#line 1 "verify/verify-unit-test/debug.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"
#line 2 "template/template.hpp"
using namespace std;
// intrinstic
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_permutation(begin(v), end(v));
}
// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
IoSetupNya() {
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetupnya;
} // namespace Nyaan
#line 64 "template/template.hpp"
// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
cerr << " ";
dump(head);
if (sizeof...(tail) != 0) cerr << ",";
trace(std::forward<Tail>(tail)...);
}
} // namespace DebugImpl
#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/debug.test.cpp"
//
#line 2 "hashmap/hashmap.hpp"
#line 2 "hashmap/hashmap-base.hpp"
#line 4 "hashmap/hashmap-base.hpp"
using namespace std;
namespace HashMapImpl {
using u32 = uint32_t;
using u64 = uint64_t;
template <typename Key, typename Data>
struct HashMapBase;
template <typename Key, typename Data>
struct itrB
: iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&> {
using base =
iterator<bidirectional_iterator_tag, Data, ptrdiff_t, Data*, Data&>;
using ptr = typename base::pointer;
using ref = typename base::reference;
u32 i;
HashMapBase<Key, Data>* p;
explicit constexpr itrB() : i(0), p(nullptr) {}
explicit constexpr itrB(u32 _i, HashMapBase<Key, Data>* _p) : i(_i), p(_p) {}
explicit constexpr itrB(u32 _i, const HashMapBase<Key, Data>* _p)
: i(_i), p(const_cast<HashMapBase<Key, Data>*>(_p)) {}
friend void swap(itrB& l, itrB& r) { swap(l.i, r.i), swap(l.p, r.p); }
friend bool operator==(const itrB& l, const itrB& r) { return l.i == r.i; }
friend bool operator!=(const itrB& l, const itrB& r) { return l.i != r.i; }
const ref operator*() const {
return const_cast<const HashMapBase<Key, Data>*>(p)->data[i];
}
ref operator*() { return p->data[i]; }
ptr operator->() const { return &(p->data[i]); }
itrB& operator++() {
assert(i != p->cap && "itr::operator++()");
do {
i++;
if (i == p->cap) break;
if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
} while (true);
return (*this);
}
itrB operator++(int) {
itrB it(*this);
++(*this);
return it;
}
itrB& operator--() {
do {
i--;
if (p->occupied_flag[i] && !p->deleted_flag[i]) break;
assert(i != 0 && "itr::operator--()");
} while (true);
return (*this);
}
itrB operator--(int) {
itrB it(*this);
--(*this);
return it;
}
};
template <typename Key, typename Data>
struct HashMapBase {
using u32 = uint32_t;
using u64 = uint64_t;
using iterator = itrB<Key, Data>;
using itr = iterator;
protected:
template <typename K>
inline u64 randomized(const K& key) const {
return u64(key) ^ r;
}
template <typename K,
enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<K>::value, nullptr_t> = nullptr>
inline u32 inner_hash(const K& key) const {
return (randomized(key) * 11995408973635179863ULL) >> shift;
}
template <
typename K, enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<decltype(K::first)>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<decltype(K::second)>::value, nullptr_t> = nullptr>
inline u32 inner_hash(const K& key) const {
u64 a = randomized(key.first), b = randomized(key.second);
a *= 11995408973635179863ULL;
b *= 10150724397891781847ULL;
return (a + b) >> shift;
}
template <typename K,
enable_if_t<is_same<K, Key>::value, nullptr_t> = nullptr,
enable_if_t<is_integral<typename K::value_type>::value, nullptr_t> =
nullptr>
inline u32 inner_hash(const K& key) const {
static constexpr u64 mod = (1LL << 61) - 1;
static constexpr u64 base = 950699498548472943ULL;
u64 res = 0;
for (auto& elem : key) {
__uint128_t x = __uint128_t(res) * base + (randomized(elem) & mod);
res = (x & mod) + (x >> 61);
}
__uint128_t x = __uint128_t(res) * base;
res = (x & mod) + (x >> 61);
if (res >= mod) res -= mod;
return res >> (shift - 3);
}
template <typename D = Data,
enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
inline u32 hash(const D& dat) const {
return inner_hash(dat);
}
template <
typename D = Data,
enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
inline u32 hash(const D& dat) const {
return inner_hash(dat.first);
}
template <typename D = Data,
enable_if_t<is_same<D, Key>::value, nullptr_t> = nullptr>
inline Key data_to_key(const D& dat) const {
return dat;
}
template <
typename D = Data,
enable_if_t<is_same<decltype(D::first), Key>::value, nullptr_t> = nullptr>
inline Key data_to_key(const D& dat) const {
return dat.first;
}
void reallocate(u32 ncap) {
vector<Data> ndata(ncap);
vector<bool> nf(ncap);
shift = 64 - __lg(ncap);
for (u32 i = 0; i < cap; i++) {
if (occupied_flag[i] && !deleted_flag[i]) {
u32 h = hash(data[i]);
while (nf[h]) h = (h + 1) & (ncap - 1);
ndata[h] = move(data[i]);
nf[h] = true;
}
}
data.swap(ndata);
occupied_flag.swap(nf);
cap = ncap;
occupied = s;
deleted_flag.resize(cap);
fill(std::begin(deleted_flag), std::end(deleted_flag), false);
}
inline bool extend_rate(u32 x) const { return x * 2 >= cap; }
inline bool shrink_rate(u32 x) const {
return HASHMAP_DEFAULT_SIZE < cap && x * 10 <= cap;
}
inline void extend() { reallocate(cap << 1); }
inline void shrink() { reallocate(cap >> 1); }
public:
u32 cap, s, occupied;
vector<Data> data;
vector<bool> occupied_flag, deleted_flag;
u32 shift;
static u64 r;
static constexpr uint32_t HASHMAP_DEFAULT_SIZE = 4;
explicit HashMapBase()
: cap(HASHMAP_DEFAULT_SIZE),
s(0),
occupied(0),
data(cap),
occupied_flag(cap),
deleted_flag(cap),
shift(64 - __lg(cap)) {}
itr begin() const {
u32 h = 0;
while (h != cap) {
if (occupied_flag[h] && !deleted_flag[h]) break;
h++;
}
return itr(h, this);
}
itr end() const { return itr(this->cap, this); }
friend itr begin(const HashMapBase& h) { return h.begin(); }
friend itr end(const HashMapBase& h) { return h.end(); }
itr find(const Key& key) const {
u32 h = inner_hash(key);
while (true) {
if (occupied_flag[h] == false) return this->end();
if (data_to_key(data[h]) == key) {
if (deleted_flag[h] == true) return this->end();
return itr(h, this);
}
h = (h + 1) & (cap - 1);
}
}
bool contain(const Key& key) const { return find(key) != this->end(); }
itr insert(const Data& d) {
u32 h = hash(d);
while (true) {
if (occupied_flag[h] == false) {
if (extend_rate(occupied + 1)) {
extend();
h = hash(d);
continue;
}
data[h] = d;
occupied_flag[h] = true;
++occupied, ++s;
return itr(h, this);
}
if (data_to_key(data[h]) == data_to_key(d)) {
if (deleted_flag[h] == true) {
data[h] = d;
deleted_flag[h] = false;
++s;
}
return itr(h, this);
}
h = (h + 1) & (cap - 1);
}
}
// tips for speed up :
// if return value is unnecessary, make argument_2 false.
itr erase(itr it, bool get_next = true) {
if (it == this->end()) return this->end();
s--;
if (!get_next) {
this->deleted_flag[it.i] = true;
if (shrink_rate(s)) shrink();
return this->end();
}
itr nxt = it;
nxt++;
this->deleted_flag[it.i] = true;
if (shrink_rate(s)) {
Data d = data[nxt.i];
shrink();
it = find(data_to_key(d));
}
return nxt;
}
itr erase(const Key& key) { return erase(find(key)); }
int count(const Key& key) { return find(key) == end() ? 0 : 1; }
bool empty() const { return s == 0; }
int size() const { return s; }
void clear() {
fill(std::begin(occupied_flag), std::end(occupied_flag), false);
fill(std::begin(deleted_flag), std::end(deleted_flag), false);
s = occupied = 0;
}
void reserve(int n) {
if (n <= 0) return;
n = 1 << min(23, __lg(n) + 2);
if (cap < u32(n)) reallocate(n);
}
};
template <typename Key, typename Data>
uint64_t HashMapBase<Key, Data>::r =
chrono::duration_cast<chrono::nanoseconds>(
chrono::high_resolution_clock::now().time_since_epoch())
.count();
} // namespace HashMapImpl
/**
* @brief Hash Map(base) (ハッシュマップ・基底クラス)
*/
#line 4 "hashmap/hashmap.hpp"
template <typename Key, typename Val>
struct HashMap : HashMapImpl::HashMapBase<Key, pair<Key, Val>> {
using base = typename HashMapImpl::HashMapBase<Key, pair<Key, Val>>;
using HashMapImpl::HashMapBase<Key, pair<Key, Val>>::HashMapBase;
using Data = pair<Key, Val>;
Val& operator[](const Key& k) {
typename base::u32 h = base::inner_hash(k);
while (true) {
if (base::occupied_flag[h] == false) {
if (base::extend_rate(base::occupied + 1)) {
base::extend();
h = base::hash(k);
continue;
}
base::data[h].first = k;
base::data[h].second = Val();
base::occupied_flag[h] = true;
++base::occupied, ++base::s;
return base::data[h].second;
}
if (base::data[h].first == k) {
if (base::deleted_flag[h] == true) {
base::data[h].second = Val();
base::deleted_flag[h] = false;
++base::s;
}
return base::data[h].second;
}
h = (h + 1) & (base::cap - 1);
}
}
typename base::itr emplace(const Key& key, const Val& val) {
return base::insert(Data(key, val));
}
};
/*
* @brief ハッシュマップ(連想配列)
* @docs docs/hashmap/hashmap.md
**/
#line 2 "hashmap/hashset.hpp"
#line 4 "hashmap/hashset.hpp"
template <typename Key>
struct HashSet : HashMapImpl::HashMapBase<Key, Key> {
using HashMapImpl::HashMapBase<Key, Key>::HashMapBase;
};
/*
* @brief ハッシュセット(集合)
* @docs docs/hashmap/hashset.md
**/
#line 2 "matrix/matrix.hpp"
#line 2 "matrix/inverse-matrix.hpp"
#line 2 "matrix/gauss-elimination.hpp"
#line 5 "matrix/gauss-elimination.hpp"
using namespace std;
// {rank, det(非正方行列の場合は未定義)} を返す
// 型が double や Rational でも動くはず？(未検証)
//
// pivot 候補 : [0, pivot_end)
template <typename T>
std::pair<int, T> GaussElimination(vector<vector<T>> &a, int pivot_end = -1,
bool diagonalize = false) {
if (a.empty()) return {0, 1};
int H = a.size(), W = a[0].size(), rank = 0;
if (pivot_end == -1) pivot_end = W;
T det = 1;
for (int j = 0; j < pivot_end; j++) {
int idx = -1;
for (int i = rank; i < H; i++) {
if (a[i][j] != T(0)) {
idx = i;
break;
}
}
if (idx == -1) {
det = 0;
continue;
}
if (rank != idx) det = -det, swap(a[rank], a[idx]);
det *= a[rank][j];
if (diagonalize && a[rank][j] != T(1)) {
T coeff = T(1) / a[rank][j];
for (int k = j; k < W; k++) a[rank][k] *= coeff;
}
int is = diagonalize ? 0 : rank + 1;
for (int i = is; i < H; i++) {
if (i == rank) continue;
if (a[i][j] != T(0)) {
T coeff = a[i][j] / a[rank][j];
for (int k = j; k < W; k++) a[i][k] -= a[rank][k] * coeff;
}
}
rank++;
}
return make_pair(rank, det);
}
#line 4 "matrix/inverse-matrix.hpp"
template <typename mint>
vector<vector<mint>> inverse_matrix(const vector<vector<mint>>& a) {
int N = a.size();
assert(N > 0);
assert(N == (int)a[0].size());
vector<vector<mint>> m(N, vector<mint>(2 * N));
for (int i = 0; i < N; i++) {
copy(begin(a[i]), end(a[i]), begin(m[i]));
m[i][N + i] = 1;
}
auto [rank, det] = GaussElimination(m, N, true);
if (rank != N) return {};
vector<vector<mint>> b(N);
for (int i = 0; i < N; i++) {
copy(begin(m[i]) + N, end(m[i]), back_inserter(b[i]));
}
return b;
}
#line 4 "matrix/matrix.hpp"
template <class T>
struct Matrix {
vector<vector<T> > A;
Matrix() = default;
Matrix(int n, int m) : A(n, vector<T>(m, T())) {}
Matrix(int n) : A(n, vector<T>(n, T())){};
int H() const { return A.size(); }
int W() const { return A[0].size(); }
int size() const { return A.size(); }
inline const vector<T> &operator[](int k) const { return A[k]; }
inline vector<T> &operator[](int k) { return A[k]; }
static Matrix I(int n) {
Matrix mat(n);
for (int i = 0; i < n; i++) mat[i][i] = 1;
return (mat);
}
Matrix &operator+=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] += B[i][j];
return (*this);
}
Matrix &operator-=(const Matrix &B) {
int n = H(), m = W();
assert(n == B.H() && m == B.W());
for (int i = 0; i < n; i++)
for (int j = 0; j < m; j++) (*this)[i][j] -= B[i][j];
return (*this);
}
Matrix &operator*=(const Matrix &B) {
int n = H(), m = B.W(), p = W();
assert(p == B.H());
vector<vector<T> > C(n, vector<T>(m, T{}));
for (int i = 0; i < n; i++)
for (int k = 0; k < p; k++)
for (int j = 0; j < m; j++) C[i][j] += (*this)[i][k] * B[k][j];
A.swap(C);
return (*this);
}
Matrix &operator^=(long long k) {
Matrix B = Matrix::I(H());
while (k > 0) {
if (k & 1) B *= *this;
*this *= *this;
k >>= 1LL;
}
A.swap(B.A);
return (*this);
}
Matrix operator+(const Matrix &B) const { return (Matrix(*this) += B); }
Matrix operator-(const Matrix &B) const { return (Matrix(*this) -= B); }
Matrix operator*(const Matrix &B) const { return (Matrix(*this) *= B); }
Matrix operator^(const long long k) const { return (Matrix(*this) ^= k); }
bool operator==(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return false;
return true;
}
bool operator!=(const Matrix &B) const {
assert(H() == B.H() && W() == B.W());
for (int i = 0; i < H(); i++)
for (int j = 0; j < W(); j++)
if (A[i][j] != B[i][j]) return true;
return false;
}
Matrix inverse() const {
assert(H() == W());
Matrix B(H());
B.A = inverse_matrix(A);
return B;
}
friend ostream &operator<<(ostream &os, const Matrix &p) {
int n = p.H(), m = p.W();
for (int i = 0; i < n; i++) {
os << (i ? " " : "") << "[";
for (int j = 0; j < m; j++) {
os << p[i][j] << (j + 1 == m ? "]\n" : ",");
}
}
return (os);
}
T determinant() const {
Matrix B(*this);
assert(H() == W());
T ret = 1;
for (int i = 0; i < H(); i++) {
int idx = -1;
for (int j = i; j < W(); j++) {
if (B[j][i] != 0) {
idx = j;
break;
}
}
if (idx == -1) return 0;
if (i != idx) {
ret *= T(-1);
swap(B[i], B[idx]);
}
ret *= B[i][i];
T inv = T(1) / B[i][i];
for (int j = 0; j < W(); j++) {
B[i][j] *= inv;
}
for (int j = i + 1; j < H(); j++) {
T a = B[j][i];
if (a == 0) continue;
for (int k = i; k < W(); k++) {
B[j][k] -= B[i][k] * a;
}
}
}
return ret;
}
};
/**
* @brief 行列ライブラリ
*/
#line 2 "modint/montgomery-modint.hpp"
template <uint32_t mod>
struct LazyMontgomeryModInt {
using mint = LazyMontgomeryModInt;
using i32 = int32_t;
using u32 = uint32_t;
using u64 = uint64_t;
static constexpr u32 get_r() {
u32 ret = mod;
for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
return ret;
}
static constexpr u32 r = get_r();
static constexpr u32 n2 = -u64(mod) % mod;
static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
static_assert(r * mod == 1, "this code has bugs.");
u32 a;
constexpr LazyMontgomeryModInt() : a(0) {}
constexpr LazyMontgomeryModInt(const int64_t &b)
: a(reduce(u64(b % mod + mod) * n2)){};
static constexpr u32 reduce(const u64 &b) {
return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
}
constexpr mint &operator+=(const mint &b) {
if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator-=(const mint &b) {
if (i32(a -= b.a) < 0) a += 2 * mod;
return *this;
}
constexpr mint &operator*=(const mint &b) {
a = reduce(u64(a) * b.a);
return *this;
}
constexpr mint &operator/=(const mint &b) {
*this *= b.inverse();
return *this;
}
constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
constexpr bool operator==(const mint &b) const {
return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
}
constexpr bool operator!=(const mint &b) const {
return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
}
constexpr mint operator-() const { return mint() - mint(*this); }
constexpr mint operator+() const { return mint(*this); }
constexpr mint pow(u64 n) const {
mint ret(1), mul(*this);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
constexpr mint inverse() const {
int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
while (y > 0) {
t = x / y;
x -= t * y, u -= t * v;
tmp = x, x = y, y = tmp;
tmp = u, u = v, v = tmp;
}
return mint{u};
}
friend ostream &operator<<(ostream &os, const mint &b) {
return os << b.get();
}
friend istream &operator>>(istream &is, mint &b) {
int64_t t;
is >> t;
b = LazyMontgomeryModInt<mod>(t);
return (is);
}
constexpr u32 get() const {
u32 ret = reduce(a);
return ret >= mod ? ret - mod : ret;
}
static constexpr u32 get_mod() { return mod; }
};
#line 9 "verify/verify-unit-test/debug.test.cpp"
using namespace Nyaan;
void test() {
using DebugImpl::trace;
// number
{
cerr << "number" << endl;
trace(1, 2, 3);
trace(inf, -inf, infLL);
trace(-infLL, 1.1, (long double)(1.2));
}
// unsigned
{
cerr << "unsigned number" << endl;
trace(1u, 2u, 3u);
trace(uint32_t(inf), -inf, uint64_t(infLL));
}
// bool
{
cerr << "bool" << endl;
bool t = true, f = false;
trace(t, f);
vector<bool> v(4);
v[0] = v[3] = true;
trace(v);
}
// pair
{
cerr << "pair" << endl;
pair<int, int> p1{1, 2};
pair<pair<int, int>, int> p2{p1, 3};
pair<vector<int>, int> p3{{1, 2}, 3};
trace(p1, p2, p3);
}
// Container
{
cerr << "container" << endl;
vector<int> vc{1, inf};
set<int> st{2, 3};
array<int, 3> ar{{1, 2, 3}};
trace(vc, st, ar);
}
// Dict
{
cerr << "dict" << endl;
map<int, int> m;
m[0] = 1, m[1] = 2;
trace(m);
}
// Native array
{
cerr << "native array" << endl;
int a[] = {1, 2, 3, 4, 5};
trace(make_pair(a, 2), make_pair(a + 3, 2));
}
// string, char
{
cerr << "char & string" << endl;
char c = 'a';
string s = "abc";
trace(c, s);
}
// other
{
cerr << "high-dimensional vector" << endl;
vector<pair<int, int>> v;
v.push_back({0, 1});
v.push_back({2, 3});
trace(v);
vector<vector<int>> a(2);
a[0] = vector<int>{0, 1};
a[1] = vector<int>{2, 3};
trace(a);
vector<vector<vector<int>>> b(2);
b[0] = b[1] = a;
trace(b);
}
// cv qualifier (int)
{
cerr << "cv qualifier (int)" << endl;
int a0 = 0;
const int a1 = 1;
int& a2 = a0;
const int& a3 = a1;
trace(a0, a1, a2, a3);
}
// cv qualifier (char)
{
cerr << "cv qualifier (char)" << endl;
char a0 = 'a';
const char a1 = 'b';
char& a2 = a0;
const char& a3 = a1;
trace(a0, a1, a2, a3);
}
// cv qualifier (string)
{
cerr << "cv qualifier (char)" << endl;
string a0 = "abc";
const string a1 = "def";
string& a2 = a0;
const string& a3 = a1;
trace(a0, a1, a2, a3);
}
// original iterator
{
cerr << "original iterator" << endl;
HashSet<int> st;
st.insert(2);
st.insert(3);
HashMap<int, int> m;
m[0] = 1, m[1] = 2;
trace(st, m);
}
// original structure
{
cerr << "original strucure" << endl;
LazyMontgomeryModInt<998244353> a(998244354);
trace(a);
Matrix<LazyMontgomeryModInt<998244353>> mat;
mat = mat.I(3);
trace(mat);
}
}
void Nyaan::solve() {
test();
int a, b;
cin >> a >> b;
cout << a + b << endl;
}
verify/verify-unit-test/debug.test.cpp