library
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test/mytest/qoj5443.test.cpp
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- Last update: 2023-08-20 22:29:01+09:00
- Problem: https://judge.yosupo.jp/problem/aplusb
- Link: https://qoj.ac/problem/5443
- Link: https://trap.jp/post/1224/
Code
#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/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;
}