結果
| 問題 | No.1919 Many Monster Battles |
| コンテスト | |
| ユーザー |
 miscalc
|
| 提出日時 | 2026-08-03 22:35:48 |
| 言語 | C++23 (gcc 15.2.0 + boost 1.90.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 40,406 bytes |
| 記録 | |
| コンパイル時間 | 3,416 ms |
| コンパイル使用メモリ | 377,280 KB |
| 実行使用メモリ | 180,764 KB |
| 最終ジャッジ日時 | 2026-08-03 22:36:11 |
| 合計ジャッジ時間 | 8,004 ms |
|
ジャッジサーバーID （参考情報） |
judge2_1 / judge1_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 10 TLE * 1 -- * 21 |
ソースコード
#define INF 4'000'000'000'000'000'037LL
#define EPS 1e-11
#include <bits/stdc++.h>
using namespace std;
namespace {
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using pll = pair<ll, ll>;
#define vc vector
template <class T>
using vvc = vc<vc<T>>;
using vl = vc<ll>;
using vpll = vc<pll>;
#ifdef __SIZEOF_INT128__
using i128 = __int128_t;
using u128 = __uint128_t;
#endif
#define cauto const auto
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(i, n) for (ll i = 0, nnnnn = ll(n); i < nnnnn; i++)
#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 repi(...) overload4(__VA_ARGS__, repi3, repi2, repi1)(__VA_ARGS__)
#define fe(...) for (auto __VA_ARGS__)
#define fec(...) for (cauto &__VA_ARGS__)
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>;
template <class T, class U>
inline bool chmin(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) { return divfloor<T>(2 * T(a) + T(b), 2 * T(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)
{
assert(b >= 0);
if (b == 0)
return 1;
if (a == 0 || a == 1)
return a;
if (a < 0 && a == -1)
return b & 1 ? -1 : 1;
T res = 1, tmp = a;
while (true)
{
if (b & 1)
res *= tmp;
b >>= 1;
if (b == 0)
break;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B, class M>
T mul_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (b == 0)
return 0;
return T(a) > T(m) / T(b) ? T(m) : T(a) * T(b);
}
template <class T = ll, class A, class B>
T mul_limited(A a, B b) { return mul_limited<T>(a, b, INF); }
template <class T = ll, class A, class B, class M>
T pow_limited(A a, B b, M m)
{
assert(a >= 0 && b >= 0 && m >= 0);
if (a <= 1 || b == 0)
return min(ipow<T>(a, b), T(m));
T res = 1, tmp = a;
while (true)
{
if (b & 1)
{
if (res > T(m) / tmp)
return m;
res *= tmp;
}
b >>= 1;
if (b == 0)
break;
if (tmp > T(m) / tmp)
return m;
tmp *= tmp;
}
return res;
}
template <class T = ll, class A, class B>
T pow_limited(A a, B b) { return pow_limited<T>(a, b, INF); }
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base)
{
assert(val >= 0);
assert(base >= 2);
if (val == 0)
return {0};
vc<T> a;
while (val > 0)
{
a.emplace_back(val % base);
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
template <class T = ll, class U, class V>
vc<T> base_repr(U val, V base, int n)
{
assert(val >= 0);
assert(base >= 2);
assert(n >= 0);
vc<T> a(n);
repi(i, n)
{
a[i] = val % base;
val /= base;
}
reverse(a.begin(), a.end());
return a;
}
#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
template <class F>
auto gen_vec(int n, const F &f)
{
vc<decltype(f(0))> res(n);
repi(i, n) res[i] = f(i);
return res;
}
template <class T, size_t d, size_t i = 0, class V>
auto dvec(const V (&sz)[d], const T &init)
{
if constexpr (i < d)
return vc(sz[i], dvec<T, d, i + 1>(sz, init));
else
return init;
}
template <class T = ll>
T ctol(const char &c, const string &s)
{
repi(i, SZ<int>(s)) if (s[i] == c) return i;
return -1;
}
template <class T, class... Ts>
vc<T> concat(vc<T> v, const vc<Ts> &...vs)
{
(v.insert(v.end(), ALL(vs)), ...);
return v;
}
template <class T, class U>
vc<T> permuted(const vc<T> &a, const vc<U> &p)
{
const int n = p.size();
vc<T> res(n);
repi(i, n)
{
assert(0 <= p[i] && p[i] < U(a.size()));
res[i] = a[p[i]];
}
return res;
}
template <class T, class U, class... Ts>
vc<T> permuted(const vc<T> &p, const vc<U> &q, const vc<Ts> &...rs)
{
return permuted(permuted(p, q), rs...);
}
template <class V>
V reversed(const V &v) { return V(v.rbegin(), v.rend()); }
#if __cplusplus < 202002L
#else
#endif
template <class V>
void unique(V &v) { v.erase(std::unique(ALL(v)), v.end()); }
template <class V>
void sortunique(V &v)
{
sort(ALL(v));
unique(v);
}
template <class V, class U>
void rotate(V &v, U k)
{
const U n = v.size();
k = (k % n + n) % n;
std::rotate(v.begin(), v.begin() + k, v.end());
}
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;
}
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 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;
}
const vpll DRULgrid = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};
const vpll DRULplane = {{0, -1}, {1, 0}, {0, 1}, {-1, 0}};
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;
#if __cplusplus < 202002L
struct identity
{
template <class T>
constexpr T &&operator()(T &&t) const noexcept
{ return forward<T>(t); }
};
namespace internal
{
template <class T = ll, class V, class Judge>
inline T bound_helper(const V &v, Judge judge)
{
int l = -1, r = v.size();
while (r - l > 1)
{
int m = (l + r) / 2;
if (judge(m))
l = m;
else
r = m;
}
return r;
}
};
template <class T = ll, class V, class Value, class Comp = less<>, class Proj = identity>
inline T LB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{
return internal::bound_helper(v, [&](int i) -> bool
{ return comp(proj(*(v.begin() + i)), val); });
}
template <class T = ll, class V, class Value, class Comp = less<>, class Proj = identity>
inline T UB(const V &v, const Value &val, Comp comp = {}, Proj proj = {})
{
return internal::bound_helper(v, [&](int i) -> bool
{ return !comp(val, proj(*(v.begin() + i))); });
}
#define DEFAULT_COMP less<>
#else
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 = {})
{ return ranges::lower_bound(v, val, comp, proj) - v.begin(); }
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 = {})
{ return ranges::upper_bound(v, val, comp, proj) - v.begin(); }
#define DEFAULT_COMP ranges::less
#endif
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>
{ return LB<T>(v, val, comp, proj) - 1; }
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>
{ return LB<T>(v, val, comp, proj); }
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>
{
auto it = v.lower_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
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>
{
auto it = v.upper_bound(val);
return it == v.begin() ? v.end() : prev(it);
}
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>
{ return v.lower_bound(val); }
template <class T>
inline constexpr ull MASK(T k) { return (1ULL << k) - 1ULL; }
#if __cplusplus < 202002L
inline constexpr ull bit_width(ull x) { return x == 0 ? 0 : 64 - __builtin_clzll(x); }
inline constexpr ull bit_floor(ull x) { return x == 0 ? 0ULL : 1ULL << (bit_width(x) - 1); }
inline constexpr ull countr_zero(ull x) { assert(x != 0); return __builtin_ctzll(x); }
inline constexpr ull popcount(ull x) { return __builtin_popcountll(x); }
#else
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); }
#endif
#define dump(...)
#define oj(...) __VA_ARGS__
template <class T, class Sequence>
vc<T> content(queue<T, Sequence> que)
{
vc<T> res;
while (!que.empty())
{
res.eb(que.front());
que.pop();
}
return res;
}
template <class T, class Sequence, class Compare>
vc<T> content(priority_queue<T, Sequence, Compare> pque)
{
vc<T> res;
while (!pque.empty())
{
res.eb(pque.top());
pque.pop();
}
return res;
}
template <class T>
auto content(const T &obj) { return obj.content(); }
namespace fastio {
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(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd1_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
pil--;
if constexpr (is_signed<T>::value || is_same_v<T, i128>)
{
if (minus) x = -x;
}
}
void rd1(ll &x) { rd1_integer(x); }
template <class T, class U>
void rd1(pair<T, U> &p) {
return rd1(p.first), rd1(p.second);
}
template <size_t N = 0, typename T>
void rd1_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd1(x);
rd1_tuple<N + 1>(t);
}
}
template <class... T>
void rd1(tuple<T...> &tpl) {
rd1_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd1(array<T, N> &x) {
for (auto &d: x) rd1(d);
}
template <class T>
void rd1(vc<T> &x) {
for (auto &d: x) rd1(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd1(h), read(t...);
}
void wt1(const char c) {
if (por == SIZ) flush();
obuf[por++] = c;
}
void wt1(const string s) {
for (char c: s) wt1(c);
}
template <typename T>
void wt1_integer(T x) {
if (por > SIZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
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); }
template <class T, class U>
void wt1(const pair<T, U> &val) {
wt1(val.first);
wt1(' ');
wt1(val.second);
}
template <size_t N = 0, typename T>
void wt1_tuple(const T &t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt1(' '); }
const auto x = std::get<N>(t);
wt1(x);
wt1_tuple<N + 1>(t);
}
}
template <class... T>
void wt1(const tuple<T...> &tpl) {
wt1_tuple(tpl);
}
template <class T, size_t S>
void wt1(const array<T, S> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class T>
void wt1(const vector<T> &val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt1(' ');
wt1(val[i]);
}
}
template <class Head, class... Tail>
void write(Head &&head, Tail &&... tail) {
wt1(head);
write(std::forward<Tail>(tail)...);
}
void print() { wt1('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt1(head);
if (sizeof...(Tail)) wt1(' ');
print(std::forward<Tail>(tail)...);
}
} // namespace fastio
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, class... Ts>
void READVECnodump(int n, vc<T> &v, vc<Ts> &...vs)
{ READVECnodump(n, v), READVECnodump(n, vs...); }
template <class T>
void READVEC2nodump(int n, int m, vvc<T> &v)
{
v.assign(n, vc<T>(m));
READnodump(v);
}
template <class T, class... Ts>
void READVEC2nodump(int n, int m, vvc<T> &v, vvc<Ts> &...vs)
{ READVEC2nodump(n, m, v), READVEC2nodump(n, m, vs...); }
template <class T>
void READJAGnodump(int n, vvc<T> &v)
{
v.resize(n);
repi(i, n)
{
int k;
READnodump(k);
READVECnodump(k, v[i]);
}
}
template <class T, class... Ts>
void READJAGnodump(int n, vvc<T> &v, vvc<Ts> &...vs)
{ READJAGnodump(n, v), READJAGnodump(n, vs...); }
}; // namespace internal
#define READ(...) internal::READnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define IN(T, ...) T __VA_ARGS__; READ(__VA_ARGS__)
#define LL(...) IN(ll, __VA_ARGS__)
#define READVEC(...) internal::READVECnodump(__VA_ARGS__); dump(__VA_ARGS__)
#define VEC(T, n, ...) vc<T> __VA_ARGS__; READVEC(n, __VA_ARGS__)
#define PRINT fastio::print
template <class T, class U, class P>
pair<T, U> operator+=(pair<T, U> &a, const P &b)
{
a.first += b.first;
a.second += b.second;
return a;
}
template <class T, class U, class P>
pair<T, U> operator+(pair<T, U> &a, const P &b) { return a += b; }
template <class T, size_t n, class A>
array<T, n> operator+=(array<T, n> &a, const A &b)
{
for (size_t i = 0; i < n; i++)
a[i] += b[i];
return a;
}
template <class T, size_t n, class A>
array<T, n> operator+(array<T, n> &a, const A &b) { return a += b; }
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;
}
}; // namespace internal
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) { return a += b; }
template <class T, const size_t m>
array<vc<T>, m> unzip(const vc<array<T, m>> &vt)
{
const size_t n = vt.size();
array<vc<T>, m> tv;
tv.fill(vc<T>(n));
for (size_t i = 0; i < n; i++)
for (size_t j = 0; j < m; j++)
tv[j][i] = vt[i][j];
return tv;
}
template <class T, const size_t m>
vc<array<T, m>> zip(const array<vc<T>, m> &tv)
{
if (tv.empty()) return {};
const size_t n = tv[0].size();
vc<array<T, m>> vt(n);
for (size_t j = 0; j < m; j++)
{
assert(tv[j].size() == n);
for (size_t i = 0; i < n; i++)
vt[i][j] = tv[j][i];
}
return vt;
}
template <class T, class U>
pair<vc<T>, vc<U>> unzip(const vc<pair<T, U>> &vt)
{
const size_t n = vt.size();
pair<vc<T>, vc<U>> tv;
tv.first.resize(n), tv.second.resize(n);
for (size_t i = 0; i < n; i++)
tie(tv.first[i], tv.second[i]) = vt[i];
return tv;
}
template <class T, class U>
vc<pair<T, U>> zip(const pair<vc<T>, vc<U>> &tv)
{
const size_t n = tv.first.size();
assert(n == tv.second.size());
vc<pair<T, U>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = make_pair(tv.first[i], tv.second[i]);
return vt;
}
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)
{ ((get<I>(tv)[index] = get<I>(t)), ...); }
template <size_t... I, class Tp>
auto tv_to_vt_impl(const Tp &tv, index_sequence<I...>, size_t index)
{ return make_tuple(get<I>(tv)[index]...); }
};
template <class... Ts>
auto unzip(const vc<tuple<Ts...>> &vt)
{
const size_t n = vt.size();
tuple<vc<Ts>...> tv;
apply([&](auto &...v)
{ ((v.resize(n)), ...); }, tv);
for (size_t i = 0; i < n; i++)
internal::vt_to_tv_impl(tv, vt[i], make_index_sequence<tuple_size_v<decltype(tv)>>{}, i);
return tv;
}
template <class... Ts>
auto zip(const tuple<vc<Ts>...> &tv)
{
size_t n = get<0>(tv).size();
apply([&](auto &...v)
{ ((assert(v.size() == n)), ...); }, tv);
vc<tuple<Ts...>> vt(n);
for (size_t i = 0; i < n; i++)
vt[i] = internal::tv_to_vt_impl(tv, index_sequence_for<Ts...>{}, i);
return vt;
}
#define ZIP(vt, ...) auto vt = zip(tuple{__VA_ARGS__})
mt19937_64 mt;
template <class T>
struct larger_int;
#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>
using larger_int_t = typename larger_int<T>::type;
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)
{
if constexpr (sizeof(T) > 4)
{
if (n <= INT_MAX)
return isprime_constexpr<int>(n);
}
if (n <= 1)
return false;
if (n == 2 || n == 7 || n == 61)
return true;
if (n % 2 == 0)
return false;
ll d = n - 1;
while (d % 2 == 0)
d /= 2;
using U = make_unsigned_t<T>;
using L = larger_int_t<U>;
auto miller_rabin = [&](const auto &bases) constexpr
{
for (ll a : bases)
{
ll t = d, y = powmod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1)
{
y = L(y) * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0)
return false;
}
return true;
};
if constexpr(sizeof(T) <= 4)
{
constexpr ll bases[3] = {2, 7, 61};
return miller_rabin(bases);
}
else
{
constexpr ll bases[7] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
return miller_rabin(bases);
}
}
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() { return M; }
static constexpr value_type umod() { return M; }
static constexpr value_type init(value_type v) { return v; }
static constexpr mod_type val(value_type v) { return v; }
static constexpr value_type mul(value_type a, value_type b)
{
return (value_type)((calc_type(a) * b) % M);
}
};
};
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) { reducer = barrett32(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return v; }
static mod_type val(value_type v) { return v; }
static value_type mul(value_type a, value_type b) { return reducer.mul(a, b); }
};
};
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
{
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) { reducer = montgomery64odd(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * 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) { reducer = montgomery64(m); }
static mod_type mod() { return reducer.umod(); }
static value_type umod() { return reducer.umod(); }
static value_type init(value_type v) { return reducer.inv_reduce(v); }
static mod_type val(value_type v) { return reducer.reduce(v); }
static value_type mul(value_type a, value_type b) { return reducer.reduce((calc_type)a * b); }
};
};
template <class T = ll>
constexpr tuple<T, T, T> extgcd(T a, T b)
{
if (a == 0 && b == 0)
return {0, 0, 0};
T x1 = 1, y1 = 0, z1 = a;
T x2 = 0, y2 = 1, z2 = b;
while (z2 != 0)
{
T q = z1 / z2;
tie(x1, x2) = make_pair(x2, x1 - q * x2);
tie(y1, y2) = make_pair(y2, y1 - q * y2);
tie(z1, z2) = make_pair(z2, z1 - q * z2);
}
if (z1 < 0)
x1 = -x1, y1 = -y1, z1 = -z1;
return {z1, x1, y1};
}
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() { return Policy::mod(); }
template <class T = Policy>
static auto set_mod(M m) -> decltype(T::set_mod(m)) { return T::set_mod(m); }
static mint raw(V v)
{
mint x;
x._v = v;
return x;
}
modint_impl() : _v(0) {}
template <class T, typename = enable_if_t<is_integral_ext<T>>>
modint_impl(T v)
{
V rem;
if constexpr (is_signed_ext<T>)
{
using S = make_signed_t<V>;
S x = v % S(Policy::umod());
if (x < 0)
x += Policy::umod();
rem = x;
}
else
rem = V(v % Policy::umod());
_v = Policy::init(rem);
};
M val() const { return Policy::val(_v); }
mint &operator+=(const mint &rhs)
{
_v += rhs._v;
if (_v >= Policy::umod())
_v -= Policy::umod();
return *this;
}
mint &operator-=(const mint &rhs)
{
_v -= rhs._v;
if (_v >= Policy::umod())
_v += Policy::umod();
return *this;
}
mint &operator*=(const mint &rhs)
{
_v = Policy::mul(_v, rhs._v);
return *this;
}
mint &operator/=(const mint &rhs)
{
return *this *= rhs.inv();
}
mint &operator++()
{
_v++;
if (_v == Policy::umod())
_v = 0;
return *this;
}
mint &operator--()
{
if (_v == 0)
_v = Policy::umod();
_v--;
return *this;
}
mint operator++(int)
{
mint res = *this;
++(*this);
return res;
}
mint operator--(int)
{
mint res = *this;
--(*this);
return res;
}
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
template <class T>
mint pow(T n) const
{
assert(n >= 0);
mint x = *this, r = 1;
while (n)
{
if (n & 1)
r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const
{
if constexpr (Policy::is_prime)
{
return pow(mod() - 2);
}
else
{
auto [g, x, y] = extgcd<M>(val(), mod());
assert(g == 1);
return mint(x);
}
}
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 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 modint1000000007 = static_modint32<1000000007>;
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 PowerTable
{
private:
decltype(mint::mod()) mod;
mint base;
vc<mint> pw;
public:
PowerTable() {}
PowerTable(const mint &base) : mod(mint::mod()), base(base), pw(1, 1) {}
void reserve(int n)
{
if (mod != mint::mod())
{
mod = mint::mod();
pw = {1};
}
int i = pw.size();
if (n < i)
return;
pw.resize(n + 1);
for (; i <= n; i++)
pw[i] = pw[i - 1] * base;
}
mint pow(int n)
{
reserve(n);
return pw[n];
}
};
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)
{
if constexpr (is_dynamic_modint_v<T>)
{
if (mod != T::mod())
{
mod = T::mod();
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
}
else
{
if (fac_.empty())
fac_ = {1, 1}, finv_ = {1, 1}, inv_ = {0, 1};
}
if (n < SZ(fac_))
return;
chmin(n, T::mod() - 1);
int si = fac_.size();
fac_.resize(n + 1), finv_.resize(n + 1), inv_.resize(n + 1);
repi(i, si, n + 1)
{
fac_[i] = fac_[i - 1] * T::raw(i);
inv_[i] = -inv_[T::mod() % i] * T::raw(T::mod() / i);
finv_[i] = finv_[i - 1] * inv_[i];
}
}
static T inv(int n)
{
assert(n != 0);
reserve(n);
return inv_[n];
}
static T P(int n, int k)
{
if (n < k)
return 0;
if (n < 0 || k < 0)
return 0;
reserve(n);
return fac_[n] * finv_[n - k];
}
};
template <class T = ll, class U = larger_int_t<T>>
pair<T, T> svp2d(const pair<T, T> &a, const pair<T, T> &b)
{
assert((a != pair<T, T>{0, 0} && b != pair<T, T>{0, 0}));
auto [a1, a2] = a;
auto [b1, b2] = b;
if ((U)a1 * a1 + (U)a2 * a2 < (U)b1 * b1 + (U)b2 * b2)
swap(a1, b1), swap(a2, b2);
while ((U)a1 * a1 + (U)a2 * a2 > (U)b1 * b1 + (U)b2 * b2)
{
swap(a1, b1), swap(a2, b2);
T k = divround<U>((U)a1 * b1 + (U)a2 * b2, (U)a1 * a1 + (U)a2 * a2);
b1 -= k * a1, b2 -= k * a2;
}
return {a1, a2};
}
#if __cplusplus >= 202302L
namespace cpp_dump
{
struct mint_to_rat_fn
{
template <class T>
constexpr auto operator()(const T &x) const -> decltype(mint_to_rat(x))
{
return mint_to_rat(x);
}
};
struct rat_closure : std::ranges::range_adaptor_closure<rat_closure>
{
template <typename T>
constexpr auto operator()(T &&t) const
{
if constexpr (!std::ranges::range<T> && std::invocable<mint_to_rat_fn, decltype(std::forward<T>(t))>)
{
return mint_to_rat_fn{}(std::forward<T>(t));
}
else if constexpr (std::ranges::range<T>)
{
using Ref = std::ranges::range_reference_t<T>;
if constexpr (std::invocable<mint_to_rat_fn, decltype(std::forward<Ref>(std::declval<Ref>()))>)
{
return std::forward<T>(t) | std::views::transform(mint_to_rat_fn{});
}
else if constexpr (std::ranges::range<Ref>)
{
return std::forward<T>(t) | std::views::transform([this](auto &&inner)
{ return (*this)(std::forward<decltype(inner)>(inner)); });
}
else
{
static_assert(false);
}
}
else
{
static_assert(false);
}
}
};
template <typename T>
requires(!std::ranges::range<T> && std::invocable<mint_to_rat_fn, T>)
constexpr auto operator|(T &&t, const rat_closure &c)
{
return c(std::forward<T>(t));
}
}
#endif
using mint = modint1000000007;
void init()
{
oj(mt.seed(random_device()()));
}
template <class T, class = void>
struct has_e1 : false_type {};
template <class T>
struct has_e1<T, void_t<decltype(T::e1())>> : true_type {};
template <class T>
inline constexpr bool has_e1_v = has_e1<T>::value;
template <class T>
struct GroupAddSub
{
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 S{};
}
static constexpr S inv(S a) { return -a; }
};
template <class G>
struct FenwickTree
{
using S = typename G::S;
private:
int n;
vc<S> dat;
public:
FenwickTree() {}
FenwickTree(int n) : n(n), dat(n + 1, G::e()) {}
FenwickTree(const vc<S> &v) : FenwickTree(v.size())
{
repi(i, n) dat[i + 1] = v[i];
repi(i, 1, n + 1)
{
int p = i + (i & -i);
if (p <= n)
dat[p] += dat[i];
}
}
template <class I = ll>
I size() const { return n; }
S sum(int r) const
{
assert(0 <= r && r <= n);
S s = G::e();
while (r > 0)
{
s = G::op(s, dat[r]);
r -= r & -r;
}
return s;
}
S sum(int l, int r) const
{
assert(0 <= l && l <= r && r <= n);
return G::op(G::inv(sum(l)), sum(r));
}
S get(int i) const
{
assert(0 <= i && i < n);
return sum(i, i + 1);
}
void add(int i, S x)
{
assert(0 <= i && i < n);
i++;
while (i <= n)
{
dat[i] = G::op(dat[i], x);
i += i & -i;
}
}
template <class I = ll>
pair<I, S> lt_max_id_sum(S w) const
{
if (w <= G::e())
return {-1, G::e()};
int k = bit_floor(n);
int x = 0;
S v = G::e();
while (k > 0)
{
if (x + k <= n)
{
S nv = G::op(v, dat[x + k]);
if (nv < w)
v = nv, x += k;
}
k >>= 1;
}
return {x, v};
}
template <class I = ll>
I lt_max(S w) const { return lt_max_id_sum<I>(w).first; }
template <class I = ll>
inline I geq_min(S w) const { return lt_max<I>(w) + 1; }
template <class I = ll>
inline I leq_max(S w) const { return lt_max<I>(w + 1); }
template <class I = ll>
inline I gt_min(S w) const { return geq_min<I>(w + 1); }
vc<S> content() const
{
vc<S> res(n);
repi(i, n) res[i] = get(i);
return res;
}
};
template <class G, class I>
struct RectangleSum
{
using S = typename G::S;
private:
struct P
{
I x, y;
S w;
P(I x, I y, const S &w) : x(x), y(y), w(w) {}
bool operator<(const P &rhs) const { return x < rhs.x; }
};
struct Q
{
I x, ly, ry;
int qi;
Q(I x, I ly, I ry, int qi) : x(x), ly(ly), ry(ry), qi(qi) {}
bool operator<(const Q &rhs) const { return x < rhs.x; }
};
vc<P> ps;
vc<Q> qs;
vc<I> ys;
public:
void point_add(I x, I y, const S &w)
{
ps.eb(x, y, w);
ys.eb(y);
}
void rectangle_sum(I lx, I rx, I ly, I ry)
{
qs.eb(lx, ly, ry, qs.size());
qs.eb(rx, ly, ry, qs.size());
}
vc<S> run()
{
const int n = ps.size(), q = qs.size();
sort(ALL(ps)), sort(ALL(qs));
sortunique(ys);
FenwickTree<G> fw(ys.size());
vc<S> res(q / 2, G::e());
for (int i = 0, j = 0; j < q; j++)
{
while (i < n && ps[i].x < qs[j].x)
{
fw.add(LB(ys, ps[i].y), ps[i].w);
i++;
}
const int qi = qs[j].qi;
const S s = fw.sum(LB(ys, qs[j].ly), LB(ys, qs[j].ry));
if (qi & 1)
res[qi >> 1] = G::op(res[qi >> 1], s);
else
res[qi >> 1] = G::op(res[qi >> 1], G::inv(s));
}
return res;
}
void clear() { ps.clear(), qs.clear(), ys.clear(); }
};
template <class G, class I>
struct PointAddRectangleSum
{
using S = typename G::S;
private:
using F = function<S(S)>;
using P = tuple<I, I, S>;
using PF = tuple<I, I, int, F>;
using Q = tuple<I, I, I, I>;
vc<variant<P, PF, Q>> qs;
RectangleSum<G, I> rs;
int qn = 0;
public:
void point_add(I x, I y, const S &w) { qs.eb(P(x, y, w)); }
void rectangle_sum(I lx, I rx, I ly, I ry)
{
qs.eb(Q(lx, rx, ly, ry));
qn++;
}
vc<S> run()
{
vc<S> res(qn, G::e());
auto dfs = [&](auto dfs, int l, int r, int li, int ri) -> void
{
if (r - l == 1)
return;
const int m = (l + r) / 2;
int mi = li;
repi(i, l, m)
{
if (holds_alternative<Q>(qs[i]))
mi++;
}
dfs(dfs, l, m, li, mi);
rs.clear();
repi(i, l, m)
{
if (holds_alternative<P>(qs[i]))
{
cauto & [ x, y, w ] = get<P>(qs[i]);
rs.point_add(x, y, w);
}
}
repi(i, m, r)
{
if (holds_alternative<Q>(qs[i]))
{
cauto & [ lx, rx, ly, ry ] = get<Q>(qs[i]);
rs.rectangle_sum(lx, rx, ly, ry);
}
}
vc<S> tmp = rs.run();
repi(i, mi, ri) res[i] = G::op(res[i], tmp[i - mi]);
repi(i, m, r)
{
if (holds_alternative<PF>(qs[i]))
{
cauto & [ x, y, qi, f ] = get<PF>(qs[i]);
if (li <= qi && qi < mi)
qs[i] = P(x, y, f(res[qi]));
}
}
dfs(dfs, m, r, mi, ri);
};
dfs(dfs, 0, qs.size(), 0, qn);
return res;
}
};
mint solve(vl A, vl B)
{
ZIP(AB, A, B);
sort(ALL(AB));
tie(A, B) = unzip(AB);
dump(A, B);
const ll N = A.size();
vl S(N), T(N);
rep(i, N) S[i] = A[i] + B[i], T[i] = A[i] - B[i];
dump(S | cp::index(), T | cp::index());
mint ans = 0;
PointAddRectangleSum<GroupAddSub<ll>, ll> rs1, rs2;
rep(i, N)
{
rs1.rectangle_sum(-INF, S[i], -INF, T[i]);
rs2.rectangle_sum(-INF, S[i], -INF, T[i]);
rs1.point_add(S[i], T[i], 1);
rs2.point_add(S[i], T[i], A[i]);
}
auto res1 = rs1.run(), res2 = rs2.run();
dump(res1 | cp::index(), res2 | cp::index());
rep(i, N) ans -= res2[i] - A[i] * res1[i];
PointAddRectangleSum<GroupAddSub<ll>, ll> rs3, rs4;
rep(i, N)
{
rs3.rectangle_sum(S[i] + 1, INF, T[i] + 1, INF);
rs4.rectangle_sum(S[i] + 1, INF, T[i] + 1, INF);
rs3.point_add(S[i], T[i], 1);
rs4.point_add(S[i], T[i], A[i]);
}
auto res3 = rs3.run(), res4 = rs4.run();
dump(res3 | cp::index(), res4 | cp::index());
rep(i, N) ans -= res2[i] - A[i] * res1[i];
return ans;
}
void main2()
{
LL(N);
VEC(ll, N, A, B);
PRINT(solve(A, B), solve(B, A));
}
void test()
{
}
template <auto init, auto main2, auto test>
struct Main
{
Main()
{
cauto CERR = [](string val, string color)
{
string s = "\033[" + color + "m" + val + "\033[m";
/* コードテストで確認する際にコメントアウトを外す
cerr << val;
//*/
};
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() {}