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test/yosupo/tree/rooted_tree_isomorphism_classification.test.cpp
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- Last update: 2024-05-17 13:49:08+09:00
- Problem: https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification
Depends on
- BinaryIndexedTree(FenwickTree, BIT)
(data-struct/segment/BinaryIndexedTree.hpp)
- Graph-template
(graph/Graph.hpp)
- ReRooting(全方位木DP)
(graph/tree/ReRooting.hpp)
- TreeHash
(graph/tree/TreeHash.hpp)
- other/monoid.hpp
- other/template.hpp
- Random
(random/Random.hpp)
- RollingHash(ロリハ)
(string/RollingHash.hpp)
- template/alias.hpp
- template/bitop.hpp
- template/func.hpp
- template/in.hpp
- template/macros.hpp
- template/out.hpp
- template/type_traits.hpp
- template/util.hpp
Code
#define PROBLEM "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"
#include "../../../other/template.hpp"
#include "../../../graph/Graph.hpp"
#include "../../../graph/tree/TreeHash.hpp"
using namespace std;
using mint = modint61;
int main() {
int N; scan >> N;
Graph<int> G(N);
rep (i, 1, N) {
int p; scan >> p;
G.add_edge(p, i);
}
TreeHash th;
auto h = th.get_hash(G);
map<ull, vector<int>> mp;
rep (i, N) mp[h[i].get()].push_back(i);
vector<int> ans(N);
int cnt = 0;
for (const auto& [_, v] : mp) {
for (int i : v) ans[i] = cnt;
++cnt;
}
prints(cnt);
prints(ans);
}#line 1 "test/yosupo/tree/rooted_tree_isomorphism_classification.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"
#line 2 "other/template.hpp"
#include <bits/stdc++.h>
#line 2 "template/macros.hpp"
#line 4 "template/macros.hpp"
#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif
#define OVERLOAD5(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c) \
for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) OVERLOAD5(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) OVERLOAD5(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) OVERLOAD5(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...) OVERLOAD5(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__)
#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)
#define all(v) std::begin(v), std::end(v)
#define rall(v) std::rbegin(v), std::rend(v)
#if __cpp_if_constexpr >= 201606L
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif
#define IO_BUFFER_SIZE (1 << 17)
#line 2 "template/alias.hpp"
#line 4 "template/alias.hpp"
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T>
using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template<class T> struct infinity {
static constexpr T value = std::numeric_limits<T>::max() / 2;
static constexpr T mvalue = std::numeric_limits<T>::lowest() / 2;
static constexpr T max = std::numeric_limits<T>::max();
static constexpr T min = std::numeric_limits<T>::lowest();
};
#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif
#if __cpp_variable_templates >= 201304L
template<class T> constexpr T INF = infinity<T>::value;
#endif
constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
#line 2 "template/type_traits.hpp"
#line 5 "template/type_traits.hpp"
template<class T, class... Args> struct function_traits_impl {
using result_type = T;
template<std::size_t idx>
using argument_type =
typename std::tuple_element<idx, std::tuple<Args...>>::type;
using argument_tuple = std::tuple<Args...>;
static constexpr std::size_t arg_size() { return sizeof...(Args); }
};
template<class> struct function_traits_helper;
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)&> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const&> {
using type = function_traits_impl<Res, Args...>;
};
#if __cpp_noexcept_function_type >= 201510L
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> {
using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> {
using type = function_traits_impl<Res, Args...>;
};
#endif
template<class F>
using function_traits = typename function_traits_helper<
decltype(&std::remove_reference<F>::type::operator())>::type;
template<class F>
using function_result_type = typename function_traits<F>::result_type;
template<class F, std::size_t idx>
using function_argument_type =
typename function_traits<F>::template argument_type<idx>;
template<class F>
using function_argument_tuple = typename function_traits<F>::argument_tuple;
template<class T>
using is_signed_int =
std::integral_constant<bool, (std::is_integral<T>::value &&
std::is_signed<T>::value) ||
std::is_same<T, i128>::value>;
template<class T>
using is_unsigned_int =
std::integral_constant<bool, (std::is_integral<T>::value &&
std::is_unsigned<T>::value) ||
std::is_same<T, u128>::value>;
template<class T>
using is_int = std::integral_constant<bool, is_signed_int<T>::value ||
is_unsigned_int<T>::value>;
template<class T>
using make_signed_int = typename std::conditional<
std::is_same<T, i128>::value || std::is_same<T, u128>::value,
std::common_type<i128>, std::make_signed<T>>::type;
template<class T>
using make_unsigned_int = typename std::conditional<
std::is_same<T, i128>::value || std::is_same<T, u128>::value,
std::common_type<u128>, std::make_unsigned<T>>::type;
template<class T, class = void> struct is_range : std::false_type {};
template<class T>
struct is_range<
T,
decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()),
(void)0)> : std::true_type {};
template<class T, bool = is_range<T>::value>
struct range_rank : std::integral_constant<std::size_t, 0> {};
template<class T>
struct range_rank<T, true>
: std::integral_constant<std::size_t,
range_rank<typename T::value_type>::value + 1> {};
template<std::size_t size> struct int_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::int_least8_t,
typename std::conditional<
size <= 16, std::int_least16_t,
typename std::conditional<
size <= 32, std::int_least32_t,
typename std::conditional<size <= 64, std::int_least64_t,
i128>::type>::type>::type>::type;
};
template<std::size_t size> using int_least_t = typename int_least<size>::type;
template<std::size_t size> struct uint_least {
static_assert(size <= 128, "size must be less than or equal to 128");
using type = typename std::conditional<
size <= 8, std::uint_least8_t,
typename std::conditional<
size <= 16, std::uint_least16_t,
typename std::conditional<
size <= 32, std::uint_least32_t,
typename std::conditional<size <= 64, std::uint_least64_t,
u128>::type>::type>::type>::type;
};
template<std::size_t size> using uint_least_t = typename uint_least<size>::type;
template<class T>
using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>;
template<class T> using double_size_int_t = typename double_size_int<T>::type;
template<class T>
using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>;
template<class T> using double_size_uint_t = typename double_size_uint<T>::type;
template<class T>
using double_size =
typename std::conditional<is_signed_int<T>::value, double_size_int<T>,
double_size_uint<T>>::type;
template<class T> using double_size_t = typename double_size<T>::type;
#line 2 "template/in.hpp"
#line 4 "template/in.hpp"
#include <unistd.h>
#line 8 "template/in.hpp"
template<std::size_t buf_size = IO_BUFFER_SIZE,
std::size_t decimal_precision = 16>
class Scanner {
private:
template<class, class = void> struct has_scan : std::false_type {};
template<class T>
struct has_scan<
T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)>
: std::true_type {};
int fd;
int idx, sz;
bool state;
std::array<char, IO_BUFFER_SIZE + 1> buffer;
inline char cur() {
if (idx == sz) load();
if (idx == sz) {
state = false;
return '\0';
}
return buffer[idx];
}
inline void next() {
if (idx == sz) load();
if (idx == sz) return;
++idx;
}
public:
inline void load() {
int len = sz - idx;
if (idx < len) return;
std::memcpy(buffer.begin(), buffer.begin() + idx, len);
sz = len + read(fd, buffer.data() + len, buf_size - len);
buffer[sz] = 0;
idx = 0;
}
Scanner(int fd) : fd(fd), idx(0), sz(0), state(true) {}
Scanner(FILE* fp) : fd(fileno(fp)), idx(0), sz(0), state(true) {}
inline char scan_char() {
if (idx == sz) load();
return idx == sz ? '\0' : buffer[idx++];
}
Scanner ignore(int n = 1) {
if (idx + n > sz) load();
idx += n;
return *this;
}
inline void discard_space() {
if (idx == sz) load();
while (('\t' <= buffer[idx] && buffer[idx] <= '\r') ||
buffer[idx] == ' ') {
if (++idx == sz) load();
}
}
void scan(char& a) {
discard_space();
a = scan_char();
}
void scan(bool& a) {
discard_space();
a = scan_char() != '0';
}
void scan(std::string& a) {
discard_space();
a.clear();
while (cur() != '\0' && (buffer[idx] < '\t' || '\r' < buffer[idx]) &&
buffer[idx] != ' ') {
a += scan_char();
}
}
template<std::size_t len> void scan(std::bitset<len>& a) {
discard_space();
if (idx + len > sz) load();
rrep (i, len) a[i] = buffer[idx++] != '0';
}
template<class T,
typename std::enable_if<is_signed_int<T>::value &&
!has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
discard_space();
if (buffer[idx] == '-') {
++idx;
if (idx + 40 > sz &&
(idx == sz || ('0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')))
load();
a = 0;
while ('0' <= buffer[idx] && buffer[idx] <= '9') {
a = a * 10 - (buffer[idx++] - '0');
}
}
else {
if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')
load();
a = 0;
while ('0' <= buffer[idx] && buffer[idx] <= '9') {
a = a * 10 + (buffer[idx++] - '0');
}
}
}
template<class T,
typename std::enable_if<is_unsigned_int<T>::value &&
!has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
discard_space();
if (idx + 40 > sz && '0' <= buffer[sz - 1] && buffer[sz - 1] <= '9')
load();
a = 0;
while ('0' <= buffer[idx] && buffer[idx] <= '9') {
a = a * 10 + (buffer[idx++] - '0');
}
}
template<class T,
typename std::enable_if<std::is_floating_point<T>::value &&
!has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
discard_space();
bool sgn = false;
if (cur() == '-') {
sgn = true;
next();
}
a = 0;
while ('0' <= cur() && cur() <= '9') {
a = a * 10 + cur() - '0';
next();
}
if (cur() == '.') {
next();
T n = 0, d = 1;
for (int i = 0;
'0' <= cur() && cur() <= '9' && i < (int)decimal_precision;
++i) {
n = n * 10 + cur() - '0';
d *= 10;
next();
}
while ('0' <= cur() && cur() <= '9') next();
a += n / d;
}
if (sgn) a = -a;
}
private:
template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) {
if IF_CONSTEXPR (i < sizeof...(Args)) {
scan(std::get<i>(a));
scan<i + 1, Args...>(a);
}
}
public:
template<class... Args> void scan(std::tuple<Args...>& a) {
scan<0, Args...>(a);
}
template<class T, class U> void scan(std::pair<T, U>& a) {
scan(a.first);
scan(a.second);
}
template<class T,
typename std::enable_if<is_range<T>::value &&
!has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
for (auto&& i : a) scan(i);
}
template<class T,
typename std::enable_if<has_scan<T>::value>::type* = nullptr>
void scan(T& a) {
a.scan(*this);
}
void operator()() {}
template<class Head, class... Args>
void operator()(Head& head, Args&... args) {
scan(head);
operator()(args...);
}
template<class T> Scanner& operator>>(T& a) {
scan(a);
return *this;
}
explicit operator bool() const { return state; }
friend Scanner& getline(Scanner& scan, std::string& a) {
a.erase();
char c;
if ((c = scan.scan_char()) == '\n' || c == '\0') return scan;
a += c;
while ((c = scan.scan_char()) != '\n' && c != '\0') a += c;
scan.state = true;
return scan;
}
};
Scanner<> scan(0);
#line 2 "template/out.hpp"
#line 8 "template/out.hpp"
struct NumberToString {
char buf[10000][4];
constexpr NumberToString() : buf{} {
rep (i, 10000) {
int n = i;
rrep (j, 4) {
buf[i][j] = (char)('0' + n % 10);
n /= 10;
}
}
}
} constexpr precalc_number_to_string;
template<std::size_t buf_size = IO_BUFFER_SIZE, bool debug = false>
class Printer {
private:
template<class, bool = debug, class = void>
struct has_print : std::false_type {};
template<class T>
struct has_print<T, false,
decltype(std::declval<T>().print(std::declval<Printer&>()),
(void)0)> : std::true_type {};
template<class T>
struct has_print<T, true,
decltype(std::declval<T>().debug(std::declval<Printer&>()),
(void)0)> : std::true_type {};
int fd;
std::size_t idx;
std::array<char, buf_size> buffer;
std::size_t decimal_precision;
public:
inline void print_char(char c) {
#if SHIO_LOCAL
buffer[idx++] = c;
if (idx == buf_size) flush();
#else
if IF_CONSTEXPR (!debug) {
buffer[idx++] = c;
if (idx == buf_size) flush();
}
#endif
}
inline void flush() {
idx = write(fd, buffer.begin(), idx);
idx = 0;
}
Printer(int fd) : fd(fd), idx(0), decimal_precision(16) {}
Printer(FILE* fp) : fd(fileno(fp)), idx(0), decimal_precision(16) {}
~Printer() { flush(); }
void set_decimal_precision(std::size_t decimal_precision) {
this->decimal_precision = decimal_precision;
}
void print(char c) {
if IF_CONSTEXPR (debug) print_char('\'');
print_char(c);
if IF_CONSTEXPR (debug) print_char('\'');
}
void print(bool b) { print_char((char)(b + '0')); }
void print(const char* a) {
if IF_CONSTEXPR (debug) print_char('"');
for (; *a != '\0'; ++a) print_char(*a);
if IF_CONSTEXPR (debug) print_char('"');
}
template<std::size_t len> void print(const char (&a)[len]) {
if IF_CONSTEXPR (debug) print_char('"');
for (auto i : a) print_char(i);
if IF_CONSTEXPR (debug) print_char('"');
}
void print(const std::string& a) {
if IF_CONSTEXPR (debug) print_char('"');
for (auto i : a) print_char(i);
if IF_CONSTEXPR (debug) print_char('"');
}
template<std::size_t len> void print(const std::bitset<len>& a) {
rrep (i, len) print_char((char)(a[i] + '0'));
}
template<class T,
typename std::enable_if<is_int<T>::value &&
!has_print<T>::value>::type* = nullptr>
void print(T a) {
if (!a) {
print_char('0');
return;
}
if IF_CONSTEXPR (is_signed_int<T>::value) {
if (a < 0) {
print_char('-');
using U = typename make_unsigned_int<T>::type;
print(static_cast<U>(-static_cast<U>(a)));
return;
}
}
if (idx + 40 >= buf_size) flush();
static char s[40];
int t = 40;
while (a >= 10000) {
int i = a % 10000;
a /= 10000;
t -= 4;
std::memcpy(s + t, precalc_number_to_string.buf[i], 4);
}
if (a >= 1000) {
std::memcpy(buffer.begin() + idx, precalc_number_to_string.buf[a],
4);
idx += 4;
}
else if (a >= 100) {
std::memcpy(buffer.begin() + idx,
precalc_number_to_string.buf[a] + 1, 3);
idx += 3;
}
else if (a >= 10) {
std::memcpy(buffer.begin() + idx,
precalc_number_to_string.buf[a] + 2, 2);
idx += 2;
}
else {
buffer[idx++] = '0' | a;
}
std::memcpy(buffer.begin() + idx, s + t, 40 - t);
idx += 40 - t;
}
template<class T,
typename std::enable_if<std::is_floating_point<T>::value &&
!has_print<T>::value>::type* = nullptr>
void print(T a) {
if (a == std::numeric_limits<T>::infinity()) {
print("inf");
return;
}
if (a == -std::numeric_limits<T>::infinity()) {
print("-inf");
return;
}
if (std::isnan(a)) {
print("nan");
return;
}
if (a < 0) {
print_char('-');
a = -a;
}
T b = a;
if (b < 1) {
print_char('0');
}
else {
std::string s;
while (b >= 1) {
s += (char)('0' + (int)std::fmod(b, 10.0));
b /= 10;
}
for (auto i = s.rbegin(); i != s.rend(); ++i) print_char(*i);
}
print_char('.');
rep (decimal_precision) {
a *= 10;
print_char((char)('0' + (int)std::fmod(a, 10.0)));
}
}
private:
template<std::size_t i, class... Args>
void print(const std::tuple<Args...>& a) {
if IF_CONSTEXPR (i < sizeof...(Args)) {
if IF_CONSTEXPR (debug) print_char(',');
print_char(' ');
print(std::get<i>(a));
print<i + 1, Args...>(a);
}
}
public:
template<class... Args> void print(const std::tuple<Args...>& a) {
if IF_CONSTEXPR (debug) print_char('(');
if IF_CONSTEXPR (sizeof...(Args) != 0) print(std::get<0>(a));
print<1, Args...>(a);
if IF_CONSTEXPR (debug) print_char(')');
}
template<class T, class U> void print(const std::pair<T, U>& a) {
if IF_CONSTEXPR (debug) print_char('(');
print(a.first);
if IF_CONSTEXPR (debug) print_char(',');
print_char(' ');
print(a.second);
if IF_CONSTEXPR (debug) print_char(')');
}
template<class T,
typename std::enable_if<is_range<T>::value &&
!has_print<T>::value>::type* = nullptr>
void print(const T& a) {
if IF_CONSTEXPR (debug) print_char('{');
for (auto i = std::begin(a); i != std::end(a); ++i) {
if (i != std::begin(a)) {
if IF_CONSTEXPR (debug) print_char(',');
print_char(' ');
}
print(*i);
}
if IF_CONSTEXPR (debug) print_char('}');
}
template<class T, typename std::enable_if<has_print<T>::value &&
!debug>::type* = nullptr>
void print(const T& a) {
a.print(*this);
}
template<class T, typename std::enable_if<has_print<T>::value &&
debug>::type* = nullptr>
void print(const T& a) {
a.debug(*this);
}
void operator()() {}
template<class Head, class... Args>
void operator()(const Head& head, const Args&... args) {
print(head);
operator()(args...);
}
template<class T> Printer& operator<<(const T& a) {
print(a);
return *this;
}
Printer& operator<<(Printer& (*pf)(Printer&)) { return pf(*this); }
};
template<std::size_t buf_size, bool debug>
Printer<buf_size, debug>& endl(Printer<buf_size, debug>& pr) {
pr.print_char('\n');
pr.flush();
return pr;
}
template<std::size_t buf_size, bool debug>
Printer<buf_size, debug>& flush(Printer<buf_size, debug>& pr) {
pr.flush();
return pr;
}
struct SetPrec {
int n;
template<class Pr> void print(Pr& pr) const { pr.set_decimal_precision(n); }
template<class Pr> void debug(Pr& pr) const { pr.set_decimal_precision(n); }
};
SetPrec setprec(int n) { return SetPrec{n}; };
Printer<> print(1), eprint(2);
void prints() { print.print_char('\n'); }
template<class T> auto prints(const T& v) -> decltype(print << v, (void)0) {
print << v;
print.print_char('\n');
}
template<class Head, class... Tail>
auto prints(const Head& head, const Tail&... tail)
-> decltype(print << head, (void)0) {
print << head;
print.print_char(' ');
prints(tail...);
}
Printer<IO_BUFFER_SIZE, true> debug(1), edebug(2);
void debugs() { debug.print_char('\n'); }
template<class T> auto debugs(const T& v) -> decltype(debug << v, (void)0) {
debug << v;
debug.print_char('\n');
}
template<class Head, class... Tail>
auto debugs(const Head& head, const Tail&... tail)
-> decltype(debug << head, (void)0) {
debug << head;
debug.print_char(' ');
debugs(tail...);
}
#line 2 "template/bitop.hpp"
#line 6 "template/bitop.hpp"
namespace bitop {
#define KTH_BIT(b, k) (((b) >> (k)) & 1)
#define POW2(k) (1ull << (k))
inline ull next_combination(int n, ull x) {
if (n == 0) return 1;
ull a = x & -x;
ull b = x + a;
return (x & ~b) / a >> 1 | b;
}
#define rep_comb(i, n, k) \
for (ull i = (1ull << (k)) - 1; i < (1ull << (n)); \
i = bitop::next_combination((n), i))
inline constexpr int msb(ull x) {
int res = x ? 0 : -1;
if (x & 0xFFFFFFFF00000000) x &= 0xFFFFFFFF00000000, res += 32;
if (x & 0xFFFF0000FFFF0000) x &= 0xFFFF0000FFFF0000, res += 16;
if (x & 0xFF00FF00FF00FF00) x &= 0xFF00FF00FF00FF00, res += 8;
if (x & 0xF0F0F0F0F0F0F0F0) x &= 0xF0F0F0F0F0F0F0F0, res += 4;
if (x & 0xCCCCCCCCCCCCCCCC) x &= 0xCCCCCCCCCCCCCCCC, res += 2;
return res + ((x & 0xAAAAAAAAAAAAAAAA) ? 1 : 0);
}
inline constexpr int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; }
inline constexpr ull reverse(ull x) {
x = ((x & 0xAAAAAAAAAAAAAAAA) >> 1) | ((x & 0x5555555555555555) << 1);
x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) | ((x & 0x3333333333333333) << 2);
x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
x = ((x & 0xFF00FF00FF00FF00) >> 8) | ((x & 0x00FF00FF00FF00FF) << 8);
x = ((x & 0xFFFF0000FFFF0000) >> 16) | ((x & 0x0000FFFF0000FFFF) << 16);
return (x >> 32) | (x << 32);
}
inline constexpr ull reverse(ull x, int n) { return reverse(x) >> (64 - n); }
} // namespace bitop
inline constexpr int popcnt(ull x) noexcept {
#if __cplusplus >= 202002L
return std::popcount(x);
#endif
x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
#line 2 "template/func.hpp"
#line 6 "template/func.hpp"
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmin(T& a, const U& b,
Comp cmp = Comp()) noexcept(noexcept(cmp(b, a))) {
return cmp(b, a) ? a = b, true : false;
}
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmax(T& a, const U& b,
Comp cmp = Comp()) noexcept(noexcept(cmp(a, b))) {
return cmp(a, b) ? a = b, true : false;
}
inline constexpr ll gcd(ll a, ll b) {
if (a < 0) a = -a;
if (b < 0) b = -b;
while (b) {
const ll c = a;
a = b;
b = c % b;
}
return a;
}
inline constexpr ll lcm(ll a, ll b) { return a / gcd(a, b) * b; }
inline constexpr bool is_prime(ll N) {
if (N <= 1) return false;
for (ll i = 2; i * i <= N; ++i) {
if (N % i == 0) return false;
}
return true;
}
inline std::vector<ll> prime_factor(ll N) {
std::vector<ll> res;
for (ll i = 2; i * i <= N; ++i) {
while (N % i == 0) {
res.push_back(i);
N /= i;
}
}
if (N != 1) res.push_back(N);
return res;
}
inline constexpr ll my_pow(ll a, ll b) {
ll res = 1;
while (b) {
if (b & 1) res *= a;
b >>= 1;
a *= a;
}
return res;
}
inline constexpr ll mod_pow(ll a, ll b, ll mod) {
assert(mod > 0);
if (mod == 1) return 0;
a %= mod;
ll res = 1;
while (b) {
if (b & 1) (res *= a) %= mod;
b >>= 1;
(a *= a) %= mod;
}
return res;
}
inline PLL extGCD(ll a, ll b) {
const ll n = a, m = b;
ll x = 1, y = 0, u = 0, v = 1;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
std::swap(y -= t * v, v);
}
if (x < 0) {
x += m;
y -= n;
}
return {x, y};
}
inline ll mod_inv(ll a, ll mod) {
ll b = mod;
ll x = 1, u = 0;
ll t;
while (b) {
t = a / b;
std::swap(a -= t * b, b);
std::swap(x -= t * u, u);
}
if (x < 0) x += mod;
assert(a == 1);
return x;
}
#line 2 "template/util.hpp"
#line 6 "template/util.hpp"
template<class F> class RecLambda {
private:
F f;
public:
explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
template<class... Args>
constexpr auto operator()(Args&&... args)
-> decltype(f(*this, std::forward<Args>(args)...)) {
return f(*this, std::forward<Args>(args)...);
}
};
template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
return RecLambda<F>(std::forward<F>(f));
}
template<class Head, class... Tail> struct multi_dim_vector {
using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> { using type = T; };
template<class T, class Arg>
constexpr std::vector<T> make_vec(int n, Arg&& arg) {
return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n,
Args&&... args) {
return typename multi_dim_vector<Args..., T>::type(
n, make_vec<T>(std::forward<Args>(args)...));
}
template<class T, class Comp = std::less<T>> class compressor {
private:
std::vector<T> dat;
Comp cmp;
bool sorted = false;
public:
compressor() : compressor(Comp()) {}
compressor(const Comp& cmp) : cmp(cmp) {}
compressor(const std::vector<T>& vec, bool f = false,
const Comp& cmp = Comp())
: dat(vec), cmp(cmp) {
if (f) build();
}
compressor(std::vector<T>&& vec, bool f = false, const Comp& cmp = Comp())
: dat(std::move(vec)), cmp(cmp) {
if (f) build();
}
compressor(std::initializer_list<T> il, bool f = false,
const Comp& cmp = Comp())
: dat(all(il)), cmp(cmp) {
if (f) build();
}
void reserve(int n) {
assert(!sorted);
dat.reserve(n);
}
void push_back(const T& v) {
assert(!sorted);
dat.push_back(v);
}
void push_back(T&& v) {
assert(!sorted);
dat.push_back(std::move(v));
}
template<class... Args> void emplace_back(Args&&... args) {
assert(!sorted);
dat.emplace_back(std::forward<Args>(args)...);
}
void push(const std::vector<T>& vec) {
assert(!sorted);
const int n = dat.size();
dat.resize(n + vec.size());
rep (i, vec.size()) dat[n + i] = vec[i];
}
int build() {
assert(!sorted);
sorted = true;
std::sort(all(dat), cmp);
dat.erase(std::unique(all(dat),
[&](const T& a, const T& b) -> bool {
return !cmp(a, b) && !cmp(b, a);
}),
dat.end());
return dat.size();
}
const T& operator[](int k) const& {
assert(sorted);
assert(0 <= k && k < (int)dat.size());
return dat[k];
}
int get(const T& val) const {
assert(sorted);
auto itr = std::lower_bound(all(dat), val, cmp);
assert(itr != dat.end() && !cmp(val, *itr));
return itr - dat.begin();
}
int lower_bound(const T& val) const {
assert(sorted);
auto itr = std::lower_bound(all(dat), val, cmp);
return itr - dat.begin();
}
int upper_bound(const T& val) const {
assert(sorted);
auto itr = std::upper_bound(all(dat), val, cmp);
return itr - dat.begin();
}
bool contains(const T& val) const {
assert(sorted);
return std::binary_search(all(dat), val, cmp);
}
std::vector<int> pressed(const std::vector<T>& vec) const {
assert(sorted);
std::vector<int> res(vec.size());
rep (i, vec.size()) res[i] = get(vec[i]);
return res;
}
void press(std::vector<T>& vec) const {
assert(sorted);
for (auto&& i : vec) i = get(i);
}
int size() const {
assert(sorted);
return dat.size();
}
};
#line 2 "graph/Graph.hpp"
#line 4 "graph/Graph.hpp"
template<class T = int> struct edge {
int from, to;
T cost;
int idx;
edge() : from(-1), to(-1) {}
edge(int f, int t, const T& c = 1, int i = -1)
: from(f), to(t), cost(c), idx(i) {}
edge(int f, int t, T&& c, int i = -1)
: from(f), to(t), cost(std::move(c)), idx(i) {}
operator int() const { return to; }
friend bool operator<(const edge<T>& lhs, const edge<T>& rhs) {
return lhs.cost < rhs.cost;
}
friend bool operator>(const edge<T>& lhs, const edge<T>& rhs) {
return lhs.cost > rhs.cost;
}
};
template<class T = int> using Edges = std::vector<edge<T>>;
template<class T = int> using GMatrix = std::vector<std::vector<T>>;
template<class T = int> class Graph : public std::vector<std::vector<edge<T>>> {
private:
using Base = std::vector<std::vector<edge<T>>>;
public:
int edge_id = 0;
using Base::Base;
int edge_size() const { return edge_id; }
int add_edge(int a, int b, const T& c, bool is_directed = false) {
assert(0 <= a && a < (int)this->size());
assert(0 <= b && b < (int)this->size());
(*this)[a].emplace_back(a, b, c, edge_id);
if (!is_directed) (*this)[b].emplace_back(b, a, c, edge_id);
return edge_id++;
}
int add_edge(int a, int b, bool is_directed = false) {
assert(0 <= a && a < (int)this->size());
assert(0 <= b && b < (int)this->size());
(*this)[a].emplace_back(a, b, 1, edge_id);
if (!is_directed) (*this)[b].emplace_back(b, a, 1, edge_id);
return edge_id++;
}
};
template<class T> GMatrix<T> ListToMatrix(const Graph<T>& G) {
const int N = G.size();
auto res = make_vec<T>(N, N, infinity<T>::value);
rep (i, N) res[i][i] = 0;
rep (i, N) {
for (const auto& e : G[i]) res[i][e.to] = e.cost;
}
return res;
}
template<class T> Edges<T> UndirectedListToEdges(const Graph<T>& G) {
const int V = G.size();
const int E = G.edge_size();
Edges<T> Ed(E);
rep (i, V) {
for (const auto& e : G[i]) Ed[e.idx] = e;
}
return Ed;
}
template<class T> Edges<T> DirectedListToEdges(const Graph<T>& G) {
const int V = G.size();
const int E = std::accumulate(
all(G), 0, [](int a, const std::vector<edge<T>>& v) -> int {
return a + v.size();
});
Edges<T> Ed(G.edge_size());
Ed.reserve(E);
rep (i, V) {
for (const auto& e : G[i]) {
if (Ed[e.idx] == -1) Ed[e.idx] = e;
else Ed.push_back(e);
}
}
return Ed;
}
template<class T> Graph<T> ReverseGraph(const Graph<T>& G) {
const int V = G.size();
Graph<T> res(V);
rep (i, V) {
for (const auto& e : G[i]) {
res[e.to].emplace_back(e.to, e.from, e.cost, e.idx);
}
}
res.edge_id = G.edge_size();
return res;
}
struct unweighted_edge {
template<class... Args> unweighted_edge(const Args&...) {}
operator int() { return 1; }
};
using UnweightedGraph = Graph<unweighted_edge>;
/**
* @brief Graph-template
* @docs docs/graph/Graph.md
*/
#line 2 "graph/tree/TreeHash.hpp"
#line 2 "random/Random.hpp"
#line 4 "random/Random.hpp"
template<class Engine> class Random {
private:
Engine rnd;
public:
using result_type = typename Engine::result_type;
Random() : Random(std::random_device{}()) {}
Random(result_type seed) : rnd(seed) {}
result_type operator()() { return rnd(); }
result_type min() const { return rnd.min(); }
result_type max() const { return rnd.max(); }
template<class IntType = ll> IntType uniform(IntType l, IntType r) {
static_assert(std::is_integral<IntType>::value,
"template argument must be an integral type");
assert(l <= r);
return std::uniform_int_distribution<IntType>{l, r}(rnd);
}
template<class RealType = double>
RealType uniform_real(RealType l, RealType r) {
static_assert(std::is_floating_point<RealType>::value,
"template argument must be an floating point type");
assert(l <= r);
return std::uniform_real_distribution<RealType>{l, r}(rnd);
}
bool uniform_bool() { return uniform<int>(0, 1) == 1; }
template<class T = ll> std::pair<T, T> uniform_pair(T l, T r) {
assert(l < r);
T a, b;
do {
a = uniform<T>(l, r);
b = uniform<T>(l, r);
} while (a == b);
if (a > b) swap(a, b);
return {a, b};
}
template<class T = ll> std::vector<T> choice(int n, T l, T r) {
assert(l <= r);
assert(T(n) <= (r - l + 1));
std::set<T> res;
while ((int)res.size() < n) res.insert(uniform<T>(l, r));
return {res.begin(), res.end()};
}
template<class Iter> void shuffle(const Iter& first, const Iter& last) {
std::shuffle(first, last, rnd);
}
template<class T> std::vector<T> permutation(T n) {
std::vector<T> res(n);
rep (i, n) res[i] = i;
shuffle(all(res));
return res;
}
template<class T = ll>
std::vector<T> choice_shuffle(int n, T l, T r, bool sorted = true) {
assert(l <= r);
assert(T(n) <= (r - l + 1));
std::vector<T> res(r - l + 1);
rep (i, l, r + 1) res[i - l] = i;
shuffle(all(res));
res.erase(res.begin() + n, res.end());
if (sorted) sort(all(res));
return res;
}
};
using Random32 = Random<std::mt19937>;
Random32 rand32;
using Random64 = Random<std::mt19937_64>;
Random64 rand64;
/**
* @brief Random
* @docs docs/random/Random.md
*/
#line 2 "string/RollingHash.hpp"
#line 2 "data-struct/segment/BinaryIndexedTree.hpp"
#line 2 "other/monoid.hpp"
#line 4 "other/monoid.hpp"
namespace Monoid {
template<class M, class = void>
class has_value_type : public std::false_type {};
template<class M>
class has_value_type<M, decltype((void)std::declval<typename M::value_type>())>
: public std::true_type {};
template<class M, class = void> class has_op : public std::false_type {};
template<class M>
class has_op<M, decltype((void)M::op)> : public std::true_type {};
template<class M, class = void> class has_id : public std::false_type {};
template<class M>
class has_id<M, decltype((void)M::id)> : public std::true_type {};
template<class M, class = void> class has_inv : public std::false_type {};
template<class M>
class has_inv<M, decltype((void)M::inv)> : public std::true_type {};
template<class M, class = void> class has_get_inv : public std::false_type {};
template<class M>
class has_get_inv<M, decltype((void)M::get_inv)> : public std::true_type {};
template<class M, class = void> class has_init : public std::false_type {};
template<class M>
class has_init<M, decltype((void)M::init(0, 0))> : public std::true_type {};
template<class A, class = void> class has_mul_op : public std::false_type {};
template<class A>
class has_mul_op<A, decltype((void)A::mul_op)> : public std::true_type {};
template<class T, class = void> class is_semigroup : public std::false_type {};
template<class T>
class is_semigroup<T, decltype(std::declval<typename T::value_type>(),
(void)T::op)> : public std::true_type {};
template<class T, class = void> class is_monoid : public std::false_type {};
template<class T>
class is_monoid<T, decltype(std::declval<typename T::value_type>(), (void)T::op,
(void)T::id)> : public std::true_type {};
template<class T, class = void> class is_group : public std::false_type {};
template<class T>
class is_group<T, decltype(std::declval<typename T::value_type>(), (void)T::op,
(void)T::id, (void)T::get_inv)>
: public std::true_type {};
template<class T, class = void> class is_action : public std::false_type {};
template<class T>
class is_action<T, typename std::enable_if<is_monoid<typename T::M>::value &&
is_semigroup<typename T::E>::value &&
(has_op<T>::value ||
has_mul_op<T>::value)>::type>
: public std::true_type {};
template<class T, class = void>
class is_distributable_action : public std::false_type {};
template<class T>
class is_distributable_action<
T,
typename std::enable_if<is_action<T>::value && !has_mul_op<T>::value>::type>
: public std::true_type {};
template<class T> struct Sum {
using value_type = T;
static constexpr T op(const T& a, const T& b) { return a + b; }
static constexpr T id() { return T{0}; }
static constexpr T inv(const T& a, const T& b) { return a - b; }
static constexpr T get_inv(const T& a) { return -a; }
};
template<class T, int i = -1> struct Min {
using value_type = T;
static T max_value;
static T op(const T& a, const T& b) { return a < b ? a : b; }
static T id() { return max_value; }
};
template<class T> struct Min<T, -1> {
using value_type = T;
static constexpr T op(const T& a, const T& b) { return a < b ? a : b; }
static constexpr T id() { return infinity<T>::value; }
};
template<class T> struct Min<T, -2> {
using value_type = T;
static constexpr T op(const T& a, const T& b) { return a < b ? a : b; }
static constexpr T id() { return infinity<T>::max; }
};
template<class T, int id> T Min<T, id>::max_value;
template<class T, int i = -1> struct Max {
using value_type = T;
static T min_value;
static T op(const T& a, const T& b) { return a > b ? a : b; }
static T id() { return min_value; }
};
template<class T> struct Max<T, -1> {
using value_type = T;
static constexpr T op(const T& a, const T& b) { return a > b ? a : b; }
static constexpr T id() { return infinity<T>::mvalue; }
};
template<class T> struct Max<T, -2> {
using value_type = T;
static constexpr T op(const T& a, const T& b) { return a > b ? a : b; }
static constexpr T id() { return infinity<T>::min; }
};
template<class T> struct Assign {
using value_type = T;
static constexpr T op(const T&, const T& b) { return b; }
};
template<class T, int id = -1> struct AssignMin {
using M = Min<T, id>;
using E = Assign<T>;
static constexpr T op(const T& a, const T&) { return a; }
};
template<class T, int id = -1> struct AssignMax {
using M = Max<T, id>;
using E = Assign<T>;
static constexpr T op(const T& a, const T&) { return a; }
};
template<class T> struct AssignSum {
using M = Sum<T>;
using E = Assign<T>;
static constexpr T mul_op(const T& a, int b, const T&) { return a * b; }
};
template<class T, int id = -1> struct AddMin {
using M = Min<T, id>;
using E = Sum<T>;
static constexpr T op(const T& a, const T& b) { return b + a; }
};
template<class T, int id = -1> struct AddMax {
using M = Max<T, id>;
using E = Sum<T>;
static constexpr T op(const T& a, const T& b) { return b + a; }
};
template<class T> struct AddSum {
using M = Sum<T>;
using E = Sum<T>;
static constexpr T mul_op(const T& a, int b, const T& c) {
return c + a * b;
}
};
template<class T, int id = -1> struct ChminMin {
using M = Min<T, id>;
using E = Min<T>;
static constexpr T op(const T& a, const T& b) { return std::min(b, a); }
};
template<class T, int id = -1> struct ChminMax {
using M = Max<T, id>;
using E = Min<T>;
static constexpr T op(const T& a, const T& b) { return std::min(b, a); }
};
template<class T, int id = -1> struct ChmaxMin {
using M = Min<T, id>;
using E = Max<T>;
static constexpr T op(const T& a, const T& b) { return std::max(b, a); }
};
template<class T, int id = -1> struct ChmaxMax {
using M = Max<T, id>;
using E = Max<T>;
static constexpr T op(const T& a, const T& b) { return std::max(b, a); }
};
template<class M> struct ReverseMonoid {
using value_type = typename M::value_type;
static value_type op(const value_type& a, const value_type& b) {
return M::op(b, a);
}
static value_type id() {
static_assert(has_id<M>::value, "id is not defined");
return M::id();
}
static value_type inv(const value_type& a, const value_type& b) {
static_assert(has_inv<M>::value, "inv is not defined");
return M::inv(b, a);
}
static value_type get_inv(const value_type& a) {
static_assert(has_get_inv<M>::value, "get_inv is not defined");
return M::get_inv(a);
}
};
template<class E_> struct MakeAction {
using M = E_;
using E = E_;
using T = typename E_::value_type;
static T op(const T& a, const T& b) { return E_::op(b, a); }
};
} // namespace Monoid
#line 5 "data-struct/segment/BinaryIndexedTree.hpp"
template<class M, bool = Monoid::is_monoid<M>::value> class BinaryIndexedTree {
private:
using T = typename M::value_type;
int n;
std::vector<T> data;
public:
BinaryIndexedTree() : BinaryIndexedTree(0) {}
BinaryIndexedTree(int n_) { init(n_); }
void init(int n_) {
n = n_;
data.assign(n + 1, M::id());
}
void apply(int k, T x) {
assert(0 <= k && k < n);
++k;
while (k <= n) {
data[k] = M::op(data[k], x);
k += k & -k;
}
}
T prod(int k) const {
assert(0 <= k && k <= n);
T res = M::id();
while (k) {
res = M::op(res, data[k]);
k -= k & -k;
}
return res;
}
template<bool AlwaysTrue = true,
typename std::enable_if<Monoid::has_inv<M>::value &&
AlwaysTrue>::type* = nullptr>
T prod(int l, int r) const {
assert(l <= r);
return M::inv(prod(r), prod(l));
}
T get(int k) const { return prod(k, k + 1); }
void set(int k, T x) { apply(k, M::inv(x, get(k))); }
};
template<class T>
class BinaryIndexedTree<T, false> : public BinaryIndexedTree<Monoid::Sum<T>> {
private:
using Base = BinaryIndexedTree<Monoid::Sum<T>>;
public:
using Base::Base;
void add(int k, T x) { this->apply(k, x); }
T sum(int k) const { return this->prod(k); }
T sum(int l, int r) const { return this->prod(l, r); }
};
/**
* @brief BinaryIndexedTree(FenwickTree, BIT)
* @docs docs/data-struct/segment/BinaryIndexedTree.md
*/
#line 6 "string/RollingHash.hpp"
class modint61 {
private:
ull val;
static constexpr ull MOD = (1ull << 61) - 1;
static constexpr ull MASK30 = (1ull << 30) - 1;
static constexpr ull MASK31 = (1ull << 31) - 1;
static constexpr ull MASK61 = MOD;
static ull calc_mod(ull a) {
ull res = (a & MASK61) + (a >> 61);
if (res >= MOD) res -= MOD;
return res;
}
static ull calc_multi(ull a, ull b) {
ull au = a >> 31, ad = a & MASK31;
ull bu = b >> 31, bd = b & MASK31;
ull mid = au * bd + ad * bu;
return calc_mod(((au * bu) << 1) + ((mid & MASK30) << 31) +
(mid >> 30) + ad * bd);
}
static ull calc_add(ull a, ull b) {
ull res = a + b;
if (res >= MOD) res -= MOD;
return res;
}
public:
constexpr modint61() : val(0) {}
template<class U, typename std::enable_if<is_signed_int<U>::value &&
std::numeric_limits<U>::digits <=
64>::type* = nullptr>
constexpr modint61(U v) {
if (v >= 0) val = calc_mod(v);
else {
v %= static_cast<ll>(MOD);
if (v < 0) v += static_cast<ll>(MOD);
val = v;
}
}
template<class U, typename std::enable_if<
is_signed_int<U>::value &&
64 < std::numeric_limits<U>::digits>::type* = nullptr>
constexpr modint61(U v) {
v %= static_cast<ll>(MOD);
if (v < 0) v += static_cast<ll>(MOD);
val = v;
}
template<class U, typename std::enable_if<is_unsigned_int<U>::value &&
std::numeric_limits<U>::digits <=
64>::type* = nullptr>
constexpr modint61(U v) : val(calc_mod(v)) {}
template<class U, typename std::enable_if<
is_unsigned_int<U>::value &&
64 < std::numeric_limits<U>::digits>::type* = nullptr>
constexpr modint61(U v) : val(v % MOD) {}
ull get() const { return val; }
static constexpr ull get_mod() { return MOD; }
static modint61 raw(ull x) {
modint61 res;
res.val = x;
return res;
}
modint61& operator++() {
++val;
if (val == MOD) val = 0;
return *this;
}
modint61 operator++(int) {
modint61 res = *this;
++*this;
return res;
}
modint61& operator--() {
if (val == 0) val = MOD;
--val;
return *this;
}
modint61 operator--(int) {
modint61 res = *this;
--*this;
return res;
}
modint61& operator+=(const modint61& other) {
val += other.val;
if (val >= MOD) val -= MOD;
return *this;
}
modint61& operator-=(const modint61& other) {
if (val < other.val) val += MOD;
val -= other.val;
return *this;
}
modint61& operator*=(const modint61& other) {
val = calc_multi(val, other.val);
return *this;
}
modint61 pow(ll n) const {
modint61 res = raw(1), x = *this;
while (n > 0) {
if (n & 1) res *= x;
x *= x;
n >>= 1;
}
return res;
}
modint61 inv() const { return pow(MOD - 2); }
modint61& operator/=(const modint61& other) {
*this *= other.inv();
return *this;
}
friend modint61 operator+(const modint61& lhs, const modint61& rhs) {
return modint61(lhs) += rhs;
}
friend modint61 operator-(const modint61& lhs, const modint61& rhs) {
return modint61(lhs) -= rhs;
}
friend modint61 operator*(const modint61& lhs, const modint61& rhs) {
return modint61(lhs) *= rhs;
}
friend modint61 operator/(const modint61& lhs, const modint61& rhs) {
return modint61(lhs) /= rhs;
}
modint61 operator+() const { return *this; }
modint61 operator-() const { return modint61() - *this; }
friend bool operator==(const modint61& lhs, const modint61& rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const modint61& lhs, const modint61& rhs) {
return lhs.val != rhs.val;
}
template<class Pr> void debug(Pr& a) const { a.print(val); }
};
class RollingHash {
private:
static constexpr ull MASK31 = (1ull << 31) - 1;
using mint = modint61;
std::vector<mint> pows, rpows;
public:
void init(int n) {
const int sz = pows.size();
if (sz <= n) {
pows.resize(n + 1);
rpows.resize(n + 1);
rep (i, sz, n + 1) pows[i] = pows[i - 1] * BASE;
rep (i, sz, n + 1) rpows[i] = rpows[i - 1] * RBASE;
}
}
mint BASE, RBASE;
void set_base() {
BASE = mint::raw((1ull << 31) + (rand32() & MASK31));
RBASE = BASE.inv();
}
mint join(mint a, mint b, ll blen) const { return a * pows[blen] + b; }
class Hash {
private:
int n;
mint BASE;
std::vector<mint> hash, pows;
public:
Hash() = default;
template<class Cont>
Hash(mint b, const std::vector<mint>& p, const Cont& str)
: n(str.size()), BASE(b), pows(p.begin(), p.begin() + n + 1) {
hash.assign(n + 1, mint{});
rep (i, n) hash[i + 1] = hash[i] * BASE + str[i];
}
mint prod(int l, int r) const {
assert(0 <= l && l <= r && r <= n);
return hash[r] - hash[l] * pows[r - l];
}
mint all_prod() const { return hash[n]; }
};
class RangeHashQuery {
private:
int n;
mint BASE;
std::vector<mint> pows, rpows;
BinaryIndexedTree<mint> bit;
public:
RangeHashQuery() = default;
template<class Cont>
RangeHashQuery(mint b, const std::vector<mint>& p,
const std::vector<mint>& rp, const Cont& str)
: n(str.size()), BASE(b), pows(p.begin(), p.begin() + n + 1),
rpows(rp.begin(), rp.begin() + n + 1), bit(n) {
rep (i, n) bit.add(i, str[i] * pows[i]);
}
mint prod(int l, int r) const { return bit.sum(l, r) * rpows[l]; }
mint all_prod() const { return bit.sum(0, n); }
template<class T> void set(int k, const T& x) {
bit.set(k, x * pows[k]);
}
};
RollingHash() {
set_base();
pows.assign(1, mint::raw(1));
rpows.assign(1, mint::raw(1));
}
template<class Cont> Hash get_hash(const Cont& str) {
init(str.size() + 1);
return Hash(BASE, pows, str);
}
template<class Cont> RangeHashQuery get_range_hash(const Cont& str) {
init(str.size() + 1);
return RangeHashQuery(BASE, pows, rpows, str);
}
};
/**
* @brief RollingHash(ロリハ)
* @docs docs/string/RollingHash.md
*/
#line 2 "graph/tree/ReRooting.hpp"
#line 5 "graph/tree/ReRooting.hpp"
template<class M, class T, class F> class ReRooting {
private:
using U = typename M::value_type;
const F& f;
int n;
const Graph<T>& G;
std::vector<U> init_data;
std::vector<std::vector<U>> dp;
std::vector<U> res;
std::vector<int> par;
void dfs1(int v, int p) {
rep (i, G[v].size()) {
const auto& e = G[v][i];
if (e.to == p) par[v] = i;
else dfs1(e.to, v);
}
rep (i, G[v].size()) {
const auto& e = G[v][i];
if (e.to == p) continue;
dp[v][par[v]] =
M::op(dp[v][par[v]],
f(dp[e.to][par[e.to]], edge<T>{e.to, v, e.cost, e.idx}));
}
if (p != -1 && G[v].size() == 1) {
dp[v][par[v]] = init_data[v];
}
}
void dfs2(int v, int p, int v_id) {
std::vector<U> memo(G[v].size());
rep (i, G[v].size()) {
const auto& e = G[v][i];
memo[i] = f(dp[e.to][e.to == p ? v_id : par[e.to]],
edge<T>{e.to, v, e.cost, e.idx});
}
dp[v][G[v].size() - 1] = M::id();
rrep (i, (int)G[v].size() - 1) {
dp[v][i] = M::op(memo[i + 1], dp[v][i + 1]);
}
U sml = M::id();
rep (i, G[v].size()) {
dp[v][i] = M::op(sml, dp[v][i]);
sml = M::op(sml, std::move(memo[i]));
}
dp[v].back() = std::move(sml);
if (G[v].size() == 1) {
dp[v][p == -1 ? 0 : par[v]] = std::move(init_data[v]);
}
rep (i, G[v].size()) {
const auto& e = G[v][i];
if (e.to != p) dfs2(e.to, v, i);
}
}
void init() {
n = G.size();
if (n == 1) {
res = std::move(init_data);
dp.assign(1, std::vector<U>{});
return;
}
dp.resize(n);
rep (i, n) dp[i].assign(G[i].size() + 1, M::id());
par.resize(n);
par[0] = G[0].size();
dfs1(0, -1);
dfs2(0, -1, -1);
res.resize(n);
rep (i, n) {
res[i] = std::move(dp[i].back());
dp[i].pop_back();
}
}
public:
ReRooting(const Graph<T>& G, const F& f)
: ReRooting(G, f, std::vector<U>(G.size(), M::id())) {}
ReRooting(const Graph<T>& G, const F& f, const std::vector<U>& ind)
: f(f), G(G), init_data(ind) {
init();
}
ReRooting(const Graph<T>& G, const F& f, std::vector<U>&& ind)
: f(f), G(G), init_data(std::move(ind)) {
init();
}
const std::vector<U>& get_res() const& { return res; }
std::vector<U> get_res() && { return std::move(res); }
const U& operator[](int v) const& { return res[v]; }
U operator[](int v) && { return std::move(res[v]); }
const std::vector<std::vector<U>>& get_dp() const& { return dp; }
std::vector<std::vector<U>> get_dp() && { return std::move(dp); }
const U& get_dp(int v, int p_idx) const& { return dp[v][p_idx]; }
U get_dp(int v, int p_idx) && { return std::move(dp[v][p_idx]); }
};
template<class M, class T, class F>
ReRooting<M, T, F> make_rerooting(const Graph<T>& G, const F& f) {
return ReRooting<M, T, F>(G, f);
}
/**
* @brief ReRooting(全方位木DP)
* @docs docs/graph/tree/ReRooting.md
*/
#line 8 "graph/tree/TreeHash.hpp"
class TreeHash {
private:
static constexpr ull MASK31 = (1ull << 31) - 1;
using mint = modint61;
std::vector<mint> base;
void init(int n) {
int m = base.size();
if (m >= n) return;
base.resize(n);
rep (i, m, n) base[i] = mint::raw((1ull << 31) + (rand32() & MASK31));
}
template<class T>
int dfs(const Graph<T>& G, std::vector<mint>& ans, int v, int p) {
mint res = 1;
int dep = 0;
for (const auto& e : G[v]) {
if (e.to == p) continue;
int d = dfs(G, ans, e.to, v);
chmax(dep, d + 1);
if ((int)base.size() == d) {
base.push_back(mint::raw((1ull << 31) + (rand32() & MASK31)));
}
res *= ans[e.to] + base[d];
}
ans[v] = res;
return dep;
}
struct M {
using value_type = std::pair<mint, int>;
static value_type id() { return {1, 0}; }
static value_type op(const value_type& a, const value_type& b) {
return {a.first * b.first, std::max(a.second, b.second)};
}
};
template<class T>
std::pair<mint, int> f(const std::pair<mint, int>& a, const edge<T>& b) {
if ((int)base.size() == a.second) {
base.push_back(mint::raw((1ull << 31) + (rand32() & MASK31)));
}
return {a.first + base[a.second], a.second + 1};
}
public:
template<class T>
std::vector<mint> get_hash(const Graph<T>& G, int root = 0) {
int n = G.size();
std::vector<mint> ans(n);
dfs(G, ans, root, -1);
return ans;
}
template<class T>
std::pair<std::vector<std::vector<mint>>, std::vector<mint>>
get_hash_rerooting(const Graph<T>& G) {
auto f = [&](const std::pair<mint, int>& a,
const edge<T>&) -> std::pair<mint, int> {
if ((int)base.size() == a.second) {
base.push_back(mint::raw((1ull << 31) + (rand32() & MASK31)));
}
return {a.first + base[a.second], a.second + 1};
};
auto rr = ReRooting<M, T, decltype(f)>(G, f);
std::vector<std::vector<mint>> dp(G.size());
std::vector<mint> res(G.size());
rep (i, G.size()) {
dp[i].resize(G[i].size());
rep (j, G[i].size()) dp[i][j] = rr.get_dp(i, j).first;
res[i] = rr[i].first;
}
return {dp, res};
}
};
/**
* @brief TreeHash
* @docs docs/graph/tree/TreeHash.md
*/
#line 5 "test/yosupo/tree/rooted_tree_isomorphism_classification.test.cpp"
using namespace std;
using mint = modint61;
int main() {
int N; scan >> N;
Graph<int> G(N);
rep (i, 1, N) {
int p; scan >> p;
G.add_edge(p, i);
}
TreeHash th;
auto h = th.get_hash(G);
map<ull, vector<int>> mp;
rep (i, N) mp[h[i].get()].push_back(i);
vector<int> ans(N);
int cnt = 0;
for (const auto& [_, v] : mp) {
for (int i : v) ans[i] = cnt;
++cnt;
}
prints(cnt);
prints(ans);
}