結果
| 問題 | No.3653 Space-Time Courier |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-09-13 21:18:03 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 692 ms / 4,000 ms |
| + 566µs | |
| コード長 | 60,280 bytes |
| 記録 | |
| コンパイル時間 | 4,491 ms |
| コンパイル使用メモリ | 391,932 KB |
| 実行使用メモリ | 126,336 KB |
| 最終ジャッジ日時 | 2026-09-13 21:18:20 |
| 合計ジャッジ時間 | 12,522 ms |
|
ジャッジサーバーID （参考情報） |
judge2_0 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 28 |
ソースコード
#define SINGLE_TESTCASE
#define FAST_IO
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
// https://github.com/miscalculation53/library/tree/wip/template/template_all.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_all_but_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_types.hpp
#include <bits/stdc++.h>
using namespace std;
using ld = decltype(EPS);
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
using tlll = tuple<ll, ll, ll>;
using tllll = tuple<ll, ll, ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
template <class T>
using vvvc = vc<vc<vc<T>>>;
using vb = vc<bool>;
using vl = vc<ll>;
using vpll = vc<pll>;
using vtlll = vc<tlll>;
using vtllll = vc<tllll>;
using vstr = vc<string>;
using vvb = vvc<bool>;
using vvl = vvc<ll>;
template <class T>
using pql = priority_queue<T, vc<T>, greater<T>>;
template <class T>
using pqg = priority_queue<T>;
using i128 = __int128_t;
using u128 = __uint128_t;
i128 stoi128(const string &s)
{
const bool neg = s.front() == '-';
u128 res = 0;
for (int i = neg; i < (int)s.size(); i++)
res = 10 * res + s[i] - '0';
if (neg)
return -i128(res - 1) - 1;
return i128(res);
}
string i128tos(i128 x)
{
if (x == 0) return "0";
string sign = "", res = "";
u128 ux;
if (x < 0)
ux = u128(-(x + 1)) + 1, sign = "-";
else
ux = x;
while (ux > 0)
{
res += '0' + ux % 10;
ux /= 10;
}
reverse(res.begin(), res.end());
return sign + res;
}
istream &operator>>(istream &is, i128 &a)
{
string s;
is >> s;
a = stoi128(s);
return is;
}
ostream &operator<<(ostream &os, const i128 &a)
{
os << i128tos(a);
return os;
}
#define cauto const auto
// https://github.com/miscalculation53/library/tree/wip/template/template_rep.hpp
#define overload4(_1,_2,_3,_4,name,...) name
#define rep1(i,n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#define rep2(i,l,r) for (ll i = ll(l), rrrrr = ll(r); i < rrrrr; i++)
#define rep3(i,l,r,d) for (ll i = ll(l), rrrrr = ll(r), ddddd = ll(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define rep(...) overload4(__VA_ARGS__, rep3, rep2, rep1)(__VA_ARGS__)
#define repi1(i,n) for (int i = 0, nnnnn = int(n); i < nnnnn; i++)
#define repi2(i,l,r) for (int i = int(l), rrrrr = int(r); i < rrrrr; i++)
#define repi3(i,l,r,d) for (int i = int(l), rrrrr = int(r), ddddd = int(d); ddddd > 0 ? i < rrrrr : i > rrrrr; i += d)
#define repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
#define fem(...) for (auto &__VA_ARGS__)
// https://github.com/miscalculation53/library/tree/wip/template/template_math.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/is_integral_ext.hpp
template <class T>
constexpr bool is_integral_ext = is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>;
template <class T>
constexpr bool is_signed_ext = is_signed_v<T> || is_same_v<T, i128>;
template <class T>
constexpr bool is_unsigned_ext = is_unsigned_v<T> || is_same_v<T, u128>;
// https://github.com/miscalculation53/library/tree/wip/utils/default_infty.hpp
namespace default_infty_detail
{
template <class T, class = void>
struct has_infty : false_type {};
template <class T>
struct has_infty<T, void_t<decltype(T::infty())>> : true_type {};
template <class T>
const T &custom_value();
template <class T>
inline constexpr bool unsupported = false;
}
template <class T>
constexpr decltype(auto) default_infty()
{
if constexpr (default_infty_detail::has_infty<T>::value)
return default_infty_detail::custom_value<T>();
else if constexpr (is_same_v<T, i128> || is_same_v<T, u128>)
return T(INF) * T(INF);
else if constexpr (is_integral_ext<T> && !is_same_v<T, bool>)
{
if constexpr (sizeof(T) >= sizeof(ll))
return T(INF);
else if constexpr (numeric_limits<T>::digits >= 31)
return (T(1) << 30) - 1;
else
return T(numeric_limits<T>::max() / 2);
}
else if constexpr (numeric_limits<T>::has_infinity)
return numeric_limits<T>::infinity();
else
static_assert(default_infty_detail::unsupported<T>, "No default infinity for this type; specify infty explicitly or define T::infty().");
}
template <class T, class U>
inline bool chmin(T &a, U b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, U b) { return a < b ? a = b, true : false; }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divfloor(U a, V b) { return T(a) / T(b) - (T(a) % T(b) && (T(a) ^ T(b)) < 0); }
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T divround(U a, V b);
template <class T = ll, class U, class V, typename = enable_if_t<is_integral_ext<U> && is_integral_ext<V>>>
inline constexpr T safemod(U a, V b) { return T(a) - T(b) * divfloor<T>(a, b); }
template <class T = ll, class U, class V>
constexpr T ipow(U a, V b);
template <class T = ll, class A, class B, class M>
T mul_limited(A a, B b, M m);
template <class T = ll, class A, class B>
T mul_limited(A a, B b);
template <class T = ll, class A, class B, class M>
T pow_limited(A a, B b, M m);
template <class T = ll, class A, class B>
T pow_limited(A a, B b);
template <class T = ll, class A, class K>
constexpr T iroot(A a, K k);
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base);
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base, int n);
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base);
template <const bool use_upper = true, class U>
string base_repr_str(U val, int base, int n);
// https://github.com/miscalculation53/library/tree/wip/template/template_vector.hpp
#define ALL(a) (a).begin(), (a).end()
template <class T = ll, class V>
inline T SZ(const V &x) { return x.size(); }
#define eb emplace_back
#define LMD(x,fx) ([&](const auto &x) { return fx; })
template <class F>
auto gen_vec(int n, const F &f);
#define GEN_VEC(n,i,fi) (gen_vec(n, LMD(i, fi)))
template <class T, size_t d, size_t i = 0, class V>
auto dvec(const V (&sz)[d], const T &init);
template <class T = ll>
T ctol(const char &c, const string &s);
template <class T = ll>
vc<T> stov(const string &s, char first);
template <class T = ll>
vc<T> stov(const string &s, const string &t);
template <class T>
string vtos(const vc<T> &v, char first);
template <class T>
string vtos(const vc<T> &v, const string &t);
template <class T>
vc<T> concat(const vvc<T> &vs);
template <class T>
vc<T> concat(const vc<T> &v);
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs);
// https://github.com/miscalculation53/library/tree/wip/template/template_algo.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_infty.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/resolved_value.hpp
template <class T, auto x, enable_if_t<!is_invocable_v<decltype(x)>, int> = 0>
constexpr T resolved_value();
template <class T, auto x, enable_if_t<is_invocable_v<decltype(x)>, long> = 0>
const T &resolved_value();
template <class T, auto x = nullptr>
constexpr decltype(auto) resolved_infty()
{
if constexpr (is_same_v<decltype(x), nullptr_t>)
return default_infty<T>();
else
return resolved_value<T, x>();
}
template <class V>
auto SUM(const V &v);
template <class T, class V>
T SUM(const V &v);
template <class V>
auto MAX(const V &v);
template <class T, class U>
vc<T> permuted(const vc<T> &a, const vc<U> &p);
template <class T, class U, class... Ts>
vc<T> permuted(const vc<T> &p, const vc<U> &q, const vc<Ts> &...rs);
template <class V>
V reversed(const V &v);
template <class V, class Equal = equal_to<>>
void unique(V &v, Equal equal = {});
template <class V, class Compare = less<>, class Equal = equal_to<>>
void sortunique(V &v, Compare comp = {}, Equal equal = {});
template <class V, class U>
void rotate(V &v, U k);
template <class T>
vvc<T> top(const vvc<T> &a)
{
if (a.empty())
return {};
const int n = a.size(), m = a[0].size();
vvc<T> b(m, vc<T>(n));
repi(i, n)
{
assert(SZ<int>(a[i]) == m);
repi(j, m) b[j][i] = a[i][j];
}
return b;
}
vstr top(const vstr &a)
{
vvc<char> a_(a.size());
repi(i, SZ<int>(a)) a_[i] = {ALL(a[i])};
vvc<char> b_ = top(a_);
vstr b(b_.size());
repi(i, SZ<int>(b)) b[i] = {ALL(b_[i])};
return b;
}
template <class T, class = void>
struct has_e0 : false_type {};
template <class T>
struct has_e0<T, void_t<decltype(T::e0())>> : true_type {};
template <class T>
inline constexpr bool has_e0_v = has_e0<T>::value;
template <class T>
struct MonoidAdd
{
using S = T;
static constexpr S op(S a, S b) { return a + b; }
static constexpr S e()
{
if constexpr (has_e0_v<S>)
return S::e0();
else
return {};
}
template <class I, class = decltype(declval<S>() * declval<I>())>
static constexpr S pow(const S &a, I k);
};
template <class T, auto infty = nullptr>
struct MonoidMin
{
using S = T;
static constexpr S op(S a, S b) { return min(a, b); }
static constexpr decltype(auto) e() { return resolved_infty<T, infty>(); }
template <class I>
static constexpr S pow(const S &a, I k);
};
template <class T, auto infty = nullptr>
struct MonoidMax
{
using S = T;
static constexpr S op(S a, S b) { return max(a, b); }
static constexpr S e() { return -resolved_infty<T, infty>(); }
template <class I>
static constexpr S pow(const S &a, I k);
};
namespace internal
{
template <class M, class I, class = void>
struct HasMonoidPow : false_type
{
};
template <class M, class I>
struct HasMonoidPow<M, I, void_t<decltype(M::pow(declval<const typename M::S &>(), declval<I>()))>> : true_type
{
};
}
template <class M, class I>
typename M::S pow_monoid(typename M::S a, I k);
template <class M>
vc<typename M::S> cuml(const vc<typename M::S> &v, int left_index = 0)
{
const int n = v.size();
vc<typename M::S> res(n + 1);
res[0] = M::e();
repi(i, n) res[i + 1] = M::op(res[i], v[i]);
res.erase(res.begin(), res.begin() + left_index);
return res;
}
template <class M>
vc<typename M::S> cumr(const vc<typename M::S> &v, int right_index = 0);
template <class T>
vc<T> cumlsum(const vc<T> &v, int left_index = 0)
{ return cuml<MonoidAdd<T>>(v, left_index); }
constexpr array<pll, 4> DRULgrid = {{{1, 0}, {0, 1}, {-1, 0}, {0, -1}}};
constexpr array<pll, 4> DRULplane = {{{0, -1}, {1, 0}, {0, 1}, {-1, 0}}};
// https://github.com/miscalculation53/library/tree/wip/template/template_binsearch.hpp
template <class T>
struct is_random_access_iterator
{
static constexpr bool value = is_same_v<
typename iterator_traits<T>::iterator_category,
random_access_iterator_tag
>;
};
template <class T>
constexpr bool is_random_access_iterator_v = is_random_access_iterator<T>::value;
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {});
template <class T = ll, class V, class Value, class Comp = ranges::less, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {});
#define DEFAULT_COMP ranges::less
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_max(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>;
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto leq_max(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>;
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto gt_min(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>;
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto geq_min(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>;
template <class T = ll, class V, class Value, class Comp = DEFAULT_COMP, class Proj = identity>
inline auto lt_cnt(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
-> enable_if_t<is_random_access_iterator_v<typename V::iterator>, T>;
template <class V, class Value>
inline auto lt_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>;
template <class V, class Value>
inline auto leq_max(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>;
template <class V, class Value>
inline auto gt_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>;
template <class V, class Value>
inline auto geq_min(const V &v, const Value &val)
-> enable_if_t<!is_random_access_iterator_v<typename V::iterator>, typename V::const_iterator>;
namespace internal
{
template <class T>
bool binsearch_adjacent(T a, T b);
};
template <class T = ll, class Judge, class InitOk, class InitNg>
pair<T, T> binsearch(const Judge &judge, InitOk init_ok, InitNg init_ng, bool check_ok = true, bool check_ng = true);
// https://github.com/miscalculation53/library/tree/wip/template/template_bit.hpp
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
inline constexpr ll bit_width(ll x) { return std::bit_width((ull)x); }
inline constexpr ll bit_floor(ll x) { return std::bit_floor((ull)x); }
inline constexpr ll bit_ceil(ll x) { return std::bit_ceil((ull)x); }
inline constexpr ll countr_zero(ll x) { assert(x != 0); return std::countr_zero((ull)x); }
inline constexpr ll popcount(ll x) { return std::popcount((ull)x); }
inline constexpr bool has_single_bit(ll x) { return std::has_single_bit((ull)x); }
inline constexpr ull lsb_pos(ull x) { assert(x != 0); return countr_zero(x); }
inline constexpr ull msb_pos(ull x) { assert(x != 0); return bit_width(x) - 1; }
inline constexpr ull lsb_mask(ull x) { assert(x != 0); return x & -x; }
inline constexpr ull msb_mask(ull x) { assert(x != 0); return bit_floor(x); }
inline constexpr bool btest(ull x, uint k) { return (x >> k) & 1; }
inline constexpr bool bsubset(ull x, ull y) { return (x & y) == x; }
inline constexpr bool bsupset(ull x, ull y) { return (x & y) == y; }
inline constexpr ull bsetminus(ull x, ull y) { return x & ~y; }
// https://github.com/miscalculation53/library/tree/wip/template/template_inout.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump.hpp
// https://github.com/miscalculation53/library/tree/wip/template/template_dump_map.hpp
#define CPP_DUMP_DEFINE_DATA(...)
#define dump(...)
#define local(...)
#define oj(...) __VA_ARGS__
#define local_oj(a,b) (b)
template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que);
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque);
template <class T>
auto content(const T &obj);
namespace fastio {
template <class T>
struct unsigned_integer
{
using type = make_unsigned_t<T>;
};
template <>
struct unsigned_integer<i128>
{
using type = u128;
};
template <>
struct unsigned_integer<u128>
{
using type = u128;
};
template <class T>
using unsigned_integer_t = typename unsigned_integer<T>::type;
static constexpr uint32_t SIZ = 1 << 17;
char ibuf[SIZ];
char obuf[SIZ];
char out[100];
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SIZ - pir + pil, stdin);
pil = 0;
if (pir < SIZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd1(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (c <= ' ');
}
void rd1(string &x) {
x.clear();
while (true) {
if (pil == pir) load();
while (pil < pir && ibuf[pil] <= ' ') ++pil;
if (pil < pir) break;
}
while (true) {
uint32_t p = pil;
while (pil < pir && ibuf[pil] > ' ') ++pil;
x.append(ibuf + p, pil - p);
if (pil < pir) {
++pil;
return;
}
load();
}
}
template <typename T>
void rd1_real(T &x) {
string s;
rd1(s);
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = from_chars(s.data(), s.data() + s.size(), x);
if (ec == errc{} && p == s.data() + s.size()) return;
}
if constexpr (is_same_v<T, long double>)
x = stold(s);
else
x = stod(s);
}
template <bool check_buffer = true, typename T>
void rd1_integer(T &x) {
using U = unsigned_integer_t<T>;
bool minus = false;
U val = 0;
if constexpr (check_buffer)
if (pil + 100 > pir) load();
uint32_t p = pil;
while (ibuf[p] < '-') ++p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (ibuf[p] == '-') minus = true, ++p;
}
while ('0' <= ibuf[p]) val = val * 10 + (ibuf[p++] & 15);
pil = p;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus)
{
const U min_abs = U(numeric_limits<T>::max()) + 1;
x = val == min_abs ? numeric_limits<T>::lowest() : -T(val);
}
else x = T(val);
}
else
x = T(val);
}
void rd1(int &x) { rd1_integer(x); }
void rd1(ll &x) { rd1_integer(x); }
void rd1(i128 &x) { rd1_integer(x); }
void rd1(uint &x) { rd1_integer(x); }
void rd1(ull &x) { rd1_integer(x); }
void rd1(u128 &x) { rd1_integer(x); }
void rd1(double &x) { rd1_real(x); }
void rd1(long double &x) { rd1_real(x); }
template <class T, class U>
void rd1(pair<T, U> &p);
template <class... T>
void rd1(tuple<T...> &tpl) {
apply([](auto &...x) { (rd1(x), ...); }, tpl);
}
template <size_t N = 0, typename T>
void rd1(array<T, N> &x);
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
template <class... T>
void read(T &...x) {
if constexpr (sizeof...(T) <= SIZ / 100 &&
((!is_same_v<T, char> &&
(is_integral_v<T> || is_same_v<T, i128> || is_same_v<T, u128>)) && ...)) {
if (pil + 100 * sizeof...(T) > pir) load();
(rd1_integer<false>(x), ...);
}
else
(rd1(x), ...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(string_view s) {
while (!s.empty()) {
if (por == SIZ) flush();
size_t n = min<size_t>(s.size(), SIZ - por);
memcpy(obuf + por, s.data(), n);
por += n;
s.remove_prefix(n);
}
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
using U = unsigned_integer_t<T>;
U ux;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (x < 0)
obuf[por++] = '-', ux = U(0) - U(x);
else
ux = U(x);
}
else
ux = x;
int outi;
for (outi = 96; ux >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[ux % 10000], 4);
ux /= 10000;
}
if (ux >= 1000) {
memcpy(obuf + por, pre.num[ux], 4);
por += 4;
} else if (ux >= 100) {
memcpy(obuf + por, pre.num[ux] + 1, 3);
por += 3;
} else if (ux >= 10) {
int q = (ux * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (ux - q * 10) | '0';
por += 2;
} else
obuf[por++] = ux | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt1_real(T x) {
if constexpr (!is_same_v<T, long double>)
{
auto [p, ec] = to_chars(out, out + sizeof(out), x, chars_format::fixed, 15);
if (ec == errc{}) {
wt1(string_view(out, p));
return;
}
}
ostringstream oss;
oss << fixed << setprecision(15) << x;
wt1(oss.str());
}
void wt1(int x) { wt1_integer(x); }
template <class T, enable_if_t<is_integral_v<T>, int> = 0>
void wt1(T x) { wt1_integer(x); }
void wt1(i128 x) { wt1_integer(x); }
void wt1(u128 x) { wt1_integer(x); }
void wt1(double x) { wt1_real(x); }
void wt1(long double x) { wt1_real(x); }
template <class T, class U>
void wt1(const pair<T, U> &val);
template <class... T>
void wt1(const tuple<T...> &tpl);
template <class T, size_t S>
void wt1(const array<T, S> &val);
template <class T>
void wt1(const vector<T> &val);
template <class... T>
void write(T &&...x) {
(wt1(std::forward<T>(x)), ...);
}
template <class... T>
void print(T &&...x) {
if constexpr (sizeof...(T))
{
int i = 0;
((i++ ? wt1(' ') : void(), wt1(std::forward<T>(x))), ...);
}
wt1('\n');
}
}
struct Dummy {
Dummy() { atexit(fastio::flush); }
} dummy;
namespace internal
{
template <class... Ts>
void READnodump(Ts &...a) { fastio::read(a...); }
template <class... T>
void READVECnodump(int n, vc<T> &...v)
{
(v.resize(n), ...);
READnodump(v...);
}
template <class... T>
void READVEC2nodump(int n, int m, vvc<T> &...v);
template <class... T>
void READJAGnodump(int n, vvc<T> &...vs);
};
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T,...) T __VA_ARGS__; READ(__VA_ARGS__)
#define CHAR(...) IN(char, __VA_ARGS__)
#define INT(...) IN(int, __VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define STR(...) IN(string, __VA_ARGS__)
#define ARR(T,n,...) array<T, n> __VA_ARGS__; READ(__VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define READVEC2(...) internal::READVEC2nodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T,n,...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define VEC2(T,n,m,...) vvc<T> __VA_ARGS__; READVEC2(n, m, __VA_ARGS__)
#define READJAG(...) internal::READJAGnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define JAG(T,n,...) vvc<T> __VA_ARGS__; READJAG(n, __VA_ARGS__)
#define ENDL '\n'
#define WRITE fastio::write
#define PRINT fastio::print
#define PRINTEXIT(...) do { PRINT(__VA_ARGS__); exit(0); } while (false)
#define PRINTRETURN(...) do { PRINT(__VA_ARGS__); return; } while (false)
template <class T>
void PRINTV(const vc<T> &v);
#define PRINTVEXIT(...) do { PRINTV(__VA_ARGS__); exit(0); } while (false)
#define PRINTVRETURN(...) do { PRINTV(__VA_ARGS__); return; } while (false)
template <class T, class U, class P>
pair<T, U> &operator+=(pair<T, U> &a, const P &b);
template <class T, class U, class P>
pair<T, U> operator+(pair<T, U> a, const P &b);
template <class T, class U, class P>
pair<T, U> &operator-=(pair<T, U> &a, const P &b);
template <class T, class U, class P>
pair<T, U> operator-(pair<T, U> a, const P &b);
template <class T, class U>
pair<T, U> operator-(pair<T, U> a);
template <class T, size_t n, class A>
array<T, n> &operator+=(array<T, n> &a, const A &b);
template <class T, size_t n, class A>
array<T, n> operator+(array<T, n> a, const A &b);
template <class T, size_t n, class A>
array<T, n> &operator-=(array<T, n> &a, const A &b);
template <class T, size_t n, class A>
array<T, n> operator-(array<T, n> a, const A &b);
template <class T, size_t n>
array<T, n> operator-(array<T, n> a);
namespace internal
{
template <size_t... I, class A, class B>
auto &tuple_add_impl(A &a, const B &b, const index_sequence<I...>)
{
((get<I>(a) += get<I>(b)), ...);
return a;
}
template <size_t... I, class A, class B>
auto &tuple_sub_impl(A &a, const B &b, const index_sequence<I...>);
template <size_t... I, class A>
auto &tuple_neg_impl(A &a, const index_sequence<I...>);
};
template <class... Ts, class Tp>
tuple<Ts...> &operator+=(tuple<Ts...> &a, const Tp &b)
{ return internal::tuple_add_impl(a, b, make_index_sequence<tuple_size_v<tuple<Ts...>>>{}); }
template <class... Ts, class Tp>
tuple<Ts...> operator+(tuple<Ts...> a, const Tp &b);
template <class... Ts, class Tp>
tuple<Ts...> &operator-=(tuple<Ts...> &a, const Tp &b);
template <class... Ts, class Tp>
tuple<Ts...> operator-(tuple<Ts...> a, const Tp &b);
template <class... Ts>
tuple<Ts...> operator-(tuple<Ts...> a);
template <class T, class Add>
void offset(vc<T> &v, const Add &add) { for (auto &vi : v) vi += add; }
template <class T, class Add>
void offset(vvc<T> &v, const Add &add) { for (auto &vi : v) for (auto &vij : vi) vij += add; }
template <class T, const size_t m>
array<vc<T>, m> unzip(const vc<array<T, m>> &vt);
template <class T, const size_t m>
vc<array<T, m>> zip(const array<vc<T>, m> &tv);
template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt);
template <class T, class U>
vc<pair<T, U>> zip(const pair<vc<T>, vc<U>> &tv);
namespace internal
{
template <size_t... I, class V, class Tp>
auto vt_to_tv_impl(V &tv, const Tp &t, index_sequence<I...>, size_t index);
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index);
};
template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt);
template <class... Ts>
auto zip(const tuple<vc<Ts>...> &tv);
#define UNZIP(vt,...) auto [__VA_ARGS__] = unzip(vt)
#define ZIP(vt,...) auto vt = zip(tuple{__VA_ARGS__})
// https://github.com/miscalculation53/library/tree/wip/template/template_random.hpp
mt19937_64 mt;
template <class T = ll, class U1, class U2>
T randint(U1 l, U2 r);
bool randbool(double p)
{
assert(0 <= p && p <= 1);
return bernoulli_distribution(p)(mt);
}
namespace internal
{
template <bool does_sort, class V, class T>
void random_sample_range(V &res, T l, T r);
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/template_modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_static.hpp
// https://github.com/miscalculation53/library/tree/wip/utils/larger_int.hpp
namespace larger_int_detail
{
template <class T>
[[deprecated("larger_int: 128-bit integer is not widened; intermediate arithmetic may overflow")]]
constexpr bool warn_no_wider_integer();
}
template <class T>
struct larger_int
{
private:
static constexpr bool check();
static_assert(check());
public:
using type = T;
};
#define LARGER_INT(T,U) template <> struct larger_int<T> { using type = U; };
LARGER_INT(signed char, short)
LARGER_INT(short, int)
LARGER_INT(int, long long)
LARGER_INT(long, __int128_t)
LARGER_INT(long long, __int128_t)
LARGER_INT(unsigned char, unsigned short)
LARGER_INT(unsigned short, unsigned int)
LARGER_INT(unsigned int, unsigned long long)
LARGER_INT(unsigned long, __uint128_t)
LARGER_INT(unsigned long long, __uint128_t)
#undef LARGER_INT
template <class T>
struct Rational;
template <class T>
struct larger_int<Rational<T>>
{
using type = Rational<typename larger_int<T>::type>;
};
template <class T>
using larger_int_t = typename larger_int<T>::type;
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_isprime.hpp
namespace internal
{
template <class T>
constexpr ll powmod_constexpr(ll x, ll n, T m)
{
if (m == 1)
return 0;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
U r = 1, y = safemod(x, m);
while (n)
{
if (n & 1)
r = L(r) * y % m;
y = L(y) * y % m;
n >>= 1;
}
return r;
}
template <class T>
constexpr bool isprime_constexpr(T n);
template <auto n>
constexpr bool isprime = isprime_constexpr(n);
};
namespace internal
{
template <auto M>
struct policy_static
{
using mod_type = decltype(M);
using value_type = make_unsigned_t<mod_type>;
using calc_type = larger_int_t<value_type>;
static constexpr bool is_prime = isprime_constexpr(M);
static constexpr mod_type mod();
static constexpr value_type umod();
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v);
static constexpr value_type mul(value_type a, value_type b);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_barrett32.hpp
namespace internal
{
struct barrett32
{
uint m;
ull im;
explicit barrett32(uint m) : m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return m; }
uint mul(uint a, uint b) const
{
ull z = a;
z *= b;
ull x = ull((u128(z) * im) >> 64);
ull y = x * m;
return uint(z - y + (z < y ? m : 0));
}
};
template <int id>
struct policy_barrett32
{
using value_type = uint;
using calc_type = ull;
using mod_type = int;
static constexpr bool is_prime = false;
static inline barrett32 reducer{998244353};
static void set_mod(mod_type m);
static mod_type mod();
static value_type umod();
static value_type init(value_type v) { return v; }
static mod_type val(value_type v);
static value_type mul(value_type a, value_type b);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/modint_internal_montgomery64.hpp
namespace internal
{
inline constexpr ull inv64(ull a)
{
ull x = a;
while (a * x != 1) x *= 2 - a * x;
return x;
}
struct montgomery64odd
{
ull m, im, sq;
explicit montgomery64odd(ull m) : m(m), im(inv64(m)), sq(-u128(m) % m) {}
ull umod() const { return m; }
ull reduce(u128 x) const
{
auto t = (x + u128(m) * (-im * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * sq); }
};
struct montgomery64
{
ull m, mx, imx, d, q;
uint b;
explicit montgomery64(ull m) : m(m)
{
b = countr_zero(m), mx = m >> b;
imx = inv64(mx);
d = powmod_constexpr((mx + 1) / 2, b, mx);
u128 sq = -u128(mx) % mx;
q = (1 + (((sq - 1) * d) << b)) % m;
}
ull umod() const { return m; }
ull reduce(u128 x) const
{
if (b == 0)
{
auto t = (x + u128(mx) * (-imx * ull(x))) >> 64;
if (t >= m) t -= m;
return (ull)t;
}
ull p = x & MASK(b);
x = (x >> b) + p * d;
ull y = p << (64 - b);
auto t = (x + u128(mx) * (imx * (y - ull(x)))) >> (64 - b);
if (t >= m) { t -= m; if (t >= m) t -= m; }
return (ull)t;
}
ull inv_reduce(i128 v) const { return reduce(u128(v % m + m) * q); }
};
template <int id>
struct policy_montgomery64_odd
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64odd reducer{(1LL << 61) - 1};
static void set_mod(mod_type m);
static mod_type mod();
static value_type umod();
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
static value_type mul(value_type a, value_type b);
};
template <int id>
struct policy_montgomery64
{
using value_type = ull;
using calc_type = u128;
using mod_type = ll;
static constexpr bool is_prime = false;
static inline montgomery64 reducer{(1LL << 61) - 1};
static void set_mod(mod_type m);
static mod_type mod();
static value_type umod();
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v);
static value_type mul(value_type a, value_type b);
};
};
// https://github.com/miscalculation53/library/tree/wip/math/extgcd.hpp
template <class T = ll>
constexpr tuple<T, T, T> extgcd(T a, T b);
namespace internal
{
template <class Policy>
struct modint_impl
{
using V = typename Policy::value_type;
using M = typename Policy::mod_type;
using mint = modint_impl;
private:
V _v;
public:
static constexpr M mod();
template <class T = Policy>
static auto set_mod(M m) -> decltype(T::set_mod(m));
static mint raw(V v);
modint_impl();
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v);
M val() const;
mint &operator+=(const mint &rhs);
mint &operator-=(const mint &rhs);
mint &operator*=(const mint &rhs);
mint &operator/=(const mint &rhs);
mint &operator++();
mint &operator--();
mint operator++(int);
mint operator--(int);
mint operator+() const;
mint operator-() const;
template <class T>
mint pow(T n) const;
mint inv() const;
friend mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend M safe_hash_key(const mint &x) { return x.val(); }
friend void rd1(mint &x)
{
long long a;
fastio::rd1(a);
x = a;
}
friend void wt1(const mint &x)
{
fastio::wt1(x.val());
}
};
};
template <int mod>
using static_modint32 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint32 = internal::modint_impl<internal::policy_barrett32<id>>;
template <ll mod>
using static_modint64 = internal::modint_impl<internal::policy_static<mod>>;
template <int id>
using dynamic_modint64_odd = internal::modint_impl<internal::policy_montgomery64_odd<id>>;
template <int id>
using dynamic_modint64 = internal::modint_impl<internal::policy_montgomery64<id>>;
using modint998244353 = static_modint32<998244353>;
using modint1000000007 = static_modint32<1000000007>;
using modint = dynamic_modint32<-1>;
using modint61 = static_modint64<(1LL << 61) - 1>;
using modint64 = dynamic_modint64<-1>;
template <class T>
struct is_modint : std::false_type
{
};
template <class Policy>
struct is_modint<internal::modint_impl<Policy>> : std::true_type
{
};
template <class T>
inline constexpr bool is_modint_v = is_modint<T>::value;
template <class T>
struct is_static_modint : false_type {};
template <int m>
struct is_static_modint<static_modint32<m>> : true_type {};
template <ll m>
struct is_static_modint<static_modint64<m>> : true_type {};
template <class T>
inline constexpr bool is_static_modint_v = is_static_modint<T>::value;
template <class T>
struct is_dynamic_modint : false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint32<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64_odd<id>> : true_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint64<id>> : true_type {};
template <class T>
inline constexpr bool is_dynamic_modint_v = is_dynamic_modint<T>::value;
template <typename, typename = void>
struct has_mod : std::false_type
{
};
template <typename T>
struct has_mod<T, std::void_t<decltype(T::mod())>> : std::true_type
{
};
template <class mint>
struct modint_less
{
bool operator()(const mint &a, const mint &b) const;
};
template <class mint>
struct modint_hash
{
auto operator()(const mint &x) const;
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/power_table.hpp
template <class mint>
struct PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
PowerTable();
PowerTable(const mint &base);
void reserve(int n);
mint pow(int n);
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/binomial.hpp
template <class T>
struct Binomial
{
private:
inline static decltype(T::mod()) mod;
public:
inline static vc<T> fac_, finv_, inv_;
static void reserve(int n);
static T inv(int n);
static T P(int n, int k);
static T C(int n, int k);
};
// https://github.com/miscalculation53/library/tree/wip/math/modint/stom.hpp
// https://github.com/miscalculation53/library/tree/wip/math/modint/to_rational.hpp
// https://github.com/miscalculation53/library/tree/wip/math/svp2d.hpp
template <class T = ll, class U = larger_int_t<T>>
pair<T, T> svp2d(const pair<T, T> &a, const pair<T, T> &b);
template <class mint>
pair<decltype(mint(0).val()), decltype(mint(0).val())>
mint_to_rat(const mint &x);
namespace cpp_dump
{
template <class T>
struct rat_value
{
T p, q;
friend ostream &operator<<(ostream &os, const rat_value &x)
{
return os << x.p << '/' << x.q;
}
};
struct mint_to_rat_fn
{
template <class T>
requires requires(const T &x)
{
{ T::mod() } -> std::convertible_to<ll>;
{ x.val() } -> std::convertible_to<ll>;
}
constexpr auto operator()(const T &x) const
-> rat_value<typename decltype(mint_to_rat(x))::first_type>;
};
template <class T>
struct rat_object
{
T value;
};
template <class T>
inline constexpr bool rat_is_map = false;
template <class... Args>
inline constexpr bool rat_is_map<std::map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::multimap<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_map<Args...>> = true;
template <class... Args>
inline constexpr bool rat_is_map<std::unordered_multimap<Args...>> = true;
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
template <class T>
static constexpr bool can_convert();
template <typename T>
requires(!requires { std::views::all | std::declval<T>(); })
constexpr decltype(auto) operator()(T &&t) const;
};
template <typename T>
requires(!requires { std::views::all | std::declval<T>(); })
constexpr decltype(auto) operator|(T &&t, rat_closure c);
constexpr rat_closure rat()
{
return rat_closure{};
}
}
using mint = modint998244353;
using bi = Binomial<mint>;
void init()
{
oj(mt.seed(random_device()()));
}
// https://github.com/miscalculation53/library/tree/wip/graph/apsp.hpp
// https://github.com/miscalculation53/library/tree/wip/graph/sssp.hpp
// https://github.com/miscalculation53/library/tree/wip/graph/graph.hpp
// https://github.com/miscalculation53/library/tree/wip/ds/csr.hpp
template <class T, bool is_erasable = false>
struct CSR
{
protected:
int n, m;
vc<int> start;
vc<T> elist;
vc<int> len;
inline int get_last(int i) const
{
if constexpr (is_erasable)
return start[i] + len[i];
else
return start[i + 1];
}
template <class Iter>
struct RowBase
{
using iterator = Iter;
using reference = typename iterator_traits<iterator>::reference;
private:
iterator begi, endi;
public:
RowBase(const iterator &begi, const iterator &endi) : begi(begi), endi(endi) {}
inline iterator begin() const { return begi; }
inline iterator end() const;
template <class I = ll>
inline I size() const { return endi - begi; }
inline bool empty() const { return size() == 0; }
inline reference operator[](int i) const { return *(begi + i); }
inline reference at(int i) const;
inline reference front() const;
inline reference back() const
{
assert(!empty());
return *prev(endi);
}
vc<T> to_v() const;
};
using Row = RowBase<typename vc<T>::iterator>;
using ConstRow = RowBase<typename vc<T>::const_iterator>;
public:
CSR() {}
CSR(const vc<int> &row_sizes)
: n(row_sizes.size())
{
fec(s : row_sizes) assert(s >= 0);
start = cumlsum(row_sizes);
m = start.back();
elist.resize(m);
if constexpr (is_erasable)
len = row_sizes;
}
template <class I>
CSR(int n, const vc<pair<I, T>> &ies) : n(n), m(ies.size()), start(n, 0), elist(m)
{
if constexpr (is_erasable)
len.resize(n);
fec([ i, e ] : ies)
{
assert(0 <= i && i < n);
start[i]++;
}
start = cumlsum(start);
if constexpr (is_erasable)
repi(i, n) len[i] = start[i + 1] - start[i];
auto cnt = start;
repi(j, m)
{
cauto & [ i, e ] = ies[j];
int &k = cnt[i];
elist[k] = e;
k++;
}
}
CSR(const vvc<T> &vv) : n(vv.size()), start(n + 1, 0)
{
m = 0;
fec(row : vv) m += row.size();
elist.resize(m);
if constexpr (is_erasable)
len.resize(n);
for (int i = 0, j = 0; i < n; i++)
{
start[i] = j;
if constexpr (is_erasable)
len[i] = vv[i].size();
fec(e : vv[i])
{
elist[j] = e;
j++;
}
}
start.back() = m;
}
Row operator[](int i) { return Row(elist.begin() + start[i], elist.begin() + get_last(i)); }
ConstRow operator[](int i) const
{ return ConstRow(elist.begin() + start[i], elist.begin() + get_last(i)); }
Row at(int i);
ConstRow at(int i) const;
void pop_back(int i);
int offset(int i) const
{
assert(0 <= i && i <= n);
return start[i];
}
void sortunique();
template <class I = ll>
I size() const { return n; }
vc<T> &get_elist();
const vc<T> &get_elist() const { return elist; }
};
template <class Cost = void>
struct Edge
{
int from, to;
Cost cost;
int index;
Edge() : from(-1), to(-1), index(-1) {}
Edge(int s, int t, Cost c, int i = -1) : from(s), to(t), cost(c), index(i) {}
operator int() const;
bool operator<(const Edge &rhs) const;
Edge rev() const;
};
template <>
struct Edge<void>
{
int from, to, index;
static constexpr int cost = 1;
Edge() : from(-1), to(-1), index(-1) {}
Edge(int s, int t, int i = -1) : from(s), to(t), index(i) {}
operator int() const { return to; }
bool operator<(const Edge &) const { return false; }
Edge rev() const { return Edge(to, from, index); }
};
template <class Cost>
vc<Edge<Cost>> rev_path(const vc<Edge<Cost>> &path);
template <bool is_directed, class Cost = void, bool is_erasable = false>
struct Graph
{
using E = Edge<Cost>;
protected:
template <class C, bool unweighted = is_void_v<C>>
struct InternalEdge
{
int to, index;
C cost;
};
template <class C>
struct InternalEdge<C, true>
{
int to, index;
static constexpr int cost = 1;
};
using GE = conditional_t<is_erasable, E, InternalEdge<Cost>>;
using Weight = conditional_t<is_void_v<Cost>, int, Cost>;
int n = 0, m = 0, era = 0;
CSR<GE, is_erasable> g;
vc<int> eid_to_elist_id;
static E make_edge(int from, int to, const Weight &cost, int index)
{
if constexpr (is_void_v<Cost>)
return E(from, to, index);
else
return E(from, to, cost, index);
}
struct OutEdgeRow;
struct OutEdgeIter
{
using iterator_category = input_iterator_tag;
using value_type = E;
using difference_type = ptrdiff_t;
using pointer = const E *;
using reference = const E &;
private:
friend struct OutEdgeRow;
int from = -1;
typename vc<GE>::const_iterator it;
mutable E e;
OutEdgeIter(int from, typename vc<GE>::const_iterator it) : from(from), it(it) {}
public:
OutEdgeIter() = default;
reference operator*() const
{
if constexpr (is_erasable)
return *it;
else
{
e = make_edge(from, it->to, it->cost, it->index);
return e;
}
}
pointer operator->() const;
OutEdgeIter &operator++()
{
++it;
return *this;
}
OutEdgeIter operator++(int);
bool operator==(const OutEdgeIter &rhs) const { return it == rhs.it; }
bool operator!=(const OutEdgeIter &rhs) const { return !(*this == rhs); }
};
struct OutEdgeRow
{
private:
const Graph *g;
int from, l, r;
OutEdgeIter iter(int pos) const
{
return {from, g->g.get_elist().begin() + pos};
}
public:
OutEdgeRow(const Graph *g, int from)
: g(g), from(from), l(g->g.offset(from)), r(l + g->g[from].size()) {}
OutEdgeIter begin() const { return iter(l); }
OutEdgeIter end() const { return iter(r); }
template <class I = ll>
I size() const { return r - l; }
bool empty() const { return l == r; }
E operator[](int i) const;
E at(int i) const;
E front() const;
E back() const
{
assert(!empty());
return (*this)[size() - 1];
}
vc<E> to_v() const;
};
E get_edge(int from, int pos) const;
template <class F>
void build(F input_edge)
{
vc<int> row_sizes(n);
repi(i, m)
{
auto [u, v, w] = input_edge(i);
assert(0 <= u && u < n && 0 <= v && v < n);
row_sizes[u]++;
if constexpr (!is_directed)
if (u != v) row_sizes[v]++;
}
g = CSR<GE, is_erasable>(row_sizes);
if constexpr (is_erasable)
eid_to_elist_id.assign((is_directed ? 1 : 2) * m, -1);
vc<int> cnt(n);
repi(i, m)
{
auto [u, v, w] = input_edge(i);
int j = cnt[u]++;
int k = g.offset(u) + j;
if constexpr (is_erasable)
g[u][j] = make_edge(u, v, w, i);
else if constexpr (is_void_v<Cost>)
g[u][j] = GE{int(v), i};
else
g[u][j] = GE{int(v), i, w};
if constexpr (is_erasable)
{
int id = is_directed ? i : 2 * i + (u <= v);
eid_to_elist_id[id] = k;
}
if constexpr (!is_directed)
{
if (u != v)
{
j = cnt[v]++;
k = g.offset(v) + j;
if constexpr (is_erasable)
g[v][j] = make_edge(v, u, w, i);
else if constexpr (is_void_v<Cost>)
g[v][j] = GE{int(u), i};
else
g[v][j] = GE{int(u), i, w};
if constexpr (is_erasable)
eid_to_elist_id[2 * i + (v <= u)] = k;
}
}
}
}
public:
Graph() {}
template <class I>
Graph(int n, const vc<pair<I, I>> &es) : n(n), m(es.size()), era(0)
{
build(LMD(i, (tuple{es[i].first, es[i].second, Weight(1)})));
}
template <class I, class C = Cost, enable_if_t<!is_void_v<C>, int> = 0>
Graph(int n, const vc<pair<I, I>> &es, const Weight &dflt_cost) : n(n), m(es.size()), era(0)
{
build(LMD(i, (tuple{es[i].first, es[i].second, dflt_cost})));
}
template <class I, class C, enable_if_t<is_same_v<C, Cost> && !is_void_v<C>, int> = 0>
Graph(int n, const vc<tuple<I, I, C>> &es) : n(n), m(es.size()), era(0)
{
build(LMD(i, es[i]));
}
Graph(int n, const vc<E> &es) : n(n), m(es.size()), era(0)
{
build(LMD(i, (tuple{es[i].from, es[i].to, es[i].cost})));
}
template <class I = ll>
I size() const { return n; }
template <class I = ll>
I num_of_edges() const { return m - era; }
auto out_edges(int v) const
{
return OutEdgeRow(this, v);
}
vc<E> edges() const
{
vc<E> res;
res.reserve(num_of_edges<int>());
if constexpr (is_directed)
{
repi(v, n) fec(e : out_edges(v))
{
res.eb(e);
}
}
else
{
repi(v, n) fec(e : out_edges(v))
{
if (e.from <= e.to) res.eb(e);
}
}
return res;
}
private:
void internal_erase(int elist_id);
};
template <bool is_directed, bool is_erasable = false, class I>
Graph(int, const vc<pair<I, I>> &) -> Graph<is_directed, void, is_erasable>;
template <bool is_directed, bool is_erasable = false, class I, class Cost>
Graph(int, const vc<tuple<I, I, Cost>> &) -> Graph<is_directed, Cost, is_erasable>;
template <bool is_directed, bool is_erasable = false, class I, class Cost>
Graph(int, const vc<pair<I, I>> &, const Cost &) -> Graph<is_directed, Cost, is_erasable>;
template <bool is_directed, bool is_erasable = false, class Cost>
Graph(int, const vc<Edge<Cost>> &) -> Graph<is_directed, Cost, is_erasable>;
template <class Cost = void, bool is_erasable = false>
using GraphDirected = Graph<true, Cost, is_erasable>;
template <class Cost = void, bool is_erasable = false>
using GraphUndirected = Graph<false, Cost, is_erasable>;
// https://github.com/miscalculation53/library/tree/wip/ds/my_queue.hpp
template <class T>
struct MyQueue
{
private:
vc<T> d;
int pos = 0;
public:
void reserve(int n);
template <class I = ll>
I size() const { return SZ<I>(d) - pos; }
bool empty() const { return pos == SZ<int>(d); }
void push(const T &t) { d.eb(t); }
T front() const;
T &front() { return d[pos]; }
void clear();
void pop() { pos++; }
T operator[](int i) const;
T &operator[](int i);
T at(int i) const;
T &at(int i);
vc<T> content();
};
template <bool is_directed, class Cost, auto infty = nullptr>
struct ShortestPath
{
using Dist = conditional_t<is_void_v<Cost>, ll, Cost>;
private:
const Graph<is_directed, Cost> &g;
static constexpr decltype(auto) inf() { return resolved_infty<Dist, infty>(); }
vc<Dist> dists;
vc<Edge<Cost>> prv;
int source = -1;
bool solved_all = false;
void init_solve(int s, int t)
{
source = s;
solved_all = (t == -1);
}
public:
explicit ShortestPath(const Graph<is_directed, Cost> &g) : g(g) {}
ShortestPath(const Graph<is_directed, Cost> &&) = delete;
vc<Dist> bfs(int s, int t = -1)
{
const int n = g.size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
MyQueue<int> que;
dists[s] = 0;
que.push(s);
while (!que.empty())
{
auto v = que.front();
que.pop();
if (v == t)
break;
fe(e : g.out_edges(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
{
prv[e.to] = e;
que.push(e.to);
}
}
}
return dists;
}
vc<Dist> bfs01(int s, int t = -1)
{
const int n = g.size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
vc<int> cur{int(s)}, nxt;
vc<unsigned char> used(n, false);
dists[s] = 0;
while (!cur.empty() || !nxt.empty())
{
if (cur.empty()) cur.swap(nxt);
int v = cur.back();
cur.pop_back();
if (used[v])
continue;
used[v] = true;
if (v == t)
break;
fe(e : g.out_edges(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
{
prv[e.to] = e;
if (e.cost == 0)
cur.eb(e.to);
else
nxt.eb(e.to);
}
}
}
return dists;
}
vc<Dist> dial(int s, int max_cost, int t = -1)
{
static_assert(is_integral_ext<Dist>);
const int n = g.size();
assert(0 <= s && s < n);
assert(0 <= max_cost);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
const int bcnt = max_cost + 1;
vc<int> head(bcnt, -1), nxt(n, -2), pre(n, -2);
int que_size = 0;
auto erase = [&](int v, int b)
{
const int p = pre[v], q = nxt[v];
if (p == -1)
head[b] = q;
else
nxt[p] = q;
if (q != -1)
pre[q] = p;
nxt[v] = pre[v] = -2;
que_size--;
};
auto push = [&](int v, int b)
{
nxt[v] = head[b], pre[v] = -1;
if (head[b] != -1)
pre[head[b]] = v;
head[b] = v, que_size++;
};
Dist cur = 0;
dists[s] = 0;
push(s, 0);
while (que_size)
{
int b = int(cur % bcnt);
while (head[b] == -1)
{
cur++;
if (++b == bcnt)
b = 0;
}
const int v = head[b];
erase(v, b);
assert(dists[v] == cur);
if (v == t)
break;
fec(e : g.out_edges(v))
{
Dist nd = dists[v] + e.cost;
if (nd < dists[e.to])
{
if (pre[e.to] != -2)
erase(e.to, int(dists[e.to] % bcnt));
dists[e.to] = nd, prv[e.to] = e;
push(e.to, int(nd % bcnt));
}
}
}
return dists;
}
vc<Dist> dijkstra(int s, int t = -1)
{
const int n = g.size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
pql<pair<Dist, int>> pque;
dists[s] = 0;
pque.push({0, s});
while (!pque.empty())
{
auto [d, v] = pque.top();
pque.pop();
if (v == t)
break;
if (dists[v] != d)
continue;
fec(e : g.out_edges(v))
{
Dist nd = dists[v] + e.cost;
if (chmin(dists[e.to], nd))
{
prv[e.to] = e;
pque.push({nd, e.to});
}
}
}
return dists;
}
vc<Dist> dijkstra_dense(int s, int t = -1)
{
const int n = g.size();
assert(0 <= s && s < n);
init_solve(s, t);
dists.assign(n, inf());
prv.assign(n, {});
vc<bool> ok(n, false);
dists[s] = 0;
repi(_, n)
{
Dist mn = inf();
int v = -1;
repi(u, n) if (!ok[u] && chmin(mn, dists[u])) v = u;
if (v == -1)
break;
if (v == t)
break;
ok[v] = true;
fec(e : g.out_edges(v))
{
if (chmin(dists[e.to], dists[v] + e.cost))
prv[e.to] = e;
}
}
return dists;
}
vc<Dist> bellman_ford(int s)
{
const int n = g.size();
assert(0 <= s && s < n);
init_solve(s, -1);
dists.assign(n, inf());
prv.assign(n, {});
dists[s] = 0;
repi(t, 2 * n)
{
repi(v, n)
{
if (dists[v] == inf())
continue;
fec(e : g.out_edges(v))
{
Dist nd = dists[v] == -inf() ? -inf() : dists[v] + e.cost;
if (dists[e.to] > nd)
{
prv[e.to] = e;
if (t == n - 1)
dists[e.to] = -inf();
else
dists[e.to] = nd;
}
}
}
}
repi(v, n) if (dists[v] == -inf()) prv[v] = {};
return dists;
}
vc<Dist> solve(int s, int t = -1)
{
if constexpr (is_void_v<Cost>)
return bfs(s, t);
else
{
bool neg = false;
int zcnt = 0;
Dist wplus1 = -inf();
Dist max_cost = 0;
bool wpluscnt_geq2 = false;
repi(v, g.size()) fec(e : g.out_edges(v))
{
if (e.cost < 0)
{
neg = true;
break;
}
chmax(max_cost, e.cost);
}
repi(v, g.size()) fec(e : g.out_edges(v))
{
if (e.cost == 0)
zcnt++;
if (e.cost > 0)
{
if (wplus1 < 0)
wplus1 = e.cost;
else if (wplus1 != e.cost)
{
wpluscnt_geq2 = true;
break;
}
}
}
if (neg)
return bellman_ford(s);
else if (wpluscnt_geq2)
{
const ll n = g.size(), m = g.num_of_edges();
if (n * n < (m << 4))
return dijkstra_dense(s, t);
else
{
if constexpr (is_integral_ext<Dist>)
{
const u128 c = u128(max_cost);
const ull lg = max<ull>(1, bit_width(ull(n)) - 1);
if (c <= u128(m) * lg / u128(n))
return dial(s, int(c), t);
}
return dijkstra(s, t);
}
}
else
{
if (zcnt == 0)
return bfs(s, t);
else
return bfs01(s, t);
}
}
}
vc<Edge<Cost>> prev_edges() const
{
const int n = g.size();
assert(SZ(dists) == n && "solve(s, t) is not called");
return prv;
}
vc<Edge<Cost>> path(int t) const;
};
template <bool is_directed, class Cost, auto infty = nullptr>
struct AllPairsShortestPath
{
using Dist = typename ShortestPath<is_directed, Cost, infty>::Dist;
using Matrix = vvc<Dist>;
private:
using SP = ShortestPath<is_directed, Cost, infty>;
const Graph<is_directed, Cost> &g;
static constexpr decltype(auto) inf() { return resolved_infty<Dist, infty>(); }
Matrix dist;
vvc<int> prev;
vc<Edge<Cost>> by_id;
bool negative = false, solved = false;
enum class Method { repeated_sssp, floyd_warshall, johnson };
Method select_method() const
{
if constexpr (is_void_v<Cost>) return Method::repeated_sssp;
bool neg = false, multiple_positive = false, have_positive = false;
Dist positive = 0;
repi(v, g.size()) fec(e : g.out_edges(v))
{
neg |= e.cost < Dist(0);
if (e.cost > Dist(0))
{
if (have_positive && e.cost != positive) multiple_positive = true;
positive = e.cost, have_positive = true;
}
}
if (!neg && !multiple_positive) return Method::repeated_sssp;
const ll n = g.size(), m = g.num_of_edges();
if (n * n < 16 * m) return Method::floyd_warshall;
if (neg) return Method::johnson;
return Method::repeated_sssp;
}
void init()
{
const int n = g.size();
negative = false, solved = true;
dist.assign(n, vc<Dist>(n, inf()));
prev.assign(n, vc<int>(n, -1));
by_id.resize(g.num_of_edges());
fec(e : g.edges()) by_id[e.index] = e;
}
Edge<Cost> ending_at(int id, int t) const;
public:
explicit AllPairsShortestPath(const Graph<is_directed, Cost> &g) : g(g) {}
AllPairsShortestPath(const Graph<is_directed, Cost> &&) = delete;
const Matrix &solve()
{
const auto method = select_method();
if (method == Method::floyd_warshall) return floyd_warshall();
if (method == Method::johnson) return johnson();
return repeated_sssp();
}
const Matrix &repeated_sssp()
{
init();
fec(e : by_id) assert(e.cost >= Dist(0));
SP sp(g);
repi(s, g.size())
{
dist[s] = sp.solve(s);
const auto row = sp.prev_edges();
repi(t, g.size()) prev[s][t] = row[t].index;
}
return dist;
}
const Matrix &floyd_warshall()
{
init();
const int n = g.size();
repi(v, n) dist[v][v] = 0;
repi(v, n) fec(e : g.out_edges(v))
{
if (chmin(dist[v][e.to], e.cost)) prev[v][e.to] = e.index;
}
repi(k, n) repi(i, n)
{
if (dist[i][k] == inf()) continue;
repi(j, n)
{
if (dist[k][j] == inf()) continue;
const Dist &a = dist[i][k], &b = dist[k][j];
Dist nd;
if (a == -inf() || b == -inf()) nd = -inf();
else if (b < Dist(0) && a < -inf() - b) nd = -inf();
else if (b > Dist(0) && a > inf() - b) nd = inf();
else nd = a + b;
if (chmin(dist[i][j], nd)) prev[i][j] = prev[k][j];
}
}
repi(k, n) if (dist[k][k] < Dist(0))
{
negative = true;
repi(s, n) if (dist[s][k] != inf())
repi(t, n) if (dist[k][t] != inf())
dist[s][t] = -inf(), prev[s][t] = -1;
}
return dist;
}
const Matrix &johnson()
{
if constexpr (is_void_v<Cost>)
return repeated_sssp();
else
{
init();
const int n = g.size();
vc<Dist> h(n, Dist(0));
repi(iter, n)
{
auto next = h;
bool changed = false;
repi(v, n) fec(e : g.out_edges(v))
if (chmin(next[e.to], h[v] + e.cost)) changed = true;
if (!changed) break;
if (iter == n - 1) return floyd_warshall();
h.swap(next);
}
auto reweighted = by_id;
for (auto &e : reweighted) e.cost = e.cost + h[e.from] - h[e.to];
Graph<is_directed, Cost> reweighted_graph(n, reweighted);
SP sp(reweighted_graph);
repi(s, n)
{
dist[s] = sp.dijkstra(s);
const auto row = sp.prev_edges();
repi(t, n)
{
if (dist[s][t] != inf()) dist[s][t] = dist[s][t] - h[s] + h[t];
prev[s][t] = row[t].index;
}
}
return dist;
}
}
bool negative_cycle() const;
vc<Edge<Cost>> prev_edges(int s) const;
vc<Edge<Cost>> path(int s, int t) const;
};
void main2()
{
LL(N, M);
VEC(ll, N, P);
VEC(tlll, M, UVW);
offset(UVW, tlll{-1, -1, 0});
GraphDirected G(N, UVW);
AllPairsShortestPath apsp(G);
auto dists = apsp.solve();
dump(dists | cp::index());
ll mn = INF, cnt = 0;
rep(i, N) rep(j, N) if (i != j)
{
ll tmp = dists[i][j] + P[i] + P[j];
if (chmin(mn, tmp))
cnt = 0;
if (tmp == mn)
cnt++;
}
PRINT(mn, cnt);
}
void test()
{
}
// https://github.com/miscalculation53/library/tree/wip/template/template_main.hpp
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
};
CERR("\n[FAST_IO]\n\n", "32");
cout << fixed << setprecision(20);
init();
CERR("\n[SINGLE_TESTCASE]\n\n", "36");
main2();
}
};
Main<init, main2, test> main_dummy;
int main() {}