結果
| 問題 | No.2205 Lights Out on Christmas Tree |
| ユーザー |
 mind_cpp
|
| 提出日時 | 2023-04-09 20:35:36 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 300 ms / 2,000 ms |
| コード長 | 57,403 bytes |
| コンパイル時間 | 5,971 ms |
| コンパイル使用メモリ | 338,628 KB |
| 実行使用メモリ | 139,056 KB |
| 最終ジャッジ日時 | 2024-10-05 00:44:12 |
| 合計ジャッジ時間 | 15,519 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,820 KB |
| testcase_02 | AC | 2 ms
6,816 KB |
| testcase_03 | AC | 2 ms
6,820 KB |
| testcase_04 | AC | 3 ms
6,820 KB |
| testcase_05 | AC | 2 ms
6,816 KB |
| testcase_06 | AC | 2 ms
6,816 KB |
| testcase_07 | AC | 2 ms
6,816 KB |
| testcase_08 | AC | 2 ms
6,816 KB |
| testcase_09 | AC | 2 ms
6,816 KB |
| testcase_10 | AC | 2 ms
6,816 KB |
| testcase_11 | AC | 215 ms
91,944 KB |
| testcase_12 | AC | 212 ms
92,196 KB |
| testcase_13 | AC | 212 ms
93,088 KB |
| testcase_14 | AC | 195 ms
96,336 KB |
| testcase_15 | AC | 273 ms
139,056 KB |
| testcase_16 | AC | 164 ms
65,868 KB |
| testcase_17 | AC | 162 ms
65,996 KB |
| testcase_18 | AC | 2 ms
6,816 KB |
| testcase_19 | AC | 239 ms
98,784 KB |
| testcase_20 | AC | 265 ms
102,632 KB |
| testcase_21 | AC | 271 ms
103,688 KB |
| testcase_22 | AC | 215 ms
94,732 KB |
| testcase_23 | AC | 251 ms
97,984 KB |
| testcase_24 | AC | 254 ms
100,812 KB |
| testcase_25 | AC | 266 ms
100,216 KB |
| testcase_26 | AC | 300 ms
106,024 KB |
| testcase_27 | AC | 234 ms
96,736 KB |
| testcase_28 | AC | 208 ms
95,704 KB |
| testcase_29 | AC | 223 ms
95,792 KB |
| testcase_30 | AC | 300 ms
108,352 KB |
| testcase_31 | AC | 234 ms
98,268 KB |
| testcase_32 | AC | 264 ms
100,080 KB |
| testcase_33 | AC | 259 ms
99,564 KB |
| testcase_34 | AC | 238 ms
96,844 KB |
| testcase_35 | AC | 284 ms
103,200 KB |
| testcase_36 | AC | 282 ms
103,236 KB |
| testcase_37 | AC | 238 ms
96,340 KB |
| testcase_38 | AC | 288 ms
105,736 KB |
| testcase_39 | AC | 243 ms
98,744 KB |
ソースコード
#ifdef INCLUDED_MAIN
// const ll ansmod = 998244353;
// const ll ansmod = 1000000007;
auto solve() {
GET(N);
GETVVLL(AB, N - 1);
GETVLL(C);
auto G = Graph(N, false);
rep(i, N - 1) {
INI2(A, B, AB[i]);
A--, B--;
G.append_edge(A, B);
}
G.dfs(0);
auto &path = G.traverse_postorder_path_;
auto &root = G.root_;
vll dp(N);
debug(path, root);
rep(i, len(path) - 1) {
ll u = path[i];
if (C[u] % 2 == 0) {
dp[root[u]] += dp[u] + 1;
C[u] ^= _1;
C[root[u]] ^= _1;
} else {
dp[root[u]] += dp[u];
}
debug(u, dp, C);
}
if (C[0] % 2 == 0) {
return -_1;
} else return dp[0];
}
int main() {
auto ans = solve();
// auto ans = (ansmod + (solve() % ansmod)) % ansmod;
print(ans);
}
// ラムダ再帰
// auto ff = [&](auto &&f, ll x) {};
// ff(ff, 0);
// 以下は動作確認未実施
#else
#define INCLUDED_MAIN
#ifdef LOCAL
#include "../mytemplate.hpp"
#else
#include <algorithm>
#include <bits/extc++.h>
#include <bitset>
#include <cassert>
#include <cctype>
#include <climits>
#include <cstddef>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string_view>
#include <type_traits>
#include <utility>
#include <regex>
#endif
using namespace std;
// clang-format off
/* accelration */
// 高速バイナリ生成
#ifndef LOCAL
#pragma GCC target("avx")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
// unordered_mapでpair, vector, tupleをkeyにするためのコード
// (参考文献) https://qiita.com/hamamu/items/4d081751b69aa3bb3557
template<class T> size_t HashCombine(const size_t seed,const T &v){
return seed^(std::hash<T>()(v)+0x9e3779b9+(seed<<6)+(seed>>2));
}
/* pair用 */
template<class T,class S> struct std::hash<std::pair<T,S>>{
size_t operator()(const std::pair<T,S> &keyval) const noexcept {
return HashCombine(std::hash<T>()(keyval.first), keyval.second);
}
};
/* vector用 */
template<class T> struct std::hash<std::vector<T>>{
size_t operator()(const std::vector<T> &keyval) const noexcept {
size_t s=0;
for (auto&& v: keyval) s=HashCombine(s,v);
return s;
}
};
/* deque用 */
template<class T> struct std::hash<std::deque<T>>{
size_t operator()(const std::deque<T> &keyval) const noexcept {
size_t s=0;
for (auto&& v: keyval) s=HashCombine(s,v);
return s;
}
};
/* tuple用 */
template<int N> struct HashTupleCore{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{
size_t s=HashTupleCore<N-1>()(keyval);
return HashCombine(s,std::get<N-1>(keyval));
}
};
template <> struct HashTupleCore<0>{
template<class Tuple> size_t operator()(const Tuple &keyval) const noexcept{ return 0; }
};
template<class... Args> struct std::hash<std::tuple<Args...>>{
size_t operator()(const tuple<Args...> &keyval) const noexcept {
return HashTupleCore<tuple_size<tuple<Args...>>::value>()(keyval);
}
};
/* alias */
using ull = __uint128_t;
// using ll = long long; // __int128でTLEするときに切り替える。
using ll = __int128;
using ld = long double;
using vi = vector<int>;
using vl = vector<long>;
using vll = vector<ll>;
using vd = vector<ld>;
using vvi = vector<vi>;
using vvl = vector<vl>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using vc = vector<char>;
using vvc = vector<vc>;
using vs = vector<string>;
using vvs = vector<vs>;
using vvvs = vector<vvs>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using umpll = unordered_map<ll, ll>;
using umpsl = unordered_map<string, ll>;
using mpll = map<ll, ll>;
using sll = set<ll>;
using msll = multiset<ll>;
using heapqll = priority_queue<ll, vll, greater<ll>>;
using heapqllrev = priority_queue<ll>;
using dll = deque<ll>;
/* REP macro */
#define _overload4(_1,_2,_3,_4,name,...) name
#define _rep(i,n) reps(i,0,n)
#define reps(i,a,n) for (ll i = (a); i < (ll)(n); ++i)
#define repsp(i,a,n,s) for (ll i = (a); i < (ll)(n); i += s)
#define rep(...) _overload4(__VA_ARGS__,repsp, reps,_rep,)(__VA_ARGS__)
#define rrep(i, n) reps(i, 1, n + 1)
#define repd(i,n) for(ll i=n-1;i>=0;i--)
#define rrepd(i,n) for(ll i=n;i>=1;i--)
#define repdict(key, value, dict) for (const auto& [key, value] : dict)
#define repset(x, st) for(auto x : st)
/* define short */
#define endl "\n"
#define pf emplace_front
#define pb emplace_back
#define popleft pop_front
#define popright pop_back
#define mp make_pair
#define ump unordered_map
#define all(obj) (obj).begin(), (obj).end()
#define rall(obj) (obj).rbegin(), (obj).rend()
#define len(x) (ll)(x.size())
#define MAX(x) *max_element(all(x))
#define MIN(x) *min_element(all(x))
#define ARGMAX(x) distance(x.begin(), max_element(all(x)))
#define ARGMIN(x) distance(x.begin(), min_element(all(x)))
#define CLAMP(L, X, R) min(max(L, X), R)
#define IN(L, X, R) (L <= X && X <= R)
#define SET(x) sll(all(x))
#define VEC(x) vll(all(x))
#define GET(x) ll x = in_ll();
#define GET2(x, y) ll x, y; {vll _A_ = in_lls(); x = _A_[0]; y = _A_[1];}
#define GET3(x, y, z) ll x, y, z; {vll _A_ = in_lls(); x = _A_[0]; y = _A_[1]; z = _A_[2];}
#define GET4(x, y, z, a) ll x, y, z, a; {vll _A_ = in_lls(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3];}
#define GET5(x, y, z, a, b) ll x, y, z, a, b; {vll _A_ = in_lls(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3]; b = _A_[4];}
#define GET6(x, y, z, a, b, c) ll x, y, z, a, b, c; {vll _A_ = in_lls(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3]; b = _A_[4]; c = _A_[5];}
#define GETVLL(x) vll x = in_lls();
#define GETVVLL(x, N) vvll x; rep(i, N) {GETVLL(ab); x.pb(ab);}
#define GETD(x) ld x = in_d();
#define GET2D(x, y) ld x, y; {vd _A_ = in_ds(); x = _A_[0]; y = _A_[1];}
#define GET3D(x, y, z) ld x, y, z; {vd _A_ = in_ds(); x = _A_[0]; y = _A_[1]; z = _A_[2];}
#define GET4D(x, y, z, a) ld x, y, z, a; {vd _A_ = in_ds(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3];}
#define GET5D(x, y, z, a, b) ld x, y, z, a, b; {vd _A_ = in_ds(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3]; b = _A_[4];}
#define GET6D(x, y, z, a, b, c) ld x, y, z, a, b, c; {vd _A_ = in_ds(); x = _A_[0]; y = _A_[1]; z = _A_[2]; a = _A_[3]; b = _A_[4]; c = _A_[5];}
#define GETVD(x) vd x = in_ds();
#define GETVVD(x, N) vvd x; rep(i, N) {GETVD(ab); x.pb(ab);}
#define GETSTR(x) string x = in_str();
#define GETSTRS(x) vs x; x = in_strs();
#define GETVVS(x, N) vvs x; rep(i, N) x.pb(in_strs());
#define GETVSTR(x, N) vs x; rep(i, N) x.pb(in_str());
#define INI(x, vec) auto x = vec[0];
#define INI2(x, y, vec) auto x = vec[0], y = vec[1];
#define INI3(x, y, z, vec) auto x = vec[0], y = vec[1], z = vec[2];
#define INI4(x, y, z, a, vec) auto x = vec[0], y = vec[1], z = vec[2], a = vec[3];
#define INI5(x, y, z, a, b, vec) auto x = vec[0], y = vec[1], z = vec[2], a = vec[3], b = vec[4];
#define INI6(x, y, z, a, b, c, vec) auto x = vec[0], y = vec[1], z = vec[2], a = vec[3], b = vec[4], c = vec[5];
#define SETPERM(x, N) vll x(N); iota(all(x), 0);
#define SETPERMS(x, s, N) vll x(N); iota(all(x), s);
#define UNUSED(x) ((void)x);
#define printF(x) print(x); cout << flush;
// [INT|LLONG|DBL|LDBL]_[MAX|MIN] 最大最小表現
// 型変換
#define CHARSTR(x) (""s + x)
#define STRBIN2LL(x) std::stoull(x, nullptr, 2)
#define STRLL(x) parse(x)
#define STRD(x) std::stod(x)
#define CHARLL(x) std::stoll(CHARSTR(x))
/* sort */
#define SORT(x) stable_sort(all(x))
#define RSORT(x) stable_sort(rall(x))
#define SORT_IDX(x, idx) stable_sort(all(x), [&](const vll &_a_, const vll &_b_){return _a_[idx] < _b_[idx];})
#define RSORT_IDX(x, idx) stable_sort(all(x), [&](const vll &_a_, const vll &_b_){return _a_[idx] > _b_[idx];})
#define LB_IDX_VEC(c, x) distance((c).begin(), lower_bound(all(c), x)) // O(log N) x未満の最大値についてその右側のidxが求まる
#define UB_IDX_VEC(c, x) distance((c).begin(), upper_bound(all(c), x)) // O(log N) x以上の最小値についてその右側のidxが求まる
#define LB_ITR_VEC(c, x) lower_bound(all(c), x)
#define UB_ITR_VEC(c, x) upper_bound(all(c), x)
// #define LB_IDX_SET(c, x) distance((c).begin(), c.lower_bound(x)) // O(N)
// #define UB_IDX_SET(c, x) distance((c).begin(), c.upper_bound(x)) // O(N)
#define LB_ITR_SET(c, x) c.lower_bound(x)
#define UB_ITR_SET(c, x) c.upper_bound(x)
#define LB_ITR_MAP(c, x) c.lower_bound(x)
#define UB_ITR_MAP(c, x) c.upper_bound(x)
#define KEY_CHANGE(c, k1, k2) { auto i_ = c.extract(k1); i_.key() = k2; c.insert(std::move(i_));}
#define EXIST(key, dict) (dict.find(key) != dict.end())
#define REV(x) reverse(all(x))
namespace // 直値のデフォルトの型をllに。
{
ll _0 = 0;
ll _1 = 1;
ll _2 = 2;
ll _3 = 3;
ll _4 = 4;
ll _5 = 5;
ll _6 = 6;
ll _7 = 7;
ll _8 = 8;
ll _9 = 9;
ll _10 = 10;
ll _11 = 11;
ll _12 = 12;
ll _13 = 13;
ll _14 = 14;
ll _15 = 15;
ll _16 = 16;
ll _17 = 17;
ll _30 = 30;
ll _31 = 31;
ll _32 = 32;
ll _33 = 33;
ll _63 = 63;
ll _64 = 64;
ll _65 = 65;
ll _66 = 66;
ll _126 = 126;
ll _127 = 127;
ll _128 = 128;
ll _129 = 129;
};
void ignore_warning() // ワーニング対策
{
_0 = _0;
_1 = _1;
_2 = _2;
_3 = _3;
_4 = _4;
_5 = _5;
_6 = _6;
_7 = _7;
_8 = _8;
_9 = _9;
_10 = _10;
_11 = _11;
_12 = _12;
_13 = _13;
_14 = _14;
_15 = _15;
_16 = _16;
_17 = _17;
_30 = _30;
_31 = _31;
_32 = _32;
_33 = _33;
_63 = _63;
_64 = _64;
_65 = _65;
_66 = _66;
_126 = _126;
_127 = _127;
_128 = _128;
_129 = _129;
}
/* helper func */
std::ostream &operator<<(std::ostream &dest, __int128 value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
ll parse(string &s) {
ll ret = 0;
bool isplus = true;
for (ll i = 0; i < s.length(); i++)
if ('0' <= s[i] && s[i] <= '9')
ret = 10 * ret + s[i] - '0';
else if (s[i] == '-')
isplus ^= isplus;
return isplus ? ret : -ret;
}
string STR(const vector<char> &cs) {
return string(cs.begin(), cs.end());
}
string RSTR(const vector<char> &cs) {
return string(cs.rbegin(), cs.rend());
}
template <typename T>
string STR(T v) {
ostringstream ss;
ss << v;
return ss.str();
}
ll SUM(const vll &v) {
ll total = 0;
rep(i, len(v)) {
total += v[i];
}
return total;
}
template<class... T>
constexpr auto min(T... a){
return min(initializer_list<common_type_t<T...>>{a...});
}
template<class... T>
constexpr auto max(T... a){
return max(initializer_list<common_type_t<T...>>{a...});
}
// search_length: 走査するベクトル長の上限(先頭から何要素目までを検索対象とするか、1始まりで)
template <typename T> inline bool vector_finder(std::vector<T> vec, T element, unsigned int search_length) {
auto itr = std::find(vec.begin(), vec.end(), element);
size_t index = std::distance( vec.begin(), itr );
if (index == vec.size() || index >= search_length) {return false;} else {return true;}
}
inline void print(const sll& v, string s = " ")
{bool first = true; for(auto &p : v) { if(first) {first = false; cout << p;} else cout << s << p;} cout << endl;}
inline void print(const msll& v, string s = " ")
{bool first = true; for(auto &p : v) { if(first) {first = false; cout << p;} else cout << s << p;} cout << endl;}
template <typename T> inline void print(const vector<T>& v, string s = " ")
{rep(i, v.size()) cout << v[i] << (i != (ll)v.size() - 1 ? s : "\n");}
inline void print(const vvll& v, string s = " ")
{rep(i, len(v)) print(v[i], s);}
template <typename T, typename S> inline void print(const pair<T, S>& p)
{cout << p.first << " " << p.second << endl;}
template <typename T> inline void print(const T& x) {cout << x << endl;}
template <typename T, typename S> inline void print(const vector<pair<T, S>>& v)
{for (auto&& p : v) print(p);}
template <typename T, typename S> inline void print(const unordered_map<T, S>& d)
{for (const auto& [key, value] : d) {cout << key << " "; print(value);}}
template <typename T, typename S> inline void print(const map<T, S>& d)
{for (const auto& [key, value] : d) {cout << key << " "; print(value);}}
inline void print(const vc &d) {rep(i, len(d)) cout << d[i]; cout << endl;}
// 第一引数と第二引数を比較し、第一引数(a)をより大きい/小さい値に上書き
template <typename T> inline bool chmin(T& a, const T& b) {bool compare = a > b; if (a > b) a = b; return compare;}
template <typename T> inline bool chmax(T& a, const T& b) {bool compare = a < b; if (a < b) a = b; return compare;}
/* func */
inline ll in_ll() {string s; getline(cin, s); return STRLL(s);}
inline ld in_d() {string s; getline(cin, s); return STRD(s);}
inline string in_str() {string s; getline(cin, s); return s;}
inline string YESNO(bool cond) {return cond ? "YES" : "NO";}
inline string yesno(bool cond) {return cond ? "yes" : "no";}
inline string YesNo(bool cond) {return cond ? "Yes" : "No";}
/* debug */
namespace debug_print_func {
std::ostream& os = std::cerr;
template <class Tp> auto has_cbegin(int) -> decltype(std::cbegin(std::declval<Tp>()), std::true_type {});
template <class Tp> auto has_cbegin(...) -> std::false_type;
template <class Tp> auto has_value_type(int) -> decltype(std::declval<typename Tp::value_type>(), std::true_type {});
template <class Tp> auto has_value_type(...) -> std::false_type;
template <class Tp>[[maybe_unused]] constexpr bool is_iteratable_container_v = decltype(has_cbegin<Tp>(int {}))::value;
template <class Tp>[[maybe_unused]] constexpr bool is_container_v = decltype(has_value_type<Tp>(int {}))::value
|| is_iteratable_container_v<Tp>;
template <> [[maybe_unused]] constexpr bool is_iteratable_container_v<std::string_view> = false;
template <> [[maybe_unused]] constexpr bool is_container_v<std::string_view> = false;
#if (defined _GLIBCXX_STRING) || (defined _LIBCPP_STRING)
template <> [[maybe_unused]] constexpr bool is_iteratable_container_v<std::string> = false;
template <> [[maybe_unused]] constexpr bool is_container_v<std::string> = false;
#endif
template <class Tp, class... Ts> struct first_element { using type = Tp; };
template <class... Ts> using first_t = typename first_element<Ts...>::type;
template <class Tp, std::enable_if_t<!decltype(has_value_type<Tp>(int {}))::value, std::nullptr_t> = nullptr>
auto check_elem(int) -> decltype(*std::cbegin(std::declval<Tp>()));
template <class Tp, std::enable_if_t<decltype(has_value_type<Tp>(int {}))::value, std::nullptr_t> = nullptr>
auto check_elem(int) -> typename Tp::value_type;
template <class Tp>
auto check_elem(...) -> void;
template <class Tp> using elem_t = decltype(check_elem<Tp>(int {}));
template <class Tp> [[maybe_unused]] constexpr bool is_multidim_container_v = is_container_v<Tp>
&& is_container_v<elem_t<Tp>>;
template <class Tp> std::enable_if_t<!is_container_v<Tp>> out(const Tp&);
void out(const char&);
void out(const char*);
void out(const std::string_view&);
#if (defined _GLIBCXX_STRING) || (defined _LIBCPP_STRING)
void out(const std::string&);
#endif
#ifdef __SIZEOF_INT128__
void out(const __int128&);
void out(const unsigned __int128&);
#endif
template <class Tp1, class Tp2> void out(const std::pair<Tp1, Tp2>&);
#if (defined _GLIBCXX_TUPLE) || (defined _LIBCPP_TUPLE)
template <class... Ts> void out(const std::tuple<Ts...>&);
#endif
#if (defined _GLIBCXX_STACK) || (defined _LIBCPP_STACK)
template <class... Ts> void out(std::stack<Ts...>);
#endif
#if (defined _GLIBCXX_QUEUE) || (defined _LIBCPP_QUEUE)
template <class... Ts> void out(std::queue<Ts...>);
template <class... Ts> void out(std::priority_queue<Ts...>);
#endif
template <class C>
std::enable_if_t<is_iteratable_container_v<C>> out(const C&);
template <class Tp> std::enable_if_t<!is_container_v<Tp>> out(const Tp& arg) {
os << arg;
}
void out(const char& arg) {
os << '\'' << arg << '\'';
}
void out(const char* arg) {
os << '\"' << arg << '\"';
}
void out(const ld arg) {
if (arg == LDBL_MAX) {
os << "∞";
} else if (arg == -LDBL_MAX) {
os << "-∞";
} else {
os << arg;
}
}
void out(const std::string_view& arg) {
os << '\"' << arg << '\"';
}
#if (defined _GLIBCXX_STRING) || (defined _LIBCPP_STRING)
void out(const std::string& arg) {
os << '\"' << arg << '\"';
}
#endif
#ifdef __SIZEOF_INT128__
void out(const __int128& arg) {
if (arg == ULLONG_MAX) {
os << "∞";
} else {
int sign = (arg < 0) ? (-1) : 1;
if (sign == -1) os << '-';
__int128 base = sign;
while (sign * arg >= sign * base * 10) base *= 10;
while (base) {
os << static_cast<char>('0' + (arg / base % 10));
base /= 10;
}
}
}
void out(const unsigned __int128& arg) {
if (arg == ULLONG_MAX) {
os << "∞";
} else {
unsigned __int128 base = 1;
while (arg >= base * 10) base *= 10;
while (base) {
os << static_cast<char>('0' + (arg / base % 10));
base /= 10;
}
}
}
#endif
template <class Tp1, class Tp2> void out(const std::pair<Tp1, Tp2>& arg) {
os << '(';
out(arg.first);
os << ", ";
out(arg.second);
os << ')';
}
#if (defined _GLIBCXX_TUPLE) || (defined _LIBCPP_TUPLE)
template <class T, std::size_t... Is> void print_tuple(const T& arg, std::index_sequence<Is...>) {
static_cast<void>(((os << (Is == 0 ? "" : ", "), out(std::get<Is>(arg))), ...));
}
template <class... Ts> void out(const std::tuple<Ts...>& arg) {
os << '(';
print_tuple(arg, std::make_index_sequence<sizeof...(Ts)>());
os << ')';
}
#endif
#if (defined _GLIBCXX_STACK) || (defined _LIBCPP_STACK)
template <class... Ts> void out(std::stack<Ts...> arg) {
if (arg.empty()) {
os << "<empty stack>";
return;
}
os << "[ ";
while (!arg.empty()) {
out(arg.top());
os << ' ';
arg.pop();
}
os << ']';
}
#endif
#if (defined _GLIBCXX_QUEUE) || (defined _LIBCPP_QUEUE)
template <class... Ts> void out(std::queue<Ts...> arg) {
if (arg.empty()) {
os << "<empty queue>";
return;
}
os << "[ ";
while (!arg.empty()) {
out(arg.front());
os << ' ';
arg.pop();
}
os << ']';
}
template <class... Ts> void out(std::priority_queue<Ts...> arg) {
if (arg.empty()) {
os << "<empty priority_queue>";
return;
}
os << "[ ";
while (!arg.empty()) {
out(arg.top());
os << ' ';
arg.pop();
}
os << ']';
}
#endif
template <class Container>
std::enable_if_t<is_iteratable_container_v<Container>> out(const Container& arg) {
if (std::distance(std::cbegin(arg), std::cend(arg)) == 0) {
os << "<empty container>";
return;
}
os << "[ ";
std::for_each(std::cbegin(arg), std::cend(arg), [](const elem_t<Container>& elem) {
out(elem);
os << ' ';
});
os << ']';
}
template <class Tp> std::enable_if_t<!is_multidim_container_v<Tp>>
print(std::string_view name, const Tp& arg) {
os << name << ": ";
out(arg);
if constexpr (is_container_v<Tp>)
os << '\n';
}
template <class Tp> std::enable_if_t<is_multidim_container_v<Tp>>
print(std::string_view name, const Tp& arg) {
os << name << ": ";
if (std::distance(std::cbegin(arg), std::cend(arg)) == 0) {
os << "<empty multidimensional container>\n";
return;
}
std::for_each(std::cbegin(arg), std::cend(arg),
[&name, is_first_elem = true](const elem_t<Tp>& elem) mutable {
if (is_first_elem)
is_first_elem = false;
else
for (std::size_t i = 0; i < name.length() + 2; i++)
os << ' ';
out(elem);
os << '\n';
});
}
template <class Tp, class... Ts> void multi_print(std::string_view names, const Tp& arg, const Ts&... args) {
if constexpr (sizeof...(Ts) == 0) {
names.remove_suffix(
std::distance(
names.crbegin(),
std::find_if_not(names.crbegin(), names.crend(),
[](const char c) { return std::isspace(c); })
)
);
print(names, arg);
if constexpr (!is_container_v<Tp>)
os << '\n';
} else {
std::size_t comma_pos = 0;
for (std::size_t i = 0, paren_depth = 0, inside_quote = false; i < names.length(); i++) {
if (!inside_quote && paren_depth == 0 && i > 0 && names[i - 1] != '\'' && names[i] == ',') {
comma_pos = i;
break;
}
if (names[i] == '\"') {
if (i > 0 && names[i - 1] == '\\') continue;
inside_quote ^= true;
}
if (!inside_quote && names[i] == '(' && (i == 0 || names[i - 1] != '\''))
paren_depth++;
if (!inside_quote && names[i] == ')' && (i == 0 || names[i - 1] != '\''))
paren_depth--;
}
const std::size_t first_varname_length = comma_pos - std::distance(
names.crend() - comma_pos,
std::find_if_not(
names.crend() - comma_pos, names.crend(),
[](const char c) { return std::isspace(c); }
)
);
print(names.substr(0, first_varname_length), arg);
if constexpr (!is_container_v<Tp>) {
if constexpr (is_container_v<first_t<Ts...>>)
os << '\n';
else
os << " | ";
}
const std::size_t next_varname_begins_at = std::distance(
names.cbegin(),
std::find_if_not(
names.cbegin() + comma_pos + 1, names.cend(),
[](const char c) { return std::isspace(c); }
)
);
names.remove_prefix(next_varname_begins_at);
multi_print(names, args...);
}
}
} // namespace debug_print
#ifdef LOCAL
# define debug(...) cerr << "\033[33m(line:" << __LINE__ << ") " << endl; debug_print_func::multi_print(#__VA_ARGS__, __VA_ARGS__); cerr << "\033[m";
#else
# define debug(...) ;
#endif
/* 標準入力 */
vs in_strs(const string &delimiter = " ")
{
string s;
getline(cin, s);
vs output;
bitset<255> delims;
for (unsigned char c: delimiter)
{
delims[c] = true;
}
string::const_iterator beg;
bool in_token = false;
for( string::const_iterator it = s.cbegin(), end = s.cend(); it != end; ++it )
{
if( delims[*it] )
{
if( in_token )
{
output.pb(beg, it);
in_token = false;
}
}
else if( !in_token )
{
beg = it;
in_token = true;
}
}
if( in_token )
output.pb(beg, s.cend());
return output;
}
inline vll in_lls()
{
vll vals;
vs tokens = in_strs();
for (string i: tokens) vals.pb(STRLL(i));
return vals;
}
inline vd in_ds()
{
vd vals;
vs tokens = in_strs();
for (string i: tokens) vals.pb(STRD(i));
return vals;
}
inline vvll in_llss(ll line) // 複数行文字列解析
{
vvll valss;
rep(i, line) valss.pb(in_lls());
return valss;
}
inline vs in_vs(ll line) // 複数行文字列解析
{
vs vecs;
rep(i, line) {
vecs.pb(in_str());
}
return vecs;
}
inline ll popcnt(ll x) { return __builtin_popcountll(x); }
template <typename T, typename U>
T ceil(T x, U y) {
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U>
T floor(T x, U y) {
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T>
class Counter
{
public:
unordered_map<T, ll> tbl_;
ll max_cnt_ = 0;
T max_key_;
ll min_cnt_ = -1;
T min_key_;
Counter(const vector<T> &vec) {
rep(i, len(vec)) {
ll v = ++tbl_[vec[i]];
if (max_cnt_ < v) {
max_cnt_ = v;
max_key_ = vec[i];
}
}
}
ll count(T key) {
return tbl_[key];
}
T maxkey() {
return max_key_;
}
ll maxcnt() {
return max_cnt_;
}
T minkey() {
if (min_cnt_ == -1) {
mincnt();
}
return min_key_;
}
ll mincnt() {
if (min_cnt_ == -1) {
min_key_ = tbl_.begin()->first;
min_cnt_ = tbl_.begin()->second;
for(auto itr = tbl_.begin(); itr != tbl_.end(); itr++){
if(min_cnt_ > itr->second) {
min_key_ = itr->first;
min_cnt_ = itr->second;
}
}
}
return min_cnt_;
}
};
template <typename T>
vector<T> accsum(const vector<T> &vec, ll ansmod = 0) {
if (len(vec) == 0) return vector<T>();
vector<T> acc = {0};
if (ansmod != 0) {
rep (i, len(vec)) acc.pb((acc[i] + vec[i]) % ansmod);
} else {
rep (i, len(vec)) acc.pb(acc[i] + vec[i]);
}
return acc;
}
template <typename T>
vector<T> accmax(const vector<T> &vec) {
if (len(vec) == 0) return vector<T>();
vector<T> acc = {vec[0]};
reps (i, 1, len(vec)) acc.pb(max(acc[i - 1], vec[i]));
return acc;
}
template <typename T>
vector<T> accmin(const vector<T> &vec) {
if (len(vec) == 0) return vector<T>();
vector<T> acc = {vec[0]};
reps (i, 1, len(vec)) acc.pb(min(acc[i - 1], vec[i]));
return acc;
}
// https://howardhinnant.github.io/combinations.html
namespace howardhinnantdetail
{
// Rotates two discontinuous ranges to put *first2 where *first1 is.
// If last1 == first2 this would be equivalent to rotate(first1, first2, last2),
// but instead the rotate "jumps" over the discontinuity [last1, first2) -
// which need not be a valid range.
// In order to make it faster, the length of [first1, last1) is passed in as d1,
// and d2 must be the length of [first2, last2).
// In a perfect world the d1 > d2 case would have used swap_ranges and
// reverse_iterator, but reverse_iterator is too inefficient.
template <class BidirIter>
void
rotate_discontinuous(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
BidirIter first2, BidirIter last2,
typename std::iterator_traits<BidirIter>::difference_type d2)
{
using std::swap;
if (d1 <= d2)
std::rotate(first2, std::swap_ranges(first1, last1, first2), last2);
else
{
BidirIter i1 = last1;
while (first2 != last2)
swap(*--i1, *--last2);
std::rotate(first1, i1, last1);
}
}
// Rotates the three discontinuous ranges to put *first2 where *first1 is.
// Just like rotate_discontinuous, except the second range is now represented by
// two discontinuous ranges: [first2, last2) + [first3, last3).
template <class BidirIter>
void
rotate_discontinuous3(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
BidirIter first2, BidirIter last2,
typename std::iterator_traits<BidirIter>::difference_type d2,
BidirIter first3, BidirIter last3,
typename std::iterator_traits<BidirIter>::difference_type d3)
{
rotate_discontinuous(first1, last1, d1, first2, last2, d2);
if (d1 <= d2)
rotate_discontinuous(std::next(first2, d2 - d1), last2, d1, first3, last3, d3);
else
{
rotate_discontinuous(std::next(first1, d2), last1, d1 - d2, first3, last3, d3);
rotate_discontinuous(first2, last2, d2, first3, last3, d3);
}
}
// Call f() for each combination of the elements [first1, last1) + [first2, last2)
// swapped/rotated into the range [first1, last1). As long as f() returns
// false, continue for every combination and then return [first1, last1) and
// [first2, last2) to their original state. If f() returns true, return
// immediately.
// Does the absolute mininum amount of swapping to accomplish its task.
// If f() always returns false it will be called (d1+d2)!/(d1!*d2!) times.
template <class BidirIter, class Function>
bool
combine_discontinuous(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
BidirIter first2, BidirIter last2,
typename std::iterator_traits<BidirIter>::difference_type d2,
Function& f,
typename std::iterator_traits<BidirIter>::difference_type d = 0)
{
typedef typename std::iterator_traits<BidirIter>::difference_type D;
using std::swap;
if (d1 == 0 || d2 == 0)
return f();
if (d1 == 1)
{
for (BidirIter i2 = first2; i2 != last2; ++i2)
{
if (f())
return true;
swap(*first1, *i2);
}
}
else
{
BidirIter f1p = std::next(first1);
BidirIter i2 = first2;
for (D d22 = d2; i2 != last2; ++i2, --d22)
{
if (combine_discontinuous(f1p, last1, d1-1, i2, last2, d22, f, d+1))
return true;
swap(*first1, *i2);
}
}
if (f())
return true;
if (d != 0)
rotate_discontinuous(first1, last1, d1, std::next(first2), last2, d2-1);
else
rotate_discontinuous(first1, last1, d1, first2, last2, d2);
return false;
}
// A binder for binding arguments to call combine_discontinuous
template <class Function, class BidirIter>
class call_combine_discontinuous
{
typedef typename std::iterator_traits<BidirIter>::difference_type D;
Function f_;
BidirIter first1_;
BidirIter last1_;
D d1_;
BidirIter first2_;
BidirIter last2_;
D d2_;
public:
call_combine_discontinuous(
BidirIter first1, BidirIter last1,
D d1,
BidirIter first2, BidirIter last2,
D d2,
Function& f)
: f_(f), first1_(first1), last1_(last1), d1_(d1),
first2_(first2), last2_(last2), d2_(d2) {}
bool operator()()
{
return combine_discontinuous(first1_, last1_, d1_, first2_, last2_, d2_, f_);
}
};
// See combine_discontinuous3
template <class BidirIter, class Function>
bool
combine_discontinuous3_(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
BidirIter first2, BidirIter last2,
typename std::iterator_traits<BidirIter>::difference_type d2,
BidirIter first3, BidirIter last3,
typename std::iterator_traits<BidirIter>::difference_type d3,
Function& f,
typename std::iterator_traits<BidirIter>::difference_type d = 0)
{
typedef typename std::iterator_traits<BidirIter>::difference_type D;
using std::swap;
if (d1 == 1)
{
for (BidirIter i2 = first2; i2 != last2; ++i2)
{
if (f())
return true;
swap(*first1, *i2);
}
if (f())
return true;
swap(*first1, *std::prev(last2));
swap(*first1, *first3);
for (BidirIter i2 = std::next(first3); i2 != last3; ++i2)
{
if (f())
return true;
swap(*first1, *i2);
}
}
else
{
BidirIter f1p = std::next(first1);
BidirIter i2 = first2;
for (D d22 = d2; i2 != last2; ++i2, --d22)
{
if (combine_discontinuous3_(f1p, last1, d1-1, i2, last2, d22, first3,
last3, d3, f, d+1))
return true;
swap(*first1, *i2);
}
i2 = first3;
for (D d22 = d3; i2 != last3; ++i2, --d22)
{
if (combine_discontinuous(f1p, last1, d1-1, i2, last3, d22, f, d+1))
return true;
swap(*first1, *i2);
}
}
if (f())
return true;
if (d1 == 1)
swap(*std::prev(last2), *first3);
if (d != 0)
{
if (d2 > 1)
rotate_discontinuous3(first1, last1, d1, std::next(first2), last2, d2-1, first3, last3, d3);
else
rotate_discontinuous(first1, last1, d1, first3, last3, d3);
}
else
rotate_discontinuous3(first1, last1, d1, first2, last2, d2, first3, last3, d3);
return false;
}
// Like combine_discontinuous, but swaps/rotates each combination out of
// [first1, last1) + [first2, last2) + [first3, last3) into [first1, last1).
// If f() always returns false, it is called (d1+d2+d3)!/(d1!*(d2+d3)!) times.
template <class BidirIter, class Function>
bool
combine_discontinuous3(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
BidirIter first2, BidirIter last2,
typename std::iterator_traits<BidirIter>::difference_type d2,
BidirIter first3, BidirIter last3,
typename std::iterator_traits<BidirIter>::difference_type d3,
Function& f)
{
typedef call_combine_discontinuous<Function&, BidirIter> F;
F fbc(first2, last2, d2, first3, last3, d3, f); // BC
return combine_discontinuous3_(first1, last1, d1, first2, last2, d2, first3, last3, d3, fbc);
}
// See permute
template <class BidirIter, class Function>
bool
permute_(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
Function& f)
{
using std::swap;
switch (d1)
{
case 0:
case 1:
return f();
case 2:
if (f())
return true;
swap(*first1, *std::next(first1));
return f();
case 3:
{
if (f())
return true;
BidirIter f2 = std::next(first1);
BidirIter f3 = std::next(f2);
swap(*f2, *f3);
if (f())
return true;
swap(*first1, *f3);
swap(*f2, *f3);
if (f())
return true;
swap(*f2, *f3);
if (f())
return true;
swap(*first1, *f2);
swap(*f2, *f3);
if (f())
return true;
swap(*f2, *f3);
return f();
}
}
BidirIter fp1 = std::next(first1);
for (BidirIter p = fp1; p != last1; ++p)
{
if (permute_(fp1, last1, d1-1, f))
return true;
std::reverse(fp1, last1);
swap(*first1, *p);
}
return permute_(fp1, last1, d1-1, f);
}
// Calls f() for each permutation of [first1, last1)
// Divided into permute and permute_ in a (perhaps futile) attempt to
// squeeze a little more performance out of it.
template <class BidirIter, class Function>
bool
permute(BidirIter first1, BidirIter last1,
typename std::iterator_traits<BidirIter>::difference_type d1,
Function& f)
{
using std::swap;
switch (d1)
{
case 0:
case 1:
return f();
case 2:
{
if (f())
return true;
BidirIter i = std::next(first1);
swap(*first1, *i);
if (f())
return true;
swap(*first1, *i);
}
break;
case 3:
{
if (f())
return true;
BidirIter f2 = std::next(first1);
BidirIter f3 = std::next(f2);
swap(*f2, *f3);
if (f())
return true;
swap(*first1, *f3);
swap(*f2, *f3);
if (f())
return true;
swap(*f2, *f3);
if (f())
return true;
swap(*first1, *f2);
swap(*f2, *f3);
if (f())
return true;
swap(*f2, *f3);
if (f())
return true;
swap(*first1, *f3);
}
break;
default:
BidirIter fp1 = std::next(first1);
for (BidirIter p = fp1; p != last1; ++p)
{
if (permute_(fp1, last1, d1-1, f))
return true;
std::reverse(fp1, last1);
swap(*first1, *p);
}
if (permute_(fp1, last1, d1-1, f))
return true;
std::reverse(first1, last1);
break;
}
return false;
}
// Creates a functor with no arguments which calls f_(first_, last_).
// Also has a variant that takes two It and ignores them.
template <class Function, class It>
class bound_range
{
Function f_;
It first_;
It last_;
public:
bound_range(Function f, It first, It last)
: f_(f), first_(first), last_(last) {}
bool
operator()()
{
return f_(first_, last_);
}
bool
operator()(It, It)
{
return f_(first_, last_);
}
};
// A binder for binding arguments to call permute
template <class Function, class It>
class call_permute
{
typedef typename std::iterator_traits<It>::difference_type D;
Function f_;
It first_;
It last_;
D d_;
public:
call_permute(Function f, It first, It last, D d)
: f_(f), first_(first), last_(last), d_(d) {}
bool
operator()()
{
return permute(first_, last_, d_, f_);
}
};
} // detail
template <class BidirIter, class Function>
Function
for_each_combination(BidirIter first, BidirIter last,
BidirIter mid, Function f)
{
howardhinnantdetail::bound_range<Function&, BidirIter> wfunc(f, first, mid);
howardhinnantdetail::combine_discontinuous(first, mid, std::distance(first, mid),
mid, last, std::distance(mid, last),
wfunc);
return f;
}
class BitwiseFullSearch
{
public:
ll count_;
std::function<void(const vll &ptn, ll &count)> checkcount_; // カウントするロジックのラムダ式を突っ込む。
BitwiseFullSearch(std::function<void(const vll &ptn, ll &count)> f) : count_(0), checkcount_(f) {}
// ここは触らなくてよい(パターンを列挙しているだけ)
bool operator()(vll::iterator it1, vll::iterator it2)
{
vll ptn;
while (it1 != it2)
{
ptn.pb(*it1);
++it1;
}
checkcount_(ptn, count_);
return false;
}
};
ll _comb_ptn_count(ll R, const std::function<void(const vll &ptn, ll &count)> &f, vll &_A_) {
auto B = BitwiseFullSearch(f);
vll::iterator _R_ = _A_.begin() + R;
B = for_each_combination(all(_A_), _R_, B);
return B.count_;
}
ll comb_ptn_count(ll N, ll R, const std::function<void(const vll &ptn, ll &count)> &f) {
SETPERM(_A_, N);
return _comb_ptn_count(R, f, _A_);
}
vvll get_comb_ptn(ll N, ll R) {
vvll cb;
auto f = [&](const vll &ptn, ll &count)
{
UNUSED(count);
cb.pb(ptn);
};
comb_ptn_count(N, R, f);
return cb;
}
ll comb_allptn_count(ll N, const std::function<void(const vll &ptn, ll &count)> &f) {
ll cnt = 0;
SETPERM(_A_, N);
rep(r, N + 1) {
cnt += _comb_ptn_count(r, f, _A_);
}
return cnt;
}
// N が 20とかだとSegmentation faultが発生する。スタック領域が足りなくなるか。
vvll get_comb_allptn(ll N) {
vvll cb;
auto f = [&](const vll &ptn, ll &count)
{
UNUSED(count);
cb.pb(ptn);
};
comb_allptn_count(N, f);
return cb;
}
vvll get_perm_ptn(ll N) {
vvll ptn;
SETPERM(_A_, N);
do {
ptn.pb(_A_);
} while(next_permutation(all(_A_)));
return ptn;
}
// n個からr個有効にしたbitパターンの数値を列挙
// 下1桁目から0, 1, 2番目が有効無効を表す。(Nは60くらいまで)
vll get_bitptn(ll N, ll R) {
vll bitptns;
auto ptns = get_comb_ptn(N, R);
rep (i, len(ptns)) {
ll bitptn = 0;
rep (j, R) {
bitptn += _1 << ptns[i][j];
}
bitptns.pb(bitptn);
}
return bitptns;
}
inline ll sumk(ll n)
{
return n * (n + 1) / 2;
}
inline ll sumk2(ll n)
{
return n * (n + 1) * (2 * n + 1) / 6;
}
ll POW(ll n, ll r)
{
if (r == 0) return 1;
else if (r % 2 == 0) return POW(n * n, (ll)(r / 2));
else return n * POW(n, r - 1);
}
inline string alpha()
{
return "abcdefghijklmnopqrstuvwxyz";
}
inline ll alpha_num(char c)
{
return ll(c) - ll('a');
}
inline string alpha_big()
{
return "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
}
inline ll alpha_big_num(char c)
{
return ll(c) - ll('A');
}
inline char alpha_big2small(char C) {
static string s = alpha();
ll idx = alpha_big_num(C);
return IN(0, idx, 25) ? s[idx] : C;
}
inline char alpha_small2big(char c) {
static string s = alpha_big();
ll idx = alpha_num(c);
return IN(0, idx, 25) ? s[idx] : c;
}
string zerofill(ll v, ll outputlen)
{
string s = STR(v);
string zerostr(outputlen - len(s), '0');
return zerostr + s;
}
// ランレングス圧縮
// auto rle = RunLengthEncoding(S);
// rep(i, len(rle)) {
// auto &[c, cnt] = rle[i];
// }
vector<pair<char, ll>> RunLengthEncoding(const string &s) {
vector<pair<char, ll>> tbl;
char c = s[0];
ll cnt = 1;
ll N = len(s);
reps (i, 1, N) {
if (c == s[i]) {
cnt++;
}
else {
tbl.pb(mp(c, cnt));
c = s[i];
cnt = 1;
}
}
tbl.pb(mp(c, cnt));
return tbl;
}
// 約数個数列挙(MAXNまで)
vll divisors_count(ll MAXN = 1000000)
{
vll div = vll(MAXN + 1, 0);
rrep(n, MAXN) repsp(m, n, MAXN + 1, n) {
div[m] += 1;
}
return div;
}
// Nの階乗がkで何回割れるかを返す。(ルジャンドルの公式)
ll LegendresFormula(ll N, ll k) {
ll v = k;
ll cnt = 0;
while(v <= N) {
cnt += floor(N, v);
v *= k;
}
return cnt;
}
// 約数列挙
// 約数の個数は大体n^(1/3)個
vll make_divisors(ll n) {
vll divisors;
for(ll i = 1; i * i <= n; ++i) {
if(n % i == 0) {
divisors.pb(i);
if(i != n / i) {
divisors.pb(n / i);
}
}
}
return divisors;
}
// N以下の素数列挙(Nはせいぜい10^7くらいまで)
inline vll eratosthenes(ll N) {
vll ps;
vector<bool> primes(N + 1);
rep(i, len(primes)) primes[i] = true;
primes[0] = primes[1] = false;
rep(i, len(primes)) {
if (primes[i]) {
ps.pb(i);
for (ull j = i + i; j < len(primes); j += i) {
primes[j] = false;
}
}
}
return ps;
}
// 高速素因数分解(MAXNの範囲まで)
class Prime
{
public:
static vll sieve; // 何回もPrimeのインスタンスを生成するときはstaticをはずして、下の実体もコメントアウトする。
Prime(ll MAXN = 10000000) {
rep(i, MAXN + 1) sieve.pb(i);
ll p = 2;
while (p * p <= MAXN) {
if (sieve[p] == p) {
repsp(q, 2 * p, MAXN + 1, p) {
if (sieve[q] == q) sieve[q] = p;
}
}
p += 1;
}
}
Counter<ll> prime(ll n) {
if (n == 1) return Counter<ll>(vll());
vll tmp;
while (n > 1) {
tmp.pb(sieve[n]);
n = (ll)(n / sieve[n]);
}
return Counter<ll>(tmp);
}
};
vll Prime::sieve = vll();
#define mod_m2p(a, m) (((m) + (a)) % (m))
#define mod_add(a, b, m) (((a) + (b)) % (m))
#define mod_sub(a, b, m) (((m) + (a) - (b)) % (m))
#define mod_mul(a, b, m) (mod_m2p(((a) % (m)) * ((b) % (m)), (m)))
ll mod_bipow_(ll x, ll y, ll m) { // x^y by bisection method
if (y == 0) return 1 % m;
else if (y == 1) return x % m;
else if (y % 2 == 0) {
ll val = mod_bipow_(x, (ll)(y / 2), m);
return mod_mul(val, val, m);
} else {
ll val = mod_bipow_(x, (ll)(y / 2), m);
return mod_mul(mod_mul(val, val, m), x, m);
}
}
ll mod_inv(ll x, ll pm) { return mod_bipow_(mod_m2p(x, pm), pm - 2, pm); } // x^{-1} = x^{MOD-2} (MOD: prime number)
ll mod_div(ll a, ll b, ll m) { return mod_mul(mod_m2p(a, m), mod_inv(mod_m2p(b, m), m), m); } // a/b = a*b^{-1}
ll mod_bipow(ll x, ll y, ll m) {
if (y < 0) {
ll xx = mod_div((ll)1, x, m);
return mod_bipow_(xx, -y, m);
}
return mod_bipow_(x, y, m);
}
ll mysqrt(ll n) {
ll ok = 0, ng = n + 1;
while (ng - ok > 1) {
ll mid = (ng + ok) >> 1;
if (mid * mid <= n) {
ok = mid;
} else {
ng = mid;
}
}
return ok;
}
// nCkをmで割った余りを求める
class Combination {
const ll n_;
const ll m_;
vll facts_;
vll inv_facts_;
public:
Combination(ll N, ll mod) : n_(2 * N), m_(mod), facts_(n_ + 1), inv_facts_(n_ + 1) {
rep(i, n_ + 1) facts_[i] = i == 0 ? 1 : mod_mul(facts_[i - 1], i, m_);
for (ll i = n_; i >= 0; i--) inv_facts_[i] = i == n_ ? mod_inv(facts_[n_], m_) : mod_mul(inv_facts_[i + 1], i + 1, m_); // (i!)^{-1}=((i+1)!)^{-1}*(i+1)
}
ll nPr(ll n, ll r) {
if (n < r) return _0;
return mod_mul(facts_[n], inv_facts_[n - r], m_);
}
ll nCr(ll n, ll r) {
if (n < r) return _0;
return mod_mul(facts_[n], mod_mul(inv_facts_[r], inv_facts_[n - r], m_), m_);
}
ll nHr(ll n, ll r) {
return nCr(n + r - 1, r);
}
ll catalan(ll n) { // https://ja.wikipedia.org/wiki/%E3%82%AB%E3%82%BF%E3%83%A9%E3%83%B3%E6%95%B0
return mod_mul(nCr(2 * n, n), mod_inv(n + 1, m_), m_);
}
// カタラン数・・・(2n C n)/(n + 1) = (2n C n) - (2n C n-1)
// c0 = 1, c_n = rep(i, n) c[i] * c[n - i - 1]
// c0から順に1,1,2,5,14,42,132,429,1430,...
// 1 <= a1 <= a2 <= a3 <= a4 <= ... <= ak <= Nの組み合わせの数。
// CombinationのコンストラクタにN + Kを入れておくこと。
ll loopcnt(ll n, ll k) {
assert(n + k <= n_);
return nCr(n - 1 + k, n - 1);
}
};
// 1-originで扱う。
class UnionFind {
ll n_;
vll size_;
vll par_;
vll link_;
vll rank_;
vll par_diff_;
public:
UnionFind(ll n) : n_(n + 1), size_(n_, 1), par_(n_), link_(n_), rank_(n_), par_diff_(n_)
{
iota(all(par_), 0);
iota(all(link_), 0);
}
ll find(ll x) {
if (par_[x] == x) return x;
else {
ll ret = find(par_[x]);
if (par_diff_[par_[x]] == LLONG_MAX) par_diff_[x] = LLONG_MAX;
else par_diff_[x] += par_diff_[par_[x]];
return par_[x] = ret;
}
}
ll operator[](ll x) { return find(x); }
bool unite(ll x, ll y, ll w = 0) {
if (x != 0 && same(x, y) && diff(x, y) != w) unite(0, y);
ll rx = find(x);
ll ry = find(y);
ll wt = w;
wt += weight(x);
wt -= weight(y);
if (rx == ry) {
return false;
}
if (ry < rx) {
swap(rx, ry);
wt = -wt;
}
size_[rx] += size_[ry];
if (rank_[rx] == rank_[ry]) rank_[rx]++;
size_[ry] = 0;
par_[ry] = rx;
par_diff_[ry] = wt;
swap(link_[rx], link_[ry]);
return true;
}
vll find_all() {
vll A(n_);
rep(i, n_) A[i] = find(i);
return A;
}
vll members(ll x) {
vll mems = vll{x};
for (ll y = link_[x]; y != x; y = link_[y]) mems.pb(y);
return mems;
}
ll size(ll x) {
return size_[find(x)];
}
bool same(ll x, ll y) {
return find(x) == find(y);
}
vll roots() {
vll rs;
reps(i, 1, n_) if (size_[i] > 0) rs.pb(i);
return rs;
}
ll group_count() {
return len(roots());
}
unordered_map<ll, vll> all_group_members() {
unordered_map<ll, vll> group_members;
reps(member, 1, n_) group_members[find(member)].pb(member);
return group_members;
}
ll weight(ll x) {
find(x);
return par_diff_[x];
}
ll diff(ll x, ll y) {
if (same(0, x) || same(0, y)) return LLONG_MAX;
return weight(y) - weight(x);
}
};
class Graph
{
private:
unordered_map<ll, vector<pll>> edges_;
unordered_map<ll, vector<pll>> ignore_edges_; // 多重辺で同じ重みの辺があるとダメ
vll outdeg_;
vll indeg_;
const ll V_;
const bool dir_;
const ll ansmod_;
// dist(-1で初期化), cntは呼び出し元でN個分の配列を与えること。connect_vtxsは空のvectorでよい。
void bfs_(ll sv, vll &dist, vll &connect_vtxs, vll &cnt, vll &root, ll search_depth = 1000000000)
{
if (dist[sv] != -1) return;
dll q = dll();
q.pb(sv);
dist[sv] = 0;
connect_vtxs.pb(sv);
cnt[sv] = 1;
if (search_depth == 0) return;
while (len(q) > 0) {
ll p = q[0];
q.popleft();
if (!EXIST(p, edges_)) continue;
vector<pll> &evw = edges_[p];
for (const auto& [ev, w] : evw) {
bool isignore = false;
rep(i, len(ignore_edges_[p])) {
const auto& [igev, igw] = ignore_edges_[p][i];
if (ev == igev && w == igw) {
isignore = true;
}
}
if (isignore) continue;
if (dist[ev] != -1) {
if (dist[ev] == dist[p] + 1) {
cnt[ev] += cnt[p];
cnt[ev] %= ansmod_;
}
continue;
}
dist[ev] = dist[p] + 1;
root[ev] = p;
cnt[ev] = cnt[p];
connect_vtxs.pb(ev);
if (dist[ev] < search_depth)
{
if (w == 0) q.pf(ev);
else q.pb(ev);
}
}
}
}
// 木で無向辺のみ対応
void dfs_(ll sv, ll pre = -1) {
connect_vtxs_.pb(sv);
root_[sv] = pre;
traverse_preorder_path_.pb(sv);
vector<pll> &evw = edges_[sv];
ll child_cnt = 0;
for (const auto& [ev, w] : evw) {
if (ev == pre) continue;
bool isignore = false; // 無効化されている辺は無視する。
rep(i, len(ignore_edges_[sv])) {
const auto& [igev, igw] = ignore_edges_[sv][i];
if (ev == igev && w == igw) {
isignore = true;
}
}
if (isignore) continue;
dfs_(ev, sv);
child_cnt++;
}
if (child_cnt == 0) { // 辺が1つのときで根でないとき
traverse_reached_[sv] = true;
traverse_inorder_path_.pb(sv);
}
if (pre != -1 && !traverse_reached_[pre]) {
traverse_reached_[pre] = true;
traverse_inorder_path_.pb(pre);
}
traverse_postorder_path_.pb(sv);
}
public:
vll path_; // dfsでたどった経路
vll traverse_preorder_path_; // dfsでたどり着けるノード順 (行きがけ順)
vll traverse_inorder_path_; // dfsでたどり着けるノード順 (通りがけ順)
vll traverse_postorder_path_; // dfsでたどり着けるノード順 (帰りがけ順) (木DPで使えそう)
vector<bool> traverse_reached_; // dfsでたどり着いたチェック
vll dist_;
vll connect_vtxs_;
vll cnt_;
vll root_;
Graph(ll V, bool dir, ll ansmod = 1000000007) : V_(V), dir_(dir), ansmod_(ansmod), traverse_reached_(V_, false), dist_(V_, -1), cnt_(V_), root_(V_, -1){
outdeg_ = vll(V);
indeg_ = vll(V);
}
void append_edge(ll sv, ll ev, ll weight = 1)
{
vector<pll> &u = edges_[sv];
pll v = make_pair(ev, weight);
u.pb(v);
outdeg_[sv]++;
indeg_[ev]++;
if (!dir_) {
swap(sv, ev);
outdeg_[sv]++;
indeg_[ev]++;
vector<pll> &ru = edges_[sv];
pll rv = make_pair(ev, weight);
ru.pb(rv);
}
}
void ignore_edge(ll sv, ll ev, ll weight = 1) {
vector<pll> &u = ignore_edges_[sv];
pll v = make_pair(ev, weight);
u.pb(v);
if (!dir_) {
swap(sv, ev);
vector<pll> &ru = ignore_edges_[sv];
pll rv = make_pair(ev, weight);
ru.pb(rv);
}
}
void ignore_edge_clear() {
ignore_edges_.clear();
}
void bfs(ll sv, bool reset = true, ll search_depth = 1000000000) {
if (reset) {
rep(i, len(connect_vtxs_)) {
dist_[connect_vtxs_[i]] = -1;
cnt_[connect_vtxs_[i]] = 0;
root_[connect_vtxs_[i]] = -1;
}
connect_vtxs_.clear();
}
bfs_(sv, dist_, connect_vtxs_, cnt_, root_, search_depth);
}
void dfs(ll sv, bool reset = false) {
if (traverse_reached_[sv]) return; // すでに到達済みの点はdfsしない
if (reset) {
traverse_preorder_path_.clear();
traverse_inorder_path_.clear();
traverse_postorder_path_.clear();
rep(i, len(connect_vtxs_)) {
traverse_reached_[connect_vtxs_[i]] = false; // 「他の始点から到達してたときは無視したい」場合はこれをコメントアウト
root_[connect_vtxs_[i]] = -1;
}
connect_vtxs_.clear();
}
dfs_(sv);
}
vll topo_sort()
{
heapqll q;
vll to = vll(V_);
vll topo_vertex_list;
repdict(u, vtxs, edges_) {
for (const auto& [ev, w] : vtxs) {
++to[ev];
}
}
rep(i, V_) {
if (to[i] != 0) continue;
q.push(i);
}
while (len(q) != 0) {
const ll v = q.top();
q.pop();
topo_vertex_list.pb(v);
for (const auto [ev, w] : edges_[v]) {
--to[ev];
if (to[ev]) continue;
q.push(ev);
}
}
return topo_vertex_list;
}
ll longest_path() { // 有向グラフで非連結グラフの最大パスの長さを求める。
dll q;
vll dist(V_);
rep (i, V_) {
if (indeg_[i] == 0) q.pb(i);
}
while (len(q) != 0) {
const ll u = q.front();
q.pop_front();
vector<pll> &v = edges_[u];
rep (i, len(v)) {
chmax(dist[v[i].first], dist[u] + 1);
indeg_[v[i].first]--;
if (indeg_[v[i].first] == 0) q.pb(v[i].first);
}
}
return MAX(dist);
}
// 無向グラフのみ対応。
// start->endのパスが無ければ空を返す
vll get_path(ll start, ll end, ll vertexidx_offset = 0) {
bfs(start);
if (dist_[end] == -1) return vll{};
ll pos = end;
vll path = {end + vertexidx_offset};
while(pos != start) {
pos = root_[pos];
path.pb(pos + vertexidx_offset);
}
REV(path);
return path;
}
// 先にbfsを実行しておく。
vll parts_tree_size() {
vvll tmp;
rep (i, V_) {
tmp.pb(vll{dist_[i], i});
}
SORT(tmp);
REV(tmp);
vll ans(V_);
rep (i, V_) {
INI2(d, idx, tmp[i]);
UNUSED(d);
if (root_[idx] != -1) ans[root_[idx]] += ans[idx] + 1;
}
return ans;
}
};
#include __FILE__
#endif