[c] = 1; } CNT[a][b] = SUM<int>(ON) - 2; CAN[a][b] = inside_polygon(AB, dat); } FOR(a, N) FOR(b, N) assert(CAN[a][b] == CAN[b][a]); FOR(a, N) FOR(b, N) assert(CNT[a][b] == CNT[b][a]); mint ANS = 0; vc<mint> POW = powertable_1<mint>(2, N); // 凸包が線分 FOR(a, N) FOR(b, a) { if (CAN[a][b]) ANS += POW[CNT[a][b]]; } // angle sort vc<pi> edge; vc<P> dir; FOR(a, N) FOR(b, N) { if (CAN[a][b]) { edge.eb(a, b); dir.eb(dat[b] - dat[a]); } } auto I = angle_sort(dir); edge = rearrange(edge, I); dir = rearrange(dir, I); FOR(s, N) { // s スタート // [0][v]:1 回だけ進んだ // [1][v]:2 回以上進んだ vv(mint, dp, 2, N); // 同じ向きの線分での遷移をまとめて更新するようにする auto SAME = [&](int i, int j) -> bool { return (dir[i].det(dir[j]) == 0 && dir[i].dot(dir[j]) > 0); }; int L = 0; while (L < len(edge)) { int R = L; while (R < len(edge) && SAME(L, R)) ++R; vc<tuple<int, int, mint>> upd; FOR(e, L, R) { auto [frm, to] = edge[e]; mint cf = POW[CNT[frm][to]]; if (frm == s) { upd.eb(0, to, cf); } else { if (to != s) upd.eb(1, to, dp[0][frm] * cf); upd.eb(1, to, dp[1][frm] * cf); } } L = R; for (auto&& [a, b, c]: upd) dp[a][b] += c; } ANS += dp[1][s]; } return ANS; } void test_QOJ5443_1() { int N = 7; vc<P> dat(N); dat[0] = {0, 2}; dat[1] = {4, 0}; dat[2] = {4, 2}; dat[3] = {7, 5}; dat[4] = {5, 7}; dat[5] = {3, 5}; dat[6] = {0, 5}; mint ANS = solve_QOJ5443(N, dat); assert(ANS.val == 56); } void test_QOJ5443_2() { int N = 12; vc<P> dat(N); dat[0] = {0, 0}; dat[1] = {4, 0}; dat[2] = {4, 5}; dat[3] = {0, 5}; dat[4] = {0, 2}; dat[5] = {2, 2}; dat[6] = {2, 3}; dat[7] = {1, 3}; dat[8] = {1, 4}; dat[9] = {3, 4}; dat[10] = {3, 1}; dat[11] = {0, 1}; mint ANS = solve_QOJ5443(N, dat); assert(ANS.val == 51); } void solve() { LL(a, b); print(a + b); } signed main() { test_QOJ5443_1(); test_QOJ5443_2(); solve(); return 0; }