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:heavy_check_mark: verify/string/palindrome_lexicographical_order.test.cpp

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Code

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

#include "../../string/palindrome_lexicographical_order.hpp"

#include <algorithm>
#include <cassert>
#include <cstdint>
#include "../../utilities/fast_io.hpp"
#include <set>
#include <string>
#include <type_traits>
#include <utility>
#include <vector>

namespace {

template <class Sequence>
bool is_palindrome(const Sequence& sequence, int left, int right) {
    while (left < right) {
        right--;
        if (sequence[left] != sequence[right]) return false;
        left++;
    }
    return true;
}

template <class Sequence>
std::vector<Sequence> naive_palindromes(const Sequence& sequence) {
    std::set<Sequence> distinct;
    int n = int(sequence.size());
    for (int left = 0; left < n; left++) {
        for (int right = left + 1; right <= n; right++) {
            if (!is_palindrome(sequence, left, right)) continue;
            distinct.emplace(sequence.begin() + left, sequence.begin() + right);
        }
    }
    return std::vector<Sequence>(distinct.begin(), distinct.end());
}

template <class Index>
void check_index(const Index& index) {
    using Tree = typename Index::eertree_type;
    using Sequence = std::remove_cvref_t<decltype(index.sequence())>;

    std::vector<Sequence> expected = naive_palindromes(index.sequence());
    assert(index.size() == int(expected.size()));
    assert(index.empty() == expected.empty());
    assert(index.text_length() == int(index.sequence().size()));
    assert(index.eertree().size() == index.size());
    assert(int(index.nodes_in_order().size()) == index.size());

    for (int order = 0; order < index.size(); order++) {
        const Sequence& palindrome = expected[order];
        int id = index.node_by_order(order);
        assert(index.nodes_in_order()[order] == id);
        assert(index.order_of_node(id) == order);
        assert(index.find(palindrome) == id);
        assert(index.contains(palindrome));
        assert(index.order_of_palindrome(palindrome) == order);
        assert(index.palindrome(order) == palindrome);
        assert(index.kth(order) == palindrome);

        auto [left, right] = index.representative_occurrence(order);
        assert(0 <= left && left < right);
        assert(right <= index.text_length());
        assert(
            Sequence(
                index.sequence().begin() + left,
                index.sequence().begin() + right
            ) == palindrome
        );
    }

    Sequence empty;
    assert(index.find(empty) == Tree::null_node);
    assert(!index.contains(empty));
    assert(index.order_of_palindrome(empty) == -1);
}

void fixed_tests() {
    using Index = m1une::string::PalindromeLexicographicalOrder<>;
    Index empty;
    check_index(empty);

    Index index(std::string("abacaba"));
    check_index(index);
    std::vector<std::string> expected = {
        "a", "aba", "abacaba", "aca", "b", "bacab", "c"
    };
    assert(naive_palindromes(index.sequence()) == expected);
    assert(index.order_of_palindrome(std::string("aca")) == 3);
    assert(index.order_of_palindrome(std::string("aa")) == -1);
    assert(index.order_of_palindrome(std::string("abc")) == -1);
    assert(!index.contains(std::string("aa")));
    assert(!index.contains(std::string("abc")));

    Index moved(std::string("aaaaa"));
    check_index(moved);
    for (int length = 1; length <= 5; length++) {
        assert(moved.palindrome(length - 1) == std::string(length, 'a'));
    }

    using IntegerIndex =
        m1une::string::PalindromeLexicographicalOrder<std::vector<int>, 4, 0>;
    std::vector<int> values;
    values.push_back(2);
    values.push_back(1);
    values.push_back(2);
    values.push_back(0);
    values.push_back(2);
    values.push_back(1);
    values.push_back(2);
    IntegerIndex integer_index(values);
    check_index(integer_index);
}

void exhaustive_tests() {
    for (int length = 0; length <= 8; length++) {
        std::uint64_t count = 1;
        for (int i = 0; i < length; i++) count *= 3;
        for (std::uint64_t code = 0; code < count; code++) {
            std::uint64_t value = code;
            std::string text(length, 'a');
            for (char& character : text) {
                character = char('a' + value % 3);
                value /= 3;
            }
            check_index(
                m1une::string::PalindromeLexicographicalOrder<
                    std::string, 3, 'a'
                >(std::move(text))
            );
        }
    }
}

void randomized_tests() {
    std::uint64_t state = 0xf4c3182d9ab760e5ULL;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1000; trial++) {
        int length = int(random() % 45);
        std::string text(length, 'a');
        for (char& character : text) {
            character = char('a' + random() % 4);
        }
        check_index(
            m1une::string::PalindromeLexicographicalOrder<
                std::string, 4, 'a'
            >(std::move(text))
        );
    }
}

int library_checker_id(int id) {
    using Tree = m1une::string::Eertree<>;
    if (id == Tree::odd_root) return 0;
    if (id == Tree::even_root) return 1;
    return id;
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    fixed_tests();
    exhaustive_tests();
    randomized_tests();

    std::string text;
    fast_input >> text;
    m1une::string::PalindromeLexicographicalOrder<> index(std::move(text));
    const auto& tree = index.eertree();

    std::vector<int> parent(tree.node_count(), -1);
    for (int id = 0; id < tree.node_count(); id++) {
        const auto& node = tree.node(id);
        for (int symbol = 0; symbol < 26; symbol++) {
            int to = node.next[symbol];
            if (to != m1une::string::Eertree<>::null_node) parent[to] = id;
        }
    }

    fast_output << tree.size() << '\n';
    for (int id = 2; id < tree.node_count(); id++) {
        fast_output << library_checker_id(parent[id]) - 1 << ' '
                    << library_checker_id(tree.node(id).suffix_link) - 1
                    << '\n';
    }
    const auto& longest_suffix = tree.longest_suffix_nodes();
    for (int i = 0; i < int(longest_suffix.size()); i++) {
        if (i) fast_output << ' ';
        fast_output << longest_suffix[i] - 1;
    }
    fast_output << '\n';
}
#line 1 "verify/string/palindrome_lexicographical_order.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/eertree"

#line 1 "string/palindrome_lexicographical_order.hpp"



#include <algorithm>
#include <cassert>
#include <string>
#include <utility>
#include <vector>

#line 1 "string/eertree.hpp"



#include <array>
#line 6 "string/eertree.hpp"
#include <cstddef>
#include <limits>
#line 10 "string/eertree.hpp"

namespace m1une {
namespace string {

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
struct Eertree {
    static_assert(0 < AlphabetSize);

    using node_id = int;
    static constexpr node_id even_root = 0;
    static constexpr node_id odd_root = 1;
    static constexpr node_id null_node = -1;

    struct Node {
        std::array<node_id, AlphabetSize> next;
        node_id suffix_link;
        node_id series_link;
        int length;
        int diff;
        int suffix_count;
        int first_end;
        long long suffix_occurrences;

        Node(int length_value = 0, node_id suffix_link_value = even_root, node_id series_link_value = even_root)
            : suffix_link(suffix_link_value),
              series_link(series_link_value),
              length(length_value),
              diff(0),
              suffix_count(0),
              first_end(0),
              suffix_occurrences(0) {
            next.fill(null_node);
        }
    };

   private:
    std::vector<Node> _nodes;
    std::vector<int> _text;
    std::vector<node_id> _longest_suffix;
    node_id _last;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    node_id find_extendable(node_id node, int position, int symbol) const {
        while (true) {
            int length = _nodes[node].length;
            int left = position - length - 1;
            if (0 <= left && _text[left] == symbol) return node;
            node = _nodes[node].suffix_link;
        }
    }

    node_id new_node(int length) {
        assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
        _nodes.emplace_back(length);
        return int(_nodes.size()) - 1;
    }

   public:
    Eertree() {
        clear();
    }

    template <class Sequence>
    explicit Eertree(const Sequence& sequence) {
        clear();
        build(sequence);
    }

    int size() const {
        return int(_nodes.size()) - 2;
    }

    bool empty() const {
        return size() == 0;
    }

    int node_count() const {
        return int(_nodes.size());
    }

    int text_length() const {
        return int(_text.size());
    }

    node_id last() const {
        return _last;
    }

    int longest_suffix_length() const {
        return _nodes[_last].length;
    }

    const Node& node(node_id id) const {
        assert(0 <= id && id < node_count());
        return _nodes[id];
    }

    const std::vector<Node>& nodes() const {
        return _nodes;
    }

    node_id longest_suffix_node(int prefix_length) const {
        assert(1 <= prefix_length && prefix_length <= text_length());
        return _longest_suffix[prefix_length - 1];
    }

    const std::vector<node_id>& longest_suffix_nodes() const {
        return _longest_suffix;
    }

    template <class Callback>
    void for_each_suffix(node_id id, Callback callback) const {
        assert(0 <= id && id < node_count());
        while (id >= 2) {
            callback(id);
            id = _nodes[id].suffix_link;
        }
    }

    template <class Callback>
    void for_each_suffix(Callback callback) const {
        for_each_suffix(_last, callback);
    }

    void reserve(std::size_t text_capacity) {
        _text.reserve(text_capacity);
        _longest_suffix.reserve(text_capacity);
        _nodes.reserve(text_capacity + 2);
    }

    void clear() {
        _nodes.clear();
        _nodes.emplace_back(0, odd_root, even_root);
        _nodes.emplace_back(-1, odd_root, odd_root);
        _text.clear();
        _longest_suffix.clear();
        _last = even_root;
    }

    template <class Symbol>
    node_id add(const Symbol& value) {
        int symbol = symbol_index(value);
        int position = int(_text.size());
        _text.push_back(symbol);

        node_id current = find_extendable(_last, position, symbol);
        node_id next = _nodes[current].next[symbol];
        if (next == null_node) {
            int length = _nodes[current].length + 2;
            next = new_node(length);
            _nodes[current].next[symbol] = next;

            node_id suffix_link = even_root;
            if (length != 1) {
                node_id candidate = find_extendable(_nodes[current].suffix_link, position, symbol);
                suffix_link = _nodes[candidate].next[symbol];
                assert(suffix_link != null_node);
            }

            Node& created = _nodes[next];
            created.suffix_link = suffix_link;
            created.diff = created.length - _nodes[suffix_link].length;
            created.series_link =
                created.diff == _nodes[suffix_link].diff ? _nodes[suffix_link].series_link : suffix_link;
            created.suffix_count = _nodes[suffix_link].suffix_count + 1;
            created.first_end = position + 1;
        }

        _last = next;
        _nodes[_last].suffix_occurrences++;
        _longest_suffix.push_back(_last);
        return _last;
    }

    template <class Sequence>
    void build(const Sequence& sequence) {
        for (const auto& symbol : sequence) add(symbol);
    }

    std::vector<long long> occurrence_counts() const {
        std::vector<long long> result(_nodes.size(), 0);
        for (node_id id = 0; id < node_count(); id++) {
            result[id] = _nodes[id].suffix_occurrences;
        }
        for (node_id id = node_count() - 1; id >= 2; id--) {
            result[_nodes[id].suffix_link] += result[id];
        }
        return result;
    }

    std::pair<int, int> first_occurrence(node_id id) const {
        assert(2 <= id && id < node_count());
        int end = _nodes[id].first_end;
        return {end - _nodes[id].length, end};
    }
};

template <int AlphabetSize = 26, int FirstCharacter = 'a'>
using PalindromicTree = Eertree<AlphabetSize, FirstCharacter>;

}  // namespace string
}  // namespace m1une


#line 1 "string/suffix_array.hpp"



#line 6 "string/suffix_array.hpp"
#include <numeric>
#line 8 "string/suffix_array.hpp"
#include <type_traits>
#line 10 "string/suffix_array.hpp"

namespace m1une {
namespace string {
namespace detail {

template <class Sequence>
std::vector<int> suffix_array_impl(const Sequence& sequence) {
    int n = int(sequence.size());
    if (n == 0) return {};

    using Value = std::remove_cv_t<std::remove_reference_t<decltype(sequence[0])>>;
    std::vector<Value> sorted(sequence.begin(), sequence.end());
    std::sort(sorted.begin(), sorted.end());
    sorted.erase(std::unique(sorted.begin(), sorted.end()), sorted.end());

    int length = n + 1;
    std::vector<int> order(length);
    std::vector<int> rank(length);
    std::vector<int> key(length);
    key[n] = 0;
    for (int i = 0; i < n; i++) {
        key[i] = int(std::lower_bound(sorted.begin(), sorted.end(), sequence[i]) - sorted.begin()) + 1;
    }

    int alphabet = int(sorted.size()) + 1;
    std::vector<int> count(std::max(length, alphabet), 0);
    for (int value : key) count[value]++;
    for (int i = 1; i < alphabet; i++) count[i] += count[i - 1];
    for (int i = length - 1; i >= 0; i--) order[--count[key[i]]] = i;

    int classes = 1;
    rank[order[0]] = 0;
    for (int i = 1; i < length; i++) {
        if (key[order[i - 1]] != key[order[i]]) classes++;
        rank[order[i]] = classes - 1;
    }

    std::vector<int> shifted(length);
    std::vector<int> next_rank(length);
    for (long long half = 1; half < length; half <<= 1) {
        for (int i = 0; i < length; i++) {
            long long position = order[i] - half;
            if (position < 0) position += length;
            shifted[i] = int(position);
        }

        count.assign(classes, 0);
        for (int position : shifted) count[rank[position]]++;
        for (int i = 1; i < classes; i++) count[i] += count[i - 1];
        for (int i = length - 1; i >= 0; i--) {
            int position = shifted[i];
            order[--count[rank[position]]] = position;
        }

        int next_classes = 1;
        next_rank[order[0]] = 0;
        for (int i = 1; i < length; i++) {
            int current = order[i];
            int previous = order[i - 1];
            int current_second = int((current + half) % length);
            int previous_second = int((previous + half) % length);
            if (
                rank[current] != rank[previous] ||
                rank[current_second] != rank[previous_second]
            ) {
                next_classes++;
            }
            next_rank[current] = next_classes - 1;
        }
        rank.swap(next_rank);
        classes = next_classes;
        if (classes == length) break;
    }

    std::vector<int> suffixes(n);
    for (int i = 0; i < n; i++) suffixes[i] = order[i + 1];
    return suffixes;
}

}  // namespace detail

template <class Sequence>
std::vector<int> suffix_array(const Sequence& sequence) {
    return detail::suffix_array_impl(sequence);
}

inline std::vector<int> suffix_array(const std::string& text) {
    std::vector<unsigned char> values;
    values.reserve(text.size());
    for (unsigned char character : text) values.push_back(character);
    return detail::suffix_array_impl(values);
}

template <class Sequence>
std::vector<int> lcp_array(const Sequence& sequence, const std::vector<int>& suffixes) {
    int n = int(sequence.size());
    assert(int(suffixes.size()) == n);
    if (n == 0) return {};

    std::vector<int> rank(n);
    for (int i = 0; i < n; i++) {
        assert(0 <= suffixes[i] && suffixes[i] < n);
        rank[suffixes[i]] = i;
    }

    std::vector<int> lcp(n - 1);
    int common = 0;
    for (int i = 0; i < n; i++) {
        int position = rank[i];
        if (position == n - 1) {
            common = 0;
            continue;
        }
        int j = suffixes[position + 1];
        while (
            i + common < n &&
            j + common < n &&
            sequence[i + common] == sequence[j + common]
        ) {
            common++;
        }
        lcp[position] = common;
        if (common > 0) common--;
    }
    return lcp;
}

}  // namespace string
}  // namespace m1une


#line 12 "string/palindrome_lexicographical_order.hpp"

namespace m1une {
namespace string {

// Indexes the distinct nonempty palindromic substrings of one sequence.
template <
    class Sequence = std::string,
    int AlphabetSize = 26,
    int FirstCharacter = 'a'
>
struct PalindromeLexicographicalOrder {
    static_assert(0 < AlphabetSize);

    using eertree_type = Eertree<AlphabetSize, FirstCharacter>;
    using node_id = typename eertree_type::node_id;

   private:
    Sequence _sequence;
    eertree_type _eertree;
    std::vector<node_id> _nodes_in_order;
    std::vector<int> _order_of_node;

    template <class Symbol>
    static int symbol_index(const Symbol& symbol) {
        int index = int(symbol) - FirstCharacter;
        assert(0 <= index && index < AlphabetSize);
        return index;
    }

    void build_order() {
        const int node_count = _eertree.node_count();
        std::vector<std::vector<node_id>> suffix_children(node_count);
        for (node_id id = 0; id < node_count; id++) {
            if (id == eertree_type::odd_root) continue;
            suffix_children[_eertree.node(id).suffix_link].push_back(id);
        }

        std::vector<int> enter(node_count);
        std::vector<int> leave(node_count);
        std::vector<std::pair<node_id, bool>> stack;
        stack.reserve(2 * node_count);
        stack.emplace_back(eertree_type::odd_root, false);
        int timer = 0;
        while (!stack.empty()) {
            auto [id, exiting] = stack.back();
            stack.pop_back();
            if (exiting) {
                leave[id] = timer;
                continue;
            }

            enter[id] = timer++;
            stack.emplace_back(id, true);
            const auto& children = suffix_children[id];
            for (int i = int(children.size()) - 1; i >= 0; i--) {
                stack.emplace_back(children[i], false);
            }
        }

        std::vector<int> suffixes = suffix_array(_sequence);
        std::vector<int> suffix_rank(_sequence.size());
        for (int rank = 0; rank < int(suffixes.size()); rank++) {
            suffix_rank[suffixes[rank]] = rank;
        }

        _nodes_in_order.resize(_eertree.size());
        for (int i = 0; i < _eertree.size(); i++) {
            _nodes_in_order[i] = i + 2;
        }

        auto is_ancestor = [&](node_id ancestor, node_id descendant) {
            return
                enter[ancestor] <= enter[descendant] &&
                leave[descendant] <= leave[ancestor];
        };
        std::sort(
            _nodes_in_order.begin(),
            _nodes_in_order.end(),
            [&](node_id first, node_id second) {
                if (first == second) return false;

                // A palindromic prefix is also a palindromic suffix, so prefix
                // cases are exactly the ancestor cases in the suffix-link tree.
                if (is_ancestor(first, second)) return true;
                if (is_ancestor(second, first)) return false;

                // Otherwise the first mismatch occurs inside both substrings,
                // and the ranks of representative suffixes give their order.
                int first_start = _eertree.first_occurrence(first).first;
                int second_start = _eertree.first_occurrence(second).first;
                return suffix_rank[first_start] < suffix_rank[second_start];
            }
        );

        _order_of_node.assign(node_count, -1);
        for (int order = 0; order < size(); order++) {
            _order_of_node[_nodes_in_order[order]] = order;
        }
    }

   public:
    PalindromeLexicographicalOrder() : _order_of_node(2, -1) {}

    explicit PalindromeLexicographicalOrder(const Sequence& sequence)
        : _sequence(sequence), _eertree(_sequence) {
        build_order();
    }

    explicit PalindromeLexicographicalOrder(Sequence&& sequence)
        : _sequence(std::move(sequence)), _eertree(_sequence) {
        build_order();
    }

    int size() const {
        return int(_nodes_in_order.size());
    }

    bool empty() const {
        return _nodes_in_order.empty();
    }

    int text_length() const {
        return int(_sequence.size());
    }

    const Sequence& sequence() const {
        return _sequence;
    }

    const eertree_type& eertree() const {
        return _eertree;
    }

    const std::vector<node_id>& nodes_in_order() const {
        return _nodes_in_order;
    }

    int order_of_node(node_id id) const {
        assert(2 <= id && id < _eertree.node_count());
        return _order_of_node[id];
    }

    node_id node_by_order(int order) const {
        assert(0 <= order && order < size());
        return _nodes_in_order[order];
    }

    template <class Palindrome>
    node_id find(const Palindrome& palindrome) const {
        const int length = int(palindrome.size());
        if (length == 0) return eertree_type::null_node;
        for (int i = 0; i < length / 2; i++) {
            if (palindrome[i] != palindrome[length - 1 - i]) {
                return eertree_type::null_node;
            }
        }

        node_id id =
            length & 1 ? eertree_type::odd_root : eertree_type::even_root;
        for (int i = (length - 1) / 2; i >= 0; i--) {
            int symbol = symbol_index(palindrome[i]);
            id = _eertree.node(id).next[symbol];
            if (id == eertree_type::null_node) return id;
        }
        return id;
    }

    template <class Palindrome>
    bool contains(const Palindrome& palindrome) const {
        return find(palindrome) != eertree_type::null_node;
    }

    template <class Palindrome>
    int order_of_palindrome(const Palindrome& palindrome) const {
        node_id id = find(palindrome);
        return id == eertree_type::null_node ? -1 : order_of_node(id);
    }

    std::pair<int, int> representative_occurrence(int order) const {
        return _eertree.first_occurrence(node_by_order(order));
    }

    Sequence palindrome(int order) const {
        auto [left, right] = representative_occurrence(order);
        return Sequence(_sequence.begin() + left, _sequence.begin() + right);
    }

    Sequence kth(int order) const {
        return palindrome(order);
    }
};

}  // namespace string
}  // namespace m1une


#line 4 "verify/string/palindrome_lexicographical_order.test.cpp"

#line 7 "verify/string/palindrome_lexicographical_order.test.cpp"
#include <cstdint>
#line 1 "utilities/fast_io.hpp"



#line 6 "utilities/fast_io.hpp"
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#line 15 "utilities/fast_io.hpp"
#include <sys/stat.h>
#line 18 "utilities/fast_io.hpp"
#include <unistd.h>
#line 20 "utilities/fast_io.hpp"

namespace m1une {
namespace utilities {

struct FastOutput;

namespace internal {

// Shared with the convenience helpers in template.hpp.
inline FastOutput* standard_output_instance = nullptr;

// Detect std::begin(x), std::end(x).
template <class T, class = void>
struct is_range : std::false_type {};

template <class T>
struct is_range<T, std::void_t<
    decltype(std::begin(std::declval<T&>())),
    decltype(std::end(std::declval<T&>()))
>> : std::true_type {};

template <class T>
inline constexpr bool is_range_v = is_range<T>::value;

template <class T>
using range_reference_t = decltype(*std::begin(std::declval<T&>()));

template <class T>
using range_value_t = std::remove_cv_t<std::remove_reference_t<range_reference_t<T>>>;

template <class T, class = void>
struct range_stored_value {
    using type = range_value_t<T>;
};

template <class T>
struct range_stored_value<T, std::void_t<typename std::remove_cv_t<std::remove_reference_t<T>>::value_type>> {
    using type = typename std::remove_cv_t<std::remove_reference_t<T>>::value_type;
};

template <class T>
using range_stored_value_t = typename range_stored_value<T>::type;

// Treat strings and C strings as scalar output objects, not as ranges.
template <class T>
struct is_char_array : std::false_type {};

template <class T, std::size_t N>
struct is_char_array<T[N]>
    : std::bool_constant<std::is_same_v<std::remove_cv_t<T>, char>> {};

template <class T>
struct is_string_like
    : std::bool_constant<
          std::is_same_v<std::decay_t<T>, std::string>
          || std::is_same_v<std::decay_t<T>, const char*>
          || std::is_same_v<std::decay_t<T>, char*>
          || is_char_array<std::remove_reference_t<T>>::value
      > {};

template <class T>
inline constexpr bool is_string_like_v = is_string_like<T>::value;

// ModInt-like type: x.val() is printable, and x can be assigned from long long.
template <class T, class = void>
struct has_val_method : std::false_type {};

template <class T>
struct has_val_method<T, std::void_t<decltype(std::declval<const T&>().val())>>
    : std::true_type {};

template <class T>
inline constexpr bool has_val_method_v = has_val_method<T>::value;

template <class T, class = void>
struct has_static_mod_raw : std::false_type {};

template <class T>
struct has_static_mod_raw<
    T, std::void_t<decltype(T::mod()), decltype(T::raw(std::declval<uint32_t>()))>>
    : std::true_type {};

template <class T>
inline constexpr bool has_static_mod_raw_v = has_static_mod_raw<T>::value;

// libstdc++ before GCC 16 does not classify __int128 as an integral type in
// strict ISO modes such as -std=c++23. Keep the fast-I/O interface independent
// of that implementation detail.
template <class T>
inline constexpr bool is_integral_v =
    std::is_integral_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>
    || std::is_same_v<std::remove_cv_t<T>, __uint128_t>;

template <class T>
inline constexpr bool is_signed_v =
    std::is_signed_v<T>
    || std::is_same_v<std::remove_cv_t<T>, __int128_t>;

template <class T>
struct make_unsigned {
    using type = std::make_unsigned_t<T>;
};

template <>
struct make_unsigned<__int128_t> {
    using type = __uint128_t;
};

template <>
struct make_unsigned<__uint128_t> {
    using type = __uint128_t;
};

template <class T>
using make_unsigned_t = typename make_unsigned<std::remove_cv_t<T>>::type;

}  // namespace internal

struct FastInput {
    static constexpr int buffer_size = 1 << 20;

   private:
    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _length;
    int _file_descriptor;
    bool _streaming;

    bool refill() {
        _position = 0;
        if (_streaming) {
            ssize_t length;
            do {
                length = ::read(_file_descriptor, _buffer, buffer_size);
            } while (length < 0 && errno == EINTR);
            if (length <= 0) {
                _length = 0;
                return false;
            }
            _length = int(length);
        } else {
            _length = int(std::fread(_buffer, 1, buffer_size, _stream));
        }
        return _length != 0;
    }

    template <class T>
    bool read_integer_from_stream(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = read_char_raw();
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = negative ? result * 10 - (c - '0')
                                  : result * 10 + (c - '0');
                c = read_char_raw();
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                result = result * 10 + T(c - '0');
                c = read_char_raw();
            }
            value = negative ? T(0) - result : result;
        }
        return true;
    }

    bool prepare_number() {
        if (_length - _position >= 64) return true;
        const int remaining = _length - _position;
        if (remaining > 0) std::memmove(_buffer, _buffer + _position, remaining);
        const int added = int(std::fread(_buffer + remaining, 1, buffer_size - remaining, _stream));
        _position = 0;
        _length = remaining + added;
        if (_length < buffer_size) _buffer[_length] = '\0';
        return _length != 0;
    }

   public:
    explicit FastInput(std::FILE* stream = stdin)
        : _stream(stream),
          _position(0),
          _length(0),
          _file_descriptor(::fileno(stream)),
          _streaming([&] {
              struct stat status;
              return _file_descriptor >= 0
                     && ::fstat(_file_descriptor, &status) == 0
                     && !S_ISREG(status.st_mode);
          }()) {}

    FastInput(const FastInput&) = delete;
    FastInput& operator=(const FastInput&) = delete;

    int read_char_raw() {
        if (_position == _length && !refill()) return EOF;
        return _buffer[_position++];
    }

    bool skip_spaces() {
        int c = read_char_raw();
        while (c != EOF && c <= ' ') c = read_char_raw();
        if (c == EOF) return false;
        --_position;
        return true;
    }

    bool read(char& value) {
        if (!skip_spaces()) return false;
        value = char(read_char_raw());
        return true;
    }

    bool read(std::string& value) {
        if (!skip_spaces()) return false;
        value.clear();
        while (true) {
            const int begin = _position;
            while (_position < _length &&
                   static_cast<unsigned char>(_buffer[_position]) > ' ') {
                ++_position;
            }
            value.append(_buffer + begin, _position - begin);
            if (_position < _length) {
                ++_position;
                return true;
            }
            if (!refill()) return true;
        }
    }

    bool read(bool& value) {
        int x;
        if (!read(x)) return false;
        value = x != 0;
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>,
        bool
    >
    read(T& value) {
        if (_streaming) return read_integer_from_stream(value);
        if (!prepare_number()) return false;
        int c = static_cast<unsigned char>(_buffer[_position++]);
        while (c <= ' ') c = static_cast<unsigned char>(_buffer[_position++]);

        bool negative = false;
        if (c == '-') {
            negative = true;
            c = static_cast<unsigned char>(_buffer[_position++]);
        }

        if constexpr (internal::is_signed_v<T>) {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const int first = c - '0';
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = negative ? result * 100 - (first * 10 + second)
                                      : result * 100 + (first * 10 + second);
                    ++_position;
                } else {
                    result = negative ? result * 10 - first : result * 10 + first;
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = result;
        } else {
            T result = 0;
            while ('0' <= c && c <= '9') {
                const unsigned first = unsigned(c - '0');
                const int second = static_cast<unsigned char>(_buffer[_position]) - '0';
                if (0 <= second && second <= 9) {
                    result = result * 100 + T(first * 10 + unsigned(second));
                    ++_position;
                } else {
                    result = result * 10 + T(first);
                }
                c = static_cast<unsigned char>(_buffer[_position++]);
            }
            value = negative ? T(0) - result : result;
        }
        if (_position > _length) _position = _length;
        return true;
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>, bool>
    read(T& value) {
        if (!skip_spaces()) return false;
        int c = read_char_raw();
        bool negative = false;
        if (c == '-' || c == '+') {
            negative = c == '-';
            c = read_char_raw();
        }

        long double result = 0;
        while ('0' <= c && c <= '9') {
            result = result * 10 + (c - '0');
            c = read_char_raw();
        }
        if (c == '.') {
            long double place = 0.1L;
            c = read_char_raw();
            while ('0' <= c && c <= '9') {
                result += (c - '0') * place;
                place *= 0.1L;
                c = read_char_raw();
            }
        }
        if (c == 'e' || c == 'E') {
            c = read_char_raw();
            bool exponent_negative = false;
            if (c == '-' || c == '+') {
                exponent_negative = c == '-';
                c = read_char_raw();
            }
            int exponent = 0;
            while ('0' <= c && c <= '9') {
                exponent = exponent * 10 + (c - '0');
                c = read_char_raw();
            }
            long double scale = 1;
            long double power = 10;
            while (exponent > 0) {
                if (exponent & 1) scale *= power;
                power *= power;
                exponent >>= 1;
            }
            result = exponent_negative ? result / scale : result * scale;
        }
        value = static_cast<T>(negative ? -result : result);
        return true;
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>,
        bool
    >
    read(T& value) {
        long long x;
        if (!read(x)) return false;
        if constexpr (internal::has_static_mod_raw_v<T>) {
            if (x >= 0 && uint64_t(x) < uint64_t(T::mod())) {
                value = T::raw(uint32_t(x));
            } else {
                value = T(x);
            }
        } else {
            value = T(x);
        }
        return true;
    }

    template <class First, class Second>
    bool read(std::pair<First, Second>& value) {
        if (!read(value.first)) return false;
        return read(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>,
        bool
    >
    read(Range& range) {
        using StoredValue = internal::range_stored_value_t<Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        for (auto&& value : range) {
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                bool x;
                if (!read(x)) return false;
                value = x;
            } else {
                if (!read(value)) return false;
            }
        }
        return true;
    }

    template <class First, class Second, class... Rest>
    bool read(First& first, Second& second, Rest&... rest) {
        if (!read(first)) return false;
        return read(second, rest...);
    }

    template <class T>
    FastInput& operator>>(T& value) {
        if (!read(value)) std::abort();
        return *this;
    }
};

struct FastOutput {
    static constexpr int buffer_size = 1 << 20;

   private:
    inline static const auto digit_quads = [] {
        std::array<char, 40000> result{};
        for (int i = 0; i < 10000; i++) {
            int value = i;
            for (int j = 3; j >= 0; j--) {
                result[4 * i + j] = char('0' + value % 10);
                value /= 10;
            }
        }
        return result;
    }();

    std::FILE* _stream;
    char _buffer[buffer_size];
    int _position;
    int _precision;
    std::chars_format _float_format;
    char _range_separator;
    std::string* _capture = nullptr;

    template <class T>
    std::string format_cell(const T& value) {
        std::string result;
        struct CaptureGuard {
            std::string*& target;
            std::string* previous;
            ~CaptureGuard() { target = previous; }
        } guard{_capture, _capture};
        _capture = &result;
        write(value);
        return result;
    }

    template <class Matrix>
    void write_aligned_matrix(const Matrix& matrix) {
        std::vector<std::vector<std::string>> rows;
        std::vector<std::size_t> widths;
        for (const auto& row : matrix) {
            auto& cells = rows.emplace_back();
            std::size_t column = 0;
            for (const auto& value : row) {
                cells.push_back(format_cell(value));
                if (column == widths.size()) widths.push_back(0);
                widths[column] = std::max(widths[column], cells.back().size());
                ++column;
            }
        }
        bool first = true;
        for (const auto& row : rows) {
            if (!first) write_char('\n');
            first = false;
            for (std::size_t column = 0; column < row.size(); ++column) {
                if (column != 0) write_char(_range_separator);
                for (std::size_t padding = row[column].size();
                     padding < widths[column]; ++padding) {
                    write_char(' ');
                }
                write(row[column]);
            }
        }
    }

   public:
    explicit FastOutput(std::FILE* stream = stdout)
        : _stream(stream),
          _position(0),
          _precision(6),
          _float_format(std::chars_format::general),
          _range_separator(' ') {
        if (_stream == stdout
            && internal::standard_output_instance == nullptr) {
            internal::standard_output_instance = this;
        }
    }

    FastOutput(const FastOutput&) = delete;
    FastOutput& operator=(const FastOutput&) = delete;

    ~FastOutput() {
        flush();
        if (internal::standard_output_instance == this) {
            internal::standard_output_instance = nullptr;
        }
    }

    void flush() {
        if (_position != 0) {
            std::fwrite(_buffer, 1, _position, _stream);
            _position = 0;
        }
        std::fflush(_stream);
    }

    void write_char(char c) {
        if (_capture != nullptr) {
            _capture->push_back(c);
            return;
        }
        if (_position == buffer_size) flush();
        _buffer[_position++] = c;
    }

    void write(const char* s) {
        while (*s != '\0') write_char(*s++);
    }

    void write(const std::string& s) {
        if (_capture != nullptr) {
            _capture->append(s);
            return;
        }
        std::size_t position = 0;
        while (position < s.size()) {
            if (_position == buffer_size) flush();
            const std::size_t copied =
                std::min<std::size_t>(buffer_size - _position, s.size() - position);
            std::memcpy(_buffer + _position, s.data() + position, copied);
            _position += int(copied);
            position += copied;
        }
    }

    void write(char c) {
        write_char(c);
    }

    void write(bool value) {
        write_char(value ? '1' : '0');
    }

    template <class T>
    std::enable_if_t<std::is_floating_point_v<T>>
    write(T value) {
        char digits[128];
        auto [end, error] = std::to_chars(
            digits,
            digits + sizeof(digits),
            value,
            _float_format,
            _precision
        );
        if (error != std::errc()) std::abort();
        for (const char* pointer = digits; pointer != end; pointer++) {
            write_char(*pointer);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::is_integral_v<T>
            && !std::is_same_v<std::remove_cv_t<T>, bool>
            && !std::is_same_v<std::remove_cv_t<T>, char>
    >
    write(T value) {
        using Raw = std::remove_cv_t<T>;
        using Unsigned = internal::make_unsigned_t<Raw>;

        Unsigned magnitude;
        if constexpr (internal::is_signed_v<Raw>) {
            if (value < 0) {
                write_char('-');
                magnitude = Unsigned(0) - Unsigned(value);
            } else {
                magnitude = Unsigned(value);
            }
        } else {
            magnitude = value;
        }

        if (magnitude == 0) {
            write_char('0');
            return;
        }

        unsigned chunks[16];
        int count = 0;
        while (magnitude >= 10000) {
            const Unsigned quotient = magnitude / 10000;
            chunks[count++] = unsigned(magnitude - quotient * 10000);
            magnitude = quotient;
        }
        if (_capture == nullptr && _position > buffer_size - 64) flush();
        char captured[64];
        char* const begin = _capture != nullptr ? captured : _buffer + _position;
        char* destination = begin;
        const unsigned leading = unsigned(magnitude);
        const char* first = digit_quads.data() + 4 * leading;
        int skip = leading < 10 ? 3 : leading < 100 ? 2 : leading < 1000 ? 1 : 0;
        for (; skip < 4; skip++) *destination++ = first[skip];
        while (count--) {
            const char* digits = digit_quads.data() + 4 * chunks[count];
            std::memcpy(destination, digits, 4);
            destination += 4;
        }
        if (_capture != nullptr) {
            _capture->append(begin, destination - begin);
        } else {
            _position += int(destination - begin);
        }
    }

    template <class T>
    std::enable_if_t<
        internal::has_val_method_v<T>
            && !internal::is_integral_v<T>
            && !internal::is_range_v<T>
    >
    write(const T& value) {
        write(value.val());
    }

    template <class First, class Second>
    void write(const std::pair<First, Second>& value) {
        write(value.first);
        write_char(' ');
        write(value.second);
    }

    template <class Range>
    std::enable_if_t<
        internal::is_range_v<Range>
            && !internal::is_string_like_v<Range>
    >
    write(const Range& range) {
        using StoredValue = internal::range_stored_value_t<const Range>;
        constexpr bool nested = internal::is_range_v<StoredValue>
                                && !internal::is_string_like_v<StoredValue>;

        bool first = true;
        for (const auto& value : range) {
            if (!first) write_char(nested ? '\n' : _range_separator);
            first = false;
            if constexpr (std::is_same_v<StoredValue, bool> && !nested) {
                write(static_cast<bool>(value));
            } else {
                write(value);
            }
        }
    }

    template <class First, class... Rest>
    void print(const First& first, const Rest&... rest) {
        write(first);
        ((write_char(' '), write(rest)), ...);
    }

    void println() {
        write_char('\n');
    }

    void set_precision(int precision) {
        _precision = precision;
    }

    void set_fixed(int precision = 6) {
        _float_format = std::chars_format::fixed;
        _precision = precision;
    }

    void set_general(int precision = 6) {
        _float_format = std::chars_format::general;
        _precision = precision;
    }

    void set_range_separator(char separator) {
        _range_separator = separator;
    }

    template <class Matrix>
    void write_aligned(const Matrix& matrix) {
        using Row = internal::range_stored_value_t<const Matrix>;
        using Cell = internal::range_stored_value_t<const Row>;
        static_assert(internal::is_range_v<Row> && !internal::is_string_like_v<Row>,
                      "write_aligned requires a two-dimensional range");
        static_assert(!internal::is_range_v<Cell> || internal::is_string_like_v<Cell>,
                      "write_aligned requires scalar cells");
        write_aligned_matrix(matrix);
    }

    template <class Matrix>
    void println_aligned(const Matrix& matrix) {
        write_aligned(matrix);
        write_char('\n');
    }

    template <class... Args>
    void println(const Args&... args) {
        print(args...);
        write_char('\n');
    }

    template <class T>
    FastOutput& operator<<(const T& value) {
        write(value);
        return *this;
    }
};

}  // namespace utilities
}  // namespace m1une


#line 9 "verify/string/palindrome_lexicographical_order.test.cpp"
#include <set>
#line 14 "verify/string/palindrome_lexicographical_order.test.cpp"

namespace {

template <class Sequence>
bool is_palindrome(const Sequence& sequence, int left, int right) {
    while (left < right) {
        right--;
        if (sequence[left] != sequence[right]) return false;
        left++;
    }
    return true;
}

template <class Sequence>
std::vector<Sequence> naive_palindromes(const Sequence& sequence) {
    std::set<Sequence> distinct;
    int n = int(sequence.size());
    for (int left = 0; left < n; left++) {
        for (int right = left + 1; right <= n; right++) {
            if (!is_palindrome(sequence, left, right)) continue;
            distinct.emplace(sequence.begin() + left, sequence.begin() + right);
        }
    }
    return std::vector<Sequence>(distinct.begin(), distinct.end());
}

template <class Index>
void check_index(const Index& index) {
    using Tree = typename Index::eertree_type;
    using Sequence = std::remove_cvref_t<decltype(index.sequence())>;

    std::vector<Sequence> expected = naive_palindromes(index.sequence());
    assert(index.size() == int(expected.size()));
    assert(index.empty() == expected.empty());
    assert(index.text_length() == int(index.sequence().size()));
    assert(index.eertree().size() == index.size());
    assert(int(index.nodes_in_order().size()) == index.size());

    for (int order = 0; order < index.size(); order++) {
        const Sequence& palindrome = expected[order];
        int id = index.node_by_order(order);
        assert(index.nodes_in_order()[order] == id);
        assert(index.order_of_node(id) == order);
        assert(index.find(palindrome) == id);
        assert(index.contains(palindrome));
        assert(index.order_of_palindrome(palindrome) == order);
        assert(index.palindrome(order) == palindrome);
        assert(index.kth(order) == palindrome);

        auto [left, right] = index.representative_occurrence(order);
        assert(0 <= left && left < right);
        assert(right <= index.text_length());
        assert(
            Sequence(
                index.sequence().begin() + left,
                index.sequence().begin() + right
            ) == palindrome
        );
    }

    Sequence empty;
    assert(index.find(empty) == Tree::null_node);
    assert(!index.contains(empty));
    assert(index.order_of_palindrome(empty) == -1);
}

void fixed_tests() {
    using Index = m1une::string::PalindromeLexicographicalOrder<>;
    Index empty;
    check_index(empty);

    Index index(std::string("abacaba"));
    check_index(index);
    std::vector<std::string> expected = {
        "a", "aba", "abacaba", "aca", "b", "bacab", "c"
    };
    assert(naive_palindromes(index.sequence()) == expected);
    assert(index.order_of_palindrome(std::string("aca")) == 3);
    assert(index.order_of_palindrome(std::string("aa")) == -1);
    assert(index.order_of_palindrome(std::string("abc")) == -1);
    assert(!index.contains(std::string("aa")));
    assert(!index.contains(std::string("abc")));

    Index moved(std::string("aaaaa"));
    check_index(moved);
    for (int length = 1; length <= 5; length++) {
        assert(moved.palindrome(length - 1) == std::string(length, 'a'));
    }

    using IntegerIndex =
        m1une::string::PalindromeLexicographicalOrder<std::vector<int>, 4, 0>;
    std::vector<int> values;
    values.push_back(2);
    values.push_back(1);
    values.push_back(2);
    values.push_back(0);
    values.push_back(2);
    values.push_back(1);
    values.push_back(2);
    IntegerIndex integer_index(values);
    check_index(integer_index);
}

void exhaustive_tests() {
    for (int length = 0; length <= 8; length++) {
        std::uint64_t count = 1;
        for (int i = 0; i < length; i++) count *= 3;
        for (std::uint64_t code = 0; code < count; code++) {
            std::uint64_t value = code;
            std::string text(length, 'a');
            for (char& character : text) {
                character = char('a' + value % 3);
                value /= 3;
            }
            check_index(
                m1une::string::PalindromeLexicographicalOrder<
                    std::string, 3, 'a'
                >(std::move(text))
            );
        }
    }
}

void randomized_tests() {
    std::uint64_t state = 0xf4c3182d9ab760e5ULL;
    auto random = [&state]() {
        state ^= state << 7;
        state ^= state >> 9;
        return state;
    };

    for (int trial = 0; trial < 1000; trial++) {
        int length = int(random() % 45);
        std::string text(length, 'a');
        for (char& character : text) {
            character = char('a' + random() % 4);
        }
        check_index(
            m1une::string::PalindromeLexicographicalOrder<
                std::string, 4, 'a'
            >(std::move(text))
        );
    }
}

int library_checker_id(int id) {
    using Tree = m1une::string::Eertree<>;
    if (id == Tree::odd_root) return 0;
    if (id == Tree::even_root) return 1;
    return id;
}

}  // namespace

int main() {
    m1une::utilities::FastInput fast_input;
    m1une::utilities::FastOutput fast_output;

    fixed_tests();
    exhaustive_tests();
    randomized_tests();

    std::string text;
    fast_input >> text;
    m1une::string::PalindromeLexicographicalOrder<> index(std::move(text));
    const auto& tree = index.eertree();

    std::vector<int> parent(tree.node_count(), -1);
    for (int id = 0; id < tree.node_count(); id++) {
        const auto& node = tree.node(id);
        for (int symbol = 0; symbol < 26; symbol++) {
            int to = node.next[symbol];
            if (to != m1une::string::Eertree<>::null_node) parent[to] = id;
        }
    }

    fast_output << tree.size() << '\n';
    for (int id = 2; id < tree.node_count(); id++) {
        fast_output << library_checker_id(parent[id]) - 1 << ' '
                    << library_checker_id(tree.node(id).suffix_link) - 1
                    << '\n';
    }
    const auto& longest_suffix = tree.longest_suffix_nodes();
    for (int i = 0; i < int(longest_suffix.size()); i++) {
        if (i) fast_output << ' ';
        fast_output << longest_suffix[i] - 1;
    }
    fast_output << '\n';
}
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