library_for_cpp

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:heavy_check_mark: verify/yosupo_library_checker/tree/Rooted_Tree_Isomorphism_Classification.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"

#include"../../../template/template.hpp"
#include"../../../Tree/Subtree_Isomorphism_Hash.hpp"

int main() {
    int N; cin >> N;
    Tree T(N);
    T.set_root(0);
    for (int i = 1; i < N; ++i) {
        int p; scanf("%d", &p);
        T.set_parent(i, p);
    }

    T.seal();
    auto h = Subtree_Isomorphism_Hash(T);

    cout << max(h) + 1 << endl;
    cout << h << endl;
}
#line 1 "verify/yosupo_library_checker/tree/Rooted_Tree_Isomorphism_Classification.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/rooted_tree_isomorphism_classification"

#line 2 "template/template.hpp"

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <concepts>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 2 "template/utility.hpp"

using ll = long long;

// a ← max(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmax(T &a, const U b){
    return (a < b ? a = b, 1: 0);
}

// a ← min(a, b) を実行する. a が更新されたら, 返り値が true.
template<typename T, typename U>
inline bool chmin(T &a, const U b){
    return (a > b ? a = b, 1: 0);
}

// a の最大値を取得する.
template<typename T>
inline T max(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *max_element(a.begin(), a.end());
}

// vector<T> a の最小値を取得する.
template<typename T>
inline T min(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return *min_element(a.begin(), a.end());
}

// vector<T> a の最大値のインデックスを取得する.
template<typename T>
inline size_t argmax(const vector<T> &a){
    if (a.empty()) throw std::invalid_argument("vector is empty.");

    return distance(a.begin(), max_element(a.begin(), a.end()));
}

// vector<T> a の最小値のインデックスを取得する.
template<typename T>
inline size_t argmin(const vector<T> &a){
    if (a.empty()) throw invalid_argument("vector is empty.");

    return distance(a.begin(), min_element(a.begin(), a.end()));
}
#line 61 "template/template.hpp"

// math
#line 2 "template/math.hpp"

// 演算子
template<typename T>
T add(const T &x, const T &y) { return x + y; }

template<typename T>
T sub(const T &x, const T &y) { return x - y; }

template<typename T>
T mul(const T &x, const T &y) { return x * y; }

template<typename T>
T neg(const T &x) { return -x; }

template<integral T>
T bitwise_and(const T &x, const T &y) { return x & y; }

template<integral T>
T bitwise_or(const T &x, const T &y) { return x | y; }

template<integral T>
T bitwise_xor(const T &x, const T &y) { return x ^ y; }

// 除算に関する関数

// floor(x / y) を求める.
template<integral T, integral U>
auto div_floor(T x, U y){
    return x / y - ((x % y != 0) && ((x < 0) != (y < 0)));
}

// ceil(x / y) を求める.
template<integral T, integral U>
auto div_ceil(T x, U y){
    return x / y + ((x % y != 0) && ((x < 0) == (y < 0)));
}

// x を y で割った余りを求める.
template<integral T, integral U>
auto safe_mod(T x, U y){
    auto q = div_floor(x, y);
    return x - q * y ;
}

// x を y で割った商と余りを求める.
template<integral T, integral U>
auto divmod(T x, U y){
    auto q = div_floor(x, y);
    return make_pair(q, x - q * y);
}

// 四捨五入を求める.
template<integral T, integral U>
auto round(T x, U y){
    auto [q, r] = divmod(x, y);
    if (y < 0) return (r <= div_floor(y, 2)) ? q + 1 : q;
    return (r >= div_ceil(y, 2)) ? q + 1 : q;
}

// 奇数かどうか判定する.
template<integral T>
bool is_odd(const T &x) { return x % 2 != 0; }

// 偶数かどうか判定する.
template<integral T>
bool is_even(const T &x) { return x % 2 == 0; }

// m の倍数かどうか判定する.
template<integral T, integral U>
bool is_multiple(const T &x, const U &m) { return x % m == 0; }

// 正かどうか判定する.
template<typename T>
bool is_positive(const T &x) { return x > 0; }

// 負かどうか判定する.
template<typename T>
bool is_negative(const T &x) { return x < 0; }

// ゼロかどうか判定する.
template<typename T>
bool is_zero(const T &x) { return x == 0; }

// 非負かどうか判定する.
template<typename T>
bool is_non_negative(const T &x) { return x >= 0; }

// 非正かどうか判定する.
template<typename T>
bool is_non_positive(const T &x) { return x <= 0; }

// 指数に関する関数

// x の y 乗を求める.
ll intpow(ll x, ll y){
    ll a = 1;
    while (y){
        if (y & 1) { a *= x; }
        x *= x;
        y >>= 1;
    }
    return a;
}

ll pow(ll x, ll y) { return intpow(x, y); }

// x の y 乗を z で割った余りを求める.
template<typename T, integral U>
T modpow(T x, U y, T z) {
    T a = 1;
    while (y) {
        if (y & 1) { (a *= x) %= z; }

        (x *= x) %= z;
        y >>= 1;
    }

    return a;
}

template<typename T>
T sum(const vector<T> &X) {
    T y = T(0);
    for (auto &&x: X) { y += x; }
    return y;
}

template<typename T>
T gcd(const T x, const T y) {
    return y == 0 ? x : gcd(y, x % y);
}

// a x + b y = gcd(a, b) を満たす整数の組 (a, b) に対して, (x, y, gcd(a, b)) を求める.
template<integral T>
tuple<T, T, T> Extended_Euclid(T a, T b) {
    T s = 1, t = 0, u = 0, v = 1;
    while (b) {
        auto [q, r] = divmod(a, b);
        a = b;
        b = r;
        tie(s, t) = make_pair(t, s - q * t);
        tie(u, v) = make_pair(v, u - q * v);
    }

    return make_tuple(s, u, a);
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll isqrt(const ll &N) { 
    if (N <= 0) { return 0; }

    ll x = sqrtl(N);
    while ((x + 1) * (x + 1) <= N) { x++; }
    while (x * x > N) { x--; }

    return x;
}

// floor(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll floor_sqrt(const ll &N) { return isqrt(N); }

// ceil(sqrt(N)) を求める (N < 0 のときは, 0 とする).
ll ceil_sqrt(const ll &N) {
    ll x = isqrt(N);
    return x * x == N ? x : x + 1;
}
#line 64 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
// 入出力
template<class... T>
void input(T&... a){ (cin >> ... >> a); }

void print(){ cout << "\n"; }

template<class T, class... Ts>
void print(const T& a, const Ts&... b){
    cout << a;
    (cout << ... << (cout << " ", b));
    cout << "\n";
}

template<typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &P){
    is >> P.first >> P.second;
    return is;
}

template<typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &P){
    os << P.first << " " << P.second;
    return os;
}

template<typename T>
vector<T> vector_input(int N, int index){
    vector<T> X(N+index);
    for (int i=index; i<index+N; i++) cin >> X[i];
    return X;
}

template<typename T>
istream &operator>>(istream &is, vector<T> &X){
    for (auto &x: X) { is >> x; }
    return is;
}

template<typename T>
ostream &operator<<(ostream &os, const vector<T> &X){
    int s = (int)X.size();
    for (int i = 0; i < s; i++) { os << (i ? " " : "") << X[i]; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &S){
    int i = 0;
    for (T a: S) {os << (i ? " ": "") << a; i++;}
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const set<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
ostream &operator<<(ostream &os, const multiset<T> &S){
    int i = 0;
    for (T a: S) { os << (i ? " ": "") << a; i++; }
    return os;
}

template<typename T>
std::vector<T> input_vector(size_t n, size_t offset = 0) {
    std::vector<T> res;
    // 最初に必要な全容量を確保（再確保を防ぐ）
    res.reserve(n + offset);
    // offset 分をデフォルト値で埋める（特別 indexed 用）
    res.assign(offset, T());
    
    for (size_t i = 0; i < n; ++i) {
        T el;
        if (!(std::cin >> el)) break;
        res.push_back(std::move(el));
    }
    return res;
}
#line 67 "template/template.hpp"

// macro
#line 2 "template/macro.hpp"

// マクロの定義
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define unless(cond) if (!(cond))
#define until(cond) while (!(cond))
#define loop while (true)

// オーバーロードマクロ
#define overload2(_1, _2, name, ...) name
#define overload3(_1, _2, _3, name, ...) name
#define overload4(_1, _2, _3, _4, name, ...) name
#define overload5(_1, _2, _3, _4, _5, name, ...) name

// 繰り返し系
#define rep1(n) for (ll i = 0; i < n; i++)
#define rep2(i, n) for (ll i = 0; i < n; i++)
#define rep3(i, a, b) for (ll i = a; i < b; i++)
#define rep4(i, a, b, c) for (ll i = a; i < b; i += c)
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)

#define foreach1(x, a) for (auto &&x: a)
#define foreach2(x, y, a) for (auto &&[x, y]: a)
#define foreach3(x, y, z, a) for (auto &&[x, y, z]: a)
#define foreach4(x, y, z, w, a) for (auto &&[x, y, z, w]: a)
#define foreach(...) overload5(__VA_ARGS__, foreach4, foreach3, foreach2, foreach1)(__VA_ARGS__)
#line 70 "template/template.hpp"

// bitop
#line 2 "template/bitop.hpp"

// 非負整数 x の bit legnth を求める.
ll bit_length(ll x) {
    if (x == 0) { return 0; }
    return (sizeof(long) * CHAR_BIT) - __builtin_clzll(x);
}

// 非負整数 x の popcount を求める.
ll popcount(ll x) { return __builtin_popcountll(x); }

// 正の整数 x に対して, floor(log2(x)) を求める.
ll floor_log2(ll x) { return bit_length(x) - 1; }

// 正の整数 x に対して, ceil(log2(x)) を求める.
ll ceil_log2(ll x) { return bit_length(x - 1); }

// x の第 k ビットを取得する
int get_bit(ll x, int k) { return (x >> k) & 1; }

// x のビット列を取得する.
// k はビット列の長さとする.
vector<int> get_bits(ll x, int k) {
    vector<int> bits(k);
    rep(i, k) {
        bits[i] = x & 1;
        x >>= 1;
    }

    return bits;
}

// x のビット列を取得する.
vector<int> get_bits(ll x) { return get_bits(x, bit_length(x)); }

// x に立っているなんかしらのビットの番号を出力する.
ll lowest_bit(const ll x) { return floor_log2(x & (-x)); }
#line 73 "template/template.hpp"

// exception
#line 2 "template/exception.hpp"

class NotExist: public exception {
    private:
    string message;

    public:
    NotExist() : message("求めようとしていたものは存在しません.") {}

    const char* what() const noexcept override {
        return message.c_str();
    }
};
#line 2 "Tree/Subtree_Isomorphism_Hash.hpp"

#line 2 "Tree/Tree.hpp"

#line 4 "Tree/Tree.hpp"

class Tree {
    private:
    int N, _offset, root;
    vector<int> parent;
    vector<vector<int>> children;

    bool locked;

    public:
    Tree(int N, int _offset = 0): N(N), _offset(_offset) {
        parent.assign(N + _offset, -1);
        locked = false;
    }

    bool is_locked() const { return locked; }

    public:
    inline void set_root(const int &x) {
        assert (!is_locked());
        root = x;
    }

    inline int vector_size() const { return order() + offset(); }

    inline int get_root() const { return root; }
    inline int get_parent(const int &x) const { return parent[x]; }
    inline vector<int> get_children(const int &x) const { return children[x]; }

    public:
    // 頂点 x の親を頂点 y に設定する.
    inline void set_parent(const int &x, const int &y) {
        assert (!is_locked());
        parent[x] = y;
    }

    // 頂点 x の子の一つに頂点 y を設定する.
    inline void set_child(const int &x, const int &y) { set_parent(y, x); }

    // 木を確定させる
    void seal() {
        assert(!is_locked());

        parent[root] = -1;
        children.assign(N + offset(), vector<int>());
        for (int v = offset(); v < N + offset(); v++) {
            unless(is_root(v)) { children[parent[v]].emplace_back(v); }
        }

        locked = true;
        bfs();
    }

    private:
    vector<int> depth;
    vector<vector<int>> tower;
    vector<int> _top_down, _bottom_up;
    void bfs() {
        assert(is_locked());

        tower.assign(N, {});
        depth.assign(N + offset(), -1);

        deque<int> Q{ root };
        tower[0] = { root };
        depth[root] = 0;

        while (!Q.empty()){
            int x = Q.front(); Q.pop_front();

            for (int y: children[x]) {
                depth[y] = depth[x] + 1;
                tower[depth[y]].emplace_back(y);
                Q.push_back(y);
            }
        }

        _top_down.clear();
        _top_down.reserve(N);
        for (const auto &layer : tower) {
            for (int v: layer) _top_down.emplace_back(v);
        }

        _bottom_up.clear();
        _bottom_up.reserve(N);
        for (auto it = tower.rbegin(); it != tower.rend(); ++it) {
            for (int v: *it) _bottom_up.emplace_back(v);
        }
    }

    public:
    const vector<int>& top_down() const { return _top_down; }

    public:
    const vector<int>& bottom_up() const { return _bottom_up; }

    // 1 頂点に関する情報
    public:

    // x は根?
    bool is_root(const int &x) const { return x == root; }

    // x は葉?
    bool is_leaf(const int &x) const {
        assert(is_locked());
        return children[x].empty();
    }

    // x の次数
    int degree(const int &x) const {
        assert(is_locked());
        int d = children[x].size();
        if (is_root(x)) { d--; }
        return d;
    }

    // 頂点 x の深さを求める.
    inline int vertex_depth(const int &x) const { return depth[x]; }

    // 2 頂点に関する条件

    // x は y の親か?
    bool is_parent(const int &x, const int &y) const {
        assert(is_locked());
        return !is_root(y) && x == parent[y];
    }

    // x は y の個か?
    inline bool is_children(const int &x, const int &y) const { return is_parent(y, x); }

    // x と y は兄弟 (親が同じ) か?
    bool is_brother(const int &x, const int &y) const {
        assert(is_locked());
        return !is_root(x) && !is_root(y) && parent[x] == parent[y];
    }

    int lowest_common_ancestor_greedy(int x, int y) const {
        assert(is_locked());

        if (vertex_depth(x) > vertex_depth(y)) { swap(x, y); }

        while (vertex_depth(x) < vertex_depth(y)) {
            y = parent[y];
        }

        while (x != y) {
            x = get_parent(x);
            y = get_parent(y);
        }

        return x;
    }

    private:
    bool has_euler_tour_vertex = false, has_euler_tour_edge = false;

    public:
    vector<int> in_time, out_time;
    vector<int> euler_tour_vertex;
    vector<tuple<int, int, int>> euler_tour_edge;

    // Euler Tour に関する計算を行う.
    void calculate_euler_tour_vertex() {
        if(has_euler_tour_vertex) { return; }

        euler_tour_vertex.clear();
        in_time.assign(N + offset(), -1);
        out_time.assign(N + offset(), -1);

        auto dfs = [&](auto self, int x) -> void {
            in_time[x] = (int)euler_tour_vertex.size();
            euler_tour_vertex.emplace_back(x);

            for (int y: children[x]) {
                self(self, y);
            }

            out_time[x] = (int)euler_tour_vertex.size() - 1;
            unless(is_root(x)) { euler_tour_vertex.emplace_back(parent[x]); }
        };

        dfs(dfs, root);

        has_euler_tour_vertex = true;
    }

    void calculate_euler_tour_edge() {
        if(has_euler_tour_edge) { return; }

        calculate_euler_tour_vertex();
        euler_tour_edge.clear();

        for (int t = 0; t < 2 * (N - 1); t++) {
            int x = euler_tour_vertex[t], y = euler_tour_vertex[t + 1];
            int k = (x == parent[y]) ? 1 : -1;
            euler_tour_edge.emplace_back(make_tuple(x, y, k));
        }

        has_euler_tour_edge = true;
    }

    vector<int> path(int u, int v) const {
        int w = lowest_common_ancestor_greedy(u, v);

        vector<int> path_first{u}, path_second{v};

        while (u != w) {
            u = get_parent(u);
            path_first.emplace_back(u);
        }

        while (v != w) {
            v = get_parent(v);
            path_second.emplace_back(v);
        }

        path_second.pop_back();
        reverse(path_second.begin(), path_second.end());

        path_first.insert(path_first.end(), make_move_iterator(path_second.begin()), make_move_iterator(path_second.end()));

        return path_first;
    }

    inline int order() const { return N; }
    inline int offset() const { return _offset; }
};

Tree Construct_Tree(int N, vector<pair<int, int>> edges, int root, int offset = 0) {
    vector<vector<int>> adj(N + offset, vector<int>());
    for (auto &[u, v]: edges) {
        adj[u].emplace_back(v);
        adj[v].emplace_back(u);
    }

    Tree T(N, offset);
    T.set_root(root);

    vector<bool> seen(N + 1, false);
    seen[root] = true;
    vector<int> stack({root});

    until(stack.empty()) {
        int v = stack.back();
        stack.pop_back();

        for (int w: adj[v]) {
            if (seen[w]) { continue; }

            seen[w] = true;
            T.set_parent(w, v);
            stack.emplace_back(w);
        }
    }

    T.seal();
    return T;
}
#line 2 "Algebra/dynamic_modint.hpp"

#line 4 "Algebra/dynamic_modint.hpp"

template<int id>
class dynamic_modint {
    public:
    uint64_t x;
    static int _mod;

    static void set_mod(const int m) { _mod = m; } 
    static int mod() { return _mod; }

    public:
    static dynamic_modint raw(int v) {
        dynamic_modint a;
        a.x = v;
        return a;
    }

    // 初期化
    constexpr dynamic_modint(): x(0) {}
    constexpr dynamic_modint(int64_t a) {
        int64_t w = (int64_t)(a) % mod();
        if (w < 0) { w += mod(); }
        x = w;
    }

    // マイナス元
    dynamic_modint operator-() const { return dynamic_modint(-x); }

    // 加法
    dynamic_modint& operator+=(const dynamic_modint &b){
        if ((x += b.x) >= mod()) x -= mod();
        return *this;
    }

    friend dynamic_modint operator+(const dynamic_modint &x, const dynamic_modint &y) { return dynamic_modint(x) += y; }

    // 減法
    dynamic_modint& operator-=(const dynamic_modint &b){
        if ((x += mod() - b.x) >= mod()) x -= mod();
        return *this;
    }

    friend dynamic_modint operator-(const dynamic_modint &x, const dynamic_modint &y) { return dynamic_modint(x) -= y; }

    // 乗法
    dynamic_modint& operator*=(const dynamic_modint &b){
        (x *= b.x) %= mod();
        return *this;
    }

    friend dynamic_modint operator*(const dynamic_modint &x, const dynamic_modint &y) { return dynamic_modint(x) *= y; }
    friend dynamic_modint operator*(const int &x, const dynamic_modint &y) { return dynamic_modint(x) *= y; }
    friend dynamic_modint operator*(const ll &x, const dynamic_modint &y) { return dynamic_modint(x) *= y; }

    // 除法
    dynamic_modint& operator/=(const dynamic_modint &b){ return (*this) *= b.inverse(); }

    friend dynamic_modint operator/(const dynamic_modint &x, const dynamic_modint &y) { return dynamic_modint(x) /= y; }

    dynamic_modint inverse() const {
        int64_t s = 1, t = 0;
        int64_t a = x, b = mod();

        while (b > 0) {
            int64_t q = a / b;

            a -= q * b; swap(a, b);
            s -= q * t; swap(s, t);
        }

        assert (a == 1);

        return dynamic_modint(s);
    }

    // 比較
    friend bool operator==(const dynamic_modint &a, const dynamic_modint &b) { return (a.x == b.x); }
    friend bool operator==(const dynamic_modint &a, const int &b) { return a.x == safe_mod(b, mod()); }
    friend bool operator!=(const dynamic_modint &a, const dynamic_modint &b) { return (a.x != b.x); }

    // 入力
    friend istream &operator>>(istream &is, dynamic_modint &a) {
        int64_t x;
        is >> x;
        a.x = (x % mod() + mod()) % mod();
        return is;
    }

    // 出力
    friend ostream &operator<<(ostream &os, const dynamic_modint &a) { return os << a.x; }

    bool is_zero() const { return x == 0; }
    bool is_member(ll a) const { return x == (a % mod() + mod()) % mod(); }
};

template<int id>
int dynamic_modint<id>::_mod = 0;

template<int id>
dynamic_modint<id> pow(dynamic_modint<id> x, long long n) {
    if (n < 0) { return pow(x, -n).inverse(); }

    auto res = dynamic_modint<id>(1);
    for (; n; n >>= 1) {
        if (n & 1) { res *= x; }
        x *= x;
    }

    return res;
}

#line 5 "Tree/Subtree_Isomorphism_Hash.hpp"

vector<int> Subtree_Isomorphism_Hash(const Tree &T, const vector<ll>& primes = {1000000007, 1000000009}) {
    using mint = dynamic_modint<1>;

    const int node_count = T.order();
    const int vector_size = T.vector_size();
    const int offset = T.offset();

    vector<vector<int>> combined_ids(vector_size);
    for (int i = offset; i < vector_size; ++i) {
        combined_ids[i].reserve(primes.size());
    }

    // 乱数生成器は一度だけ初期化
    static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());

    auto compress_vals = [&](const auto& vals_to_compress) -> vector<int> {
        using T_val = typename std::decay<decltype(vals_to_compress[offset])>::type;
        vector<T_val> vals;

        vals.reserve(node_count);
        for (int i = offset; i < vector_size; ++i) vals.push_back(vals_to_compress[i]);

        sort(vals.begin(), vals.end());
        vals.erase(unique(vals.begin(), vals.end()), vals.end());

        vector<int> res(vector_size, -1);
        for (int i = offset; i < vector_size; ++i) {
            res[i] = lower_bound(vals.begin(), vals.end(), vals_to_compress[i]) - vals.begin();
        }

        return res;
    };

    auto generate_seeds = [&](int count, ll prime) {
        vector<mint> seeds(count + 1);
        for (int d = 0; d <= count; ++d) {
            seeds[d] = mint(static_cast<long long>(gen() % prime));
        }
        return seeds;
    };

    vector<int> height(vector_size, 0);
    for (int x : T.bottom_up()) {
        for (int y : T.get_children(x)) {
            if (height[x] < height[y] + 1) height[x] = height[y] + 1;
        }
    }

    auto calculate_ranks = [&](ll prime) {
        mint::set_mod(prime);
        vector<mint> hash(vector_size, mint(1));

        auto seeds = generate_seeds(node_count, prime);

        for (int x: T.bottom_up()) {
            mint a = seeds[height[x]];
            for (auto y : T.get_children(x)) {
                hash[x] = hash[x] * (a + hash[y]);
            }
        }

        vector<uint64_t> hash_raw(vector_size);
        for (int i = offset; i < vector_size; ++i) hash_raw[i] = hash[i].x;
        return compress_vals(hash_raw);
    };

    for (ll prime : primes) {
        auto ranks = calculate_ranks(prime);
        for (int i = offset; i < vector_size; i++) {
            combined_ids[i].push_back(ranks[i]);
        }
    }

    // すべてのプライムでの ID を統合して座標圧縮
    return compress_vals(combined_ids);
}
#line 5 "verify/yosupo_library_checker/tree/Rooted_Tree_Isomorphism_Classification.test.cpp"

int main() {
    int N; cin >> N;
    Tree T(N);
    T.set_root(0);
    for (int i = 1; i < N; ++i) {
        int p; scanf("%d", &p);
        T.set_parent(i, p);
    }

    T.seal();
    auto h = Subtree_Isomorphism_Hash(T);

    cout << max(h) + 1 << endl;
    cout << h << endl;
}
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