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:heavy_check_mark: verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp

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Code

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

#include "../../../ds/dynamic_array/persistent_dynamic_monoid_array.hpp"

#include <algorithm>
#include <cassert>
#include "../../../utilities/fast_io.hpp"
#include <numeric>
#include <random>
#include <string>
#include <utility>
#include <vector>

#include "../../../monoid/add.hpp"

struct StringMonoid {
    using value_type = std::string;

    static std::string id() {
        return "";
    }

    static std::string op(const std::string& a, const std::string& b) {
        return a + b;
    }
};

std::string join(const std::vector<std::string>& a, int l, int r) {
    std::string res;
    for (int i = l; i < r; i++) res += a[i];
    return res;
}

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

    using Array = m1une::ds::PersistentDynamicMonoidArray<StringMonoid>;

    Array a = {"a", "b", "c", "d", "e"};
    Array b = a.insert(2, "X");
    Array c = b.reverse(1, 5);
    Array d = c.rotate(1, 3, 6);
    Array e = d.set(0, "Z");
    Array f = e.erase(2);

    assert(a.to_vector() == (std::vector<std::string>{"a", "b", "c", "d", "e"}));
    assert(b.to_vector() == (std::vector<std::string>{"a", "b", "X", "c", "d", "e"}));
    assert(c.to_vector() == (std::vector<std::string>{"a", "d", "c", "X", "b", "e"}));
    assert(d.to_vector() == (std::vector<std::string>{"a", "X", "b", "e", "d", "c"}));
    assert(e.to_vector() == (std::vector<std::string>{"Z", "X", "b", "e", "d", "c"}));
    assert(f.to_vector() == (std::vector<std::string>{"Z", "X", "e", "d", "c"}));
    assert(c.prod(0, c.size()) == "adcXbe");
    assert(c.prod(1, 5) == "dcXb");
    assert(f.all_prod() == "ZXedc");
    assert(f.get(2) == "e");
    assert(f.front() == "Z");
    assert(f.back() == "c");

    auto [left, right] = f.split(2);
    assert(left.to_vector() == (std::vector<std::string>{"Z", "X"}));
    assert(right.to_vector() == (std::vector<std::string>{"e", "d", "c"}));
    assert(left.append(right).to_vector() == f.to_vector());
    assert(f.split_off(3).to_vector() == (std::vector<std::string>{"d", "c"}));
    assert(f.clear().empty());

    std::mt19937 rng(1);
    std::vector<std::pair<Array, std::vector<std::string>>> versions;
    versions.push_back({Array(), {}});
    for (int step = 0; step < 300; step++) {
        int id = int(rng() % versions.size());
        Array cur = versions[id].first;
        std::vector<std::string> expected = versions[id].second;
        assert(cur.to_vector() == expected);

        Array next = cur;
        std::vector<std::string> next_expected = expected;
        int op = int(rng() % 8);
        if (op == 0 || next_expected.empty()) {
            int pos = int(rng() % (next_expected.size() + 1));
            std::string value(1, char('a' + int(rng() % 26)));
            next = cur.insert(pos, value);
            next_expected.insert(next_expected.begin() + pos, value);
        } else if (op == 1) {
            int pos = int(rng() % next_expected.size());
            next = cur.erase(pos);
            next_expected.erase(next_expected.begin() + pos);
        } else if (op == 2) {
            int l = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > r) std::swap(l, r);
            next = cur.erase(l, r);
            next_expected.erase(next_expected.begin() + l, next_expected.begin() + r);
        } else if (op == 3) {
            int pos = int(rng() % next_expected.size());
            std::string value(1, char('A' + int(rng() % 26)));
            next = cur.set(pos, value);
            next_expected[pos] = value;
        } else if (op == 4) {
            int l = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > r) std::swap(l, r);
            next = cur.reverse(l, r);
            std::reverse(next_expected.begin() + l, next_expected.begin() + r);
        } else if (op == 5) {
            int l = int(rng() % (next_expected.size() + 1));
            int m = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > m) std::swap(l, m);
            if (m > r) std::swap(m, r);
            if (l > m) std::swap(l, m);
            next = cur.rotate(l, m, r);
            std::rotate(next_expected.begin() + l, next_expected.begin() + m, next_expected.begin() + r);
        } else if (op == 6 && next_expected.size() < 80) {
            int other_id = int(rng() % versions.size());
            next = cur.append(versions[other_id].first);
            next_expected.insert(next_expected.end(), versions[other_id].second.begin(), versions[other_id].second.end());
        } else {
            next = cur.reverse();
            std::reverse(next_expected.begin(), next_expected.end());
        }

        assert(cur.to_vector() == expected);
        assert(next.to_vector() == next_expected);
        assert(next.all_prod() == join(next_expected, 0, int(next_expected.size())));
        for (int l = 0; l <= int(next_expected.size()); l++) {
            for (int r = l; r <= int(next_expected.size()); r++) {
                assert(next.prod(l, r) == join(next_expected, l, r));
            }
        }
        if (!next_expected.empty()) {
            int pos = int(rng() % next_expected.size());
            assert(next[pos] == next_expected[pos]);
        }
        int split_pos = int(rng() % (next_expected.size() + 1));
        auto [prefix, suffix] = next.split(split_pos);
        assert(prefix.to_vector() == std::vector<std::string>(next_expected.begin(), next_expected.begin() + split_pos));
        assert(suffix.to_vector() == std::vector<std::string>(next_expected.begin() + split_pos, next_expected.end()));

        if (next_expected.size() <= 100) versions.push_back({next, next_expected});
    }

    int size, query_count;
    fast_input >> size >> query_count;
    std::vector<long long> values(size);
    for (long long& value : values) fast_input >> value;

    using SumArray =
        m1une::ds::PersistentDynamicMonoidArray<m1une::monoid::Add<long long>>;
    SumArray current(values);
    while (query_count--) {
        int type, left_index, right_index;
        fast_input >> type >> left_index >> right_index;
        if (type == 0) {
            current = current.reverse(left_index, right_index);
        } else {
            fast_output << current.prod(left_index, right_index) << '\n';
        }
    }
}
#line 1 "verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/range_reverse_range_sum"

#line 1 "ds/dynamic_array/persistent_dynamic_monoid_array.hpp"



#include <cassert>
#include <chrono>
#include <concepts>
#include <cstddef>
#include <cstdint>
#include <initializer_list>
#include <memory>
#include <utility>
#include <vector>

#line 1 "monoid/concept.hpp"



#line 5 "monoid/concept.hpp"

namespace m1une {
namespace monoid {

// Concept to check if a type satisfies the requirements of a Monoid.
// A Monoid must have a `value_type`, an identity element `id()`, and an associative binary operation `op()`.
template <typename M>
concept IsMonoid = requires(typename M::value_type a, typename M::value_type b) {
    // 1. Must define `value_type`
    typename M::value_type;

    // 2. Must have a static method `id()` returning `value_type`
    { M::id() } -> std::same_as<typename M::value_type>;

    // 3. Must have a static method `op(a, b)` returning `value_type`
    { M::op(a, b) } -> std::same_as<typename M::value_type>;
};

// Concept for groups. A type satisfying this concept must also obey the group
// laws; concepts can check the interface but not the algebraic properties.
template <typename M>
concept IsGroup = IsMonoid<M> && requires(typename M::value_type a) {
    { M::inv(a) } -> std::same_as<typename M::value_type>;
};

// Concept for commutative groups. Commutativity is a semantic requirement and
// cannot be checked by a C++ concept.
template <typename M>
concept IsCommutativeGroup = IsGroup<M>;

}  // namespace monoid
}  // namespace m1une


#line 1 "ds/detail/persistent_binary_node_pool.hpp"



#line 6 "ds/detail/persistent_binary_node_pool.hpp"
#include <deque>
#include <limits>
#include <optional>
#line 11 "ds/detail/persistent_binary_node_pool.hpp"

namespace m1une {
namespace ds {
namespace detail {

// Node must have integer `l` and `r` members. New nodes initially have no
// owner; discard_unreferenced() removes temporary path-copy nodes after the
// result roots have been retained.
template <class Node, int null_node = -1>
struct PersistentBinaryNodePool {
   private:
    std::deque<std::optional<Node>> _nodes;
    std::vector<int> _references;
    std::vector<int> _next_free;
    std::vector<int> _unowned;
    int _first_free = -1;
    std::size_t _live_nodes = 0;

    void release_zero(int node) {
        assert(node != null_node && _nodes[node].has_value());
        int left = (*_nodes[node]).l;
        int right = (*_nodes[node]).r;
        _nodes[node].reset();
        _next_free[node] = _first_free;
        _first_free = node;
        --_live_nodes;
        if (left != null_node && --_references[left] == 0) release_zero(left);
        if (right != null_node && --_references[right] == 0) release_zero(right);
    }

   public:
    PersistentBinaryNodePool() {
        if constexpr (null_node == 0) {
            _nodes.emplace_back();
            _references.push_back(0);
            _next_free.push_back(-1);
        }
    }

    Node& operator[](int node) {
        assert(node != null_node && _nodes[node].has_value());
        return *_nodes[node];
    }

    const Node& operator[](int node) const {
        assert(node != null_node && _nodes[node].has_value());
        return *_nodes[node];
    }

    template <class... Args>
    int emplace(Args&&... args) {
        int result;
        if (_first_free == -1) {
            assert(_nodes.size() < std::size_t(std::numeric_limits<int>::max()));
            result = int(_nodes.size());
            _nodes.emplace_back(std::in_place, std::forward<Args>(args)...);
            _references.push_back(0);
            _next_free.push_back(-1);
        } else {
            result = _first_free;
            _first_free = _next_free[result];
            _nodes[result].emplace(std::forward<Args>(args)...);
            _references[result] = 0;
        }
        retain((*_nodes[result]).l);
        retain((*_nodes[result]).r);
        _unowned.push_back(result);
        ++_live_nodes;
        return result;
    }

    void retain(int node) {
        if (node != null_node) {
            assert(_nodes[node].has_value());
            ++_references[node];
        }
    }

    void release(int node) {
        if (node == null_node) return;
        assert(_nodes[node].has_value() && _references[node] > 0);
        if (--_references[node] == 0) release_zero(node);
    }

    bool unique(int node) const {
        return node == null_node || _references[node] == 1;
    }

    int clone(int node) {
        assert(node != null_node && _nodes[node].has_value());
        return emplace(*_nodes[node]);
    }

    // Returns node itself when it has one owner, otherwise an unowned clone.
    // A returned clone becomes owned when a root or parent edge retains it.
    int clone_if_shared(int node) {
        if (unique(node)) return node;
        return clone(node);
    }

    void replace(int& edge, int node) {
        if (edge == node) return;
        retain(node);
        int old = edge;
        edge = node;
        release(old);
    }

    void discard_unreferenced() {
        while (!_unowned.empty()) {
            int node = _unowned.back();
            _unowned.pop_back();
            if (_nodes[node].has_value() && _references[node] == 0) release_zero(node);
        }
    }

    void reserve(std::size_t) {}

    int next_index() const { return _first_free == -1 ? int(_nodes.size()) : _first_free; }

    std::size_t size() const { return _live_nodes; }
};

}  // namespace detail
}  // namespace ds
}  // namespace m1une


#line 16 "ds/dynamic_array/persistent_dynamic_monoid_array.hpp"

namespace m1une {
namespace ds {

template <m1une::monoid::IsMonoid Monoid>
struct PersistentDynamicMonoidArray {
    using T = typename Monoid::value_type;

   private:
    struct Node {
        T val, prod, rprod;
        int priority;
        int count;
        int l, r;
        bool rev;

        Node(T value, T product, T reverse_product, int node_priority, int node_count, int left, int right,
             bool reversed)
            : val(std::move(value)),
              prod(std::move(product)),
              rprod(std::move(reverse_product)),
              priority(node_priority),
              count(node_count),
              l(left),
              r(right),
              rev(reversed) {}
    };

    struct BuildNode {
        T val;
        int priority;
        int l, r;

        BuildNode(T value, int node_priority) : val(std::move(value)), priority(node_priority), l(-1), r(-1) {}
    };

    int root;
    std::uint32_t rng_state;
    using Pool = detail::PersistentBinaryNodePool<Node>;

    std::shared_ptr<Pool> pool;

    int subtree_size(int t) const {
        return t == -1 ? 0 : (*pool)[t].count;
    }

    T node_prod(int t) const {
        return t == -1 ? Monoid::id() : (*pool)[t].prod;
    }

    T node_rprod(int t) const {
        return t == -1 ? Monoid::id() : (*pool)[t].rprod;
    }

    static std::uint32_t next_state(std::uint32_t state) {
        state ^= state << 13;
        state ^= state >> 17;
        state ^= state << 5;
        return state == 0 ? 1 : state;
    }

    static int next_priority(std::uint32_t& state) {
        state = next_state(state);
        return int(state);
    }

    template <typename U>
    static T make_value(const U& value) {
        if constexpr (requires(U x) { Monoid::make(x); }) {
            return Monoid::make(value);
        } else {
            return static_cast<T>(value);
        }
    }

    int make_node(T val, int priority, bool rev, int l, int r) const {
        T prod = Monoid::op(Monoid::op(node_prod(l), val), node_prod(r));
        T rprod = Monoid::op(Monoid::op(node_rprod(r), val), node_rprod(l));
        if (rev) std::swap(prod, rprod);
        int count = 1 + subtree_size(l) + subtree_size(r);
        return pool->emplace(std::move(val), std::move(prod), std::move(rprod), priority, count, l, r, rev);
    }

    int reversed_node(int t) const {
        if (t == -1) return -1;
        Node node = (*pool)[t];
        return make_node(std::move(node.val), node.priority, !node.rev, node.l, node.r);
    }

    int push(int t) const {
        if (t == -1 || !(*pool)[t].rev) return t;
        Node node = (*pool)[t];
        int l = reversed_node(node.r);
        int r = reversed_node(node.l);
        return make_node(std::move(node.val), node.priority, false, l, r);
    }

    int merge(int l, int r) const {
        if (l == -1 || r == -1) return l == -1 ? r : l;
        if ((*pool)[l].priority > (*pool)[r].priority) {
            Node node = (*pool)[push(l)];
            int right = merge(node.r, r);
            return make_node(std::move(node.val), node.priority, false, node.l, right);
        }
        Node node = (*pool)[push(r)];
        int left = merge(l, node.l);
        return make_node(std::move(node.val), node.priority, false, left, node.r);
    }

    std::pair<int, int> split_node(int t, int pos) const {
        if (t == -1) return {-1, -1};
        Node node = (*pool)[push(t)];
        int left_count = subtree_size(node.l);
        if (pos <= left_count) {
            auto [a, b] = split_node(node.l, pos);
            return {a, make_node(std::move(node.val), node.priority, false, b, node.r)};
        }
        auto [a, b] = split_node(node.r, pos - left_count - 1);
        return {make_node(std::move(node.val), node.priority, false, node.l, a), b};
    }

    int set_node(int t, int pos, T val) const {
        Node node = (*pool)[push(t)];
        int left_count = subtree_size(node.l);
        if (pos < left_count) {
            int l = set_node(node.l, pos, std::move(val));
            return make_node(std::move(node.val), node.priority, false, l, node.r);
        }
        if (pos == left_count) {
            return make_node(std::move(val), node.priority, false, node.l, node.r);
        }
        int r = set_node(node.r, pos - left_count - 1, std::move(val));
        return make_node(std::move(node.val), node.priority, false, node.l, r);
    }

    void pull(int t) const {
        Node& node = (*pool)[t];
        node.prod = Monoid::op(Monoid::op(node_prod(node.l), node.val), node_prod(node.r));
        node.rprod = Monoid::op(Monoid::op(node_rprod(node.r), node.val), node_rprod(node.l));
        if (node.rev) std::swap(node.prod, node.rprod);
    }

    int set_node_inplace(int t, int pos, T val, bool inherited_reversed = false) const {
        t = pool->clone_if_shared(t);
        const bool reversed = inherited_reversed ^ (*pool)[t].rev;
        const int logical_left = reversed ? (*pool)[t].r : (*pool)[t].l;
        const int left_count = subtree_size(logical_left);
        if (pos < left_count) {
            int child = set_node_inplace(logical_left, pos, std::move(val), reversed);
            if (reversed) {
                pool->replace((*pool)[t].r, child);
            } else {
                pool->replace((*pool)[t].l, child);
            }
        } else if (pos == left_count) {
            (*pool)[t].val = std::move(val);
        } else {
            const int logical_right = reversed ? (*pool)[t].l : (*pool)[t].r;
            int child = set_node_inplace(logical_right, pos - left_count - 1, std::move(val), reversed);
            if (reversed) {
                pool->replace((*pool)[t].l, child);
            } else {
                pool->replace((*pool)[t].r, child);
            }
        }
        pull(t);
        return t;
    }

    int find_node(int t, int pos) const {
        bool reversed = false;
        while (t != -1) {
            const Node& node = (*pool)[t];
            bool cur_reversed = reversed ^ node.rev;
            int l = cur_reversed ? node.r : node.l;
            int r = cur_reversed ? node.l : node.r;
            int left_count = subtree_size(l);
            if (pos < left_count) {
                t = l;
                reversed = cur_reversed;
            } else if (pos == left_count) {
                return t;
            } else {
                pos -= left_count + 1;
                t = r;
                reversed = cur_reversed;
            }
        }
        return -1;
    }

    T prod_dfs(int t, int ql, int qr, int offset, bool reversed = false) const {
        if (t == -1 || qr <= offset || offset + (*pool)[t].count <= ql) return Monoid::id();
        const Node& node = (*pool)[t];
        if (ql <= offset && offset + node.count <= qr) return reversed ? node.rprod : node.prod;
        bool cur_reversed = reversed ^ node.rev;
        int l = cur_reversed ? node.r : node.l;
        int r = cur_reversed ? node.l : node.r;
        int left_count = subtree_size(l);
        int node_pos = offset + left_count;
        T res = prod_dfs(l, ql, qr, offset, cur_reversed);
        if (ql <= node_pos && node_pos < qr) res = Monoid::op(res, node.val);
        return Monoid::op(res, prod_dfs(r, ql, qr, node_pos + 1, cur_reversed));
    }

    void dump_dfs(int t, std::vector<T>& res, bool reversed = false) const {
        if (t == -1) return;
        const Node& node = (*pool)[t];
        bool cur_reversed = reversed ^ node.rev;
        int l = cur_reversed ? node.r : node.l;
        int r = cur_reversed ? node.l : node.r;
        dump_dfs(l, res, cur_reversed);
        res.push_back(node.val);
        dump_dfs(r, res, cur_reversed);
    }

    void dump_range_dfs(int t, int ql, int qr, int offset, std::vector<T>& res, bool reversed = false) const {
        if (t == -1 || qr <= offset || offset + (*pool)[t].count <= ql) return;
        const Node& node = (*pool)[t];
        bool cur_reversed = reversed ^ node.rev;
        int l = cur_reversed ? node.r : node.l;
        int r = cur_reversed ? node.l : node.r;
        int left_count = subtree_size(l);
        int node_pos = offset + left_count;
        dump_range_dfs(l, ql, qr, offset, res, cur_reversed);
        if (ql <= node_pos && node_pos < qr) res.push_back(node.val);
        dump_range_dfs(r, ql, qr, node_pos + 1, res, cur_reversed);
    }

    int build_from_nodes(std::vector<BuildNode>& nodes, int t) const {
        if (t == -1) return -1;
        int l = build_from_nodes(nodes, nodes[t].l);
        int r = build_from_nodes(nodes, nodes[t].r);
        return make_node(std::move(nodes[t].val), nodes[t].priority, false, l, r);
    }

    int build_cartesian(std::vector<BuildNode>& nodes) const {
        if (nodes.empty()) return -1;
        std::vector<int> stack;
        stack.reserve(nodes.size());
        for (int i = 0; i < int(nodes.size()); i++) {
            int left_child = -1;
            while (!stack.empty() && nodes[stack.back()].priority < nodes[i].priority) {
                left_child = stack.back();
                stack.pop_back();
            }
            nodes[i].l = left_child;
            if (!stack.empty()) nodes[stack.back()].r = i;
            stack.push_back(i);
        }
        return build_from_nodes(nodes, stack.front());
    }

    int build_from_vector(const std::vector<T>& v, std::uint32_t& state) const {
        std::vector<BuildNode> nodes;
        nodes.reserve(v.size());
        for (const T& x : v) nodes.emplace_back(x, next_priority(state));
        return build_cartesian(nodes);
    }

    int build_from_vector(std::vector<T>&& v, std::uint32_t& state) const {
        std::vector<BuildNode> nodes;
        nodes.reserve(v.size());
        for (T& x : v) nodes.emplace_back(std::move(x), next_priority(state));
        return build_cartesian(nodes);
    }

    template <typename U>
    int build_from_values(const std::vector<U>& v, std::uint32_t& state) const {
        std::vector<BuildNode> nodes;
        nodes.reserve(v.size());
        for (const U& x : v) nodes.emplace_back(make_value(x), next_priority(state));
        return build_cartesian(nodes);
    }

    int import_node(const PersistentDynamicMonoidArray& other, int t) const {
        if (t == -1) return -1;
        if (pool == other.pool) return t;
        const Node& node = (*other.pool)[t];
        int l = import_node(other, node.l);
        int r = import_node(other, node.r);
        return make_node(node.val, node.priority, node.rev, l, r);
    }

    explicit PersistentDynamicMonoidArray(int node, std::uint32_t state,
                                          std::shared_ptr<Pool> node_pool)
        : root(node), rng_state(state), pool(std::move(node_pool)) {
        pool->retain(root);
    }

    PersistentDynamicMonoidArray make_version(int node, std::uint32_t state) const {
        PersistentDynamicMonoidArray result(node, state, pool);
        pool->discard_unreferenced();
        return result;
    }

   public:
    PersistentDynamicMonoidArray()
        : root(-1),
          rng_state(std::uint32_t(std::chrono::steady_clock::now().time_since_epoch().count())),
          pool(std::make_shared<Pool>()) {
        if (rng_state == 0) rng_state = 1;
    }

    explicit PersistentDynamicMonoidArray(int n) : PersistentDynamicMonoidArray(n, Monoid::id()) {}

    PersistentDynamicMonoidArray(int n, const T& value) : PersistentDynamicMonoidArray() {
        assert(0 <= n);
        pool->reserve(n);
        std::vector<T> v(n, value);
        root = build_from_vector(std::move(v), rng_state);
        pool->retain(root);
        pool->discard_unreferenced();
    }

    explicit PersistentDynamicMonoidArray(const std::vector<T>& v) : PersistentDynamicMonoidArray() {
        pool->reserve(v.size());
        root = build_from_vector(v, rng_state);
        pool->retain(root);
        pool->discard_unreferenced();
    }

    explicit PersistentDynamicMonoidArray(std::vector<T>&& v) : PersistentDynamicMonoidArray() {
        pool->reserve(v.size());
        root = build_from_vector(std::move(v), rng_state);
        pool->retain(root);
        pool->discard_unreferenced();
    }

    template <typename U>
        requires(!std::same_as<U, T>) && (requires(U x) { Monoid::make(x); } || std::convertible_to<U, T>)
    explicit PersistentDynamicMonoidArray(const std::vector<U>& v) : PersistentDynamicMonoidArray() {
        pool->reserve(v.size());
        root = build_from_values(v, rng_state);
        pool->retain(root);
        pool->discard_unreferenced();
    }

    PersistentDynamicMonoidArray(std::initializer_list<T> init)
        : PersistentDynamicMonoidArray(std::vector<T>(init)) {}

    PersistentDynamicMonoidArray(const PersistentDynamicMonoidArray& other)
        : root(other.root), rng_state(other.rng_state), pool(other.pool) {
        if (pool) pool->retain(root);
    }

    PersistentDynamicMonoidArray(PersistentDynamicMonoidArray&& other) noexcept
        : root(other.root), rng_state(other.rng_state), pool(std::move(other.pool)) {
        other.root = -1;
    }

    PersistentDynamicMonoidArray& operator=(const PersistentDynamicMonoidArray& other) {
        if (this == &other) return *this;
        if (other.pool) other.pool->retain(other.root);
        if (pool) pool->release(root);
        root = other.root;
        rng_state = other.rng_state;
        pool = other.pool;
        return *this;
    }

    PersistentDynamicMonoidArray& operator=(PersistentDynamicMonoidArray&& other) noexcept {
        if (this == &other) return *this;
        if (pool) pool->release(root);
        root = other.root;
        rng_state = other.rng_state;
        pool = std::move(other.pool);
        other.root = -1;
        return *this;
    }

    ~PersistentDynamicMonoidArray() {
        if (pool) pool->release(root);
    }

    int size() const {
        return subtree_size(root);
    }

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

    void release() {
        if (pool) pool->release(root);
        root = -1;
        pool = std::make_shared<Pool>();
    }

    std::size_t node_count() const { return pool ? pool->size() : 0; }

    PersistentDynamicMonoidArray clear() const {
        return make_version(-1, rng_state);
    }

    PersistentDynamicMonoidArray insert(int pos, T value) const {
        assert(0 <= pos && pos <= size());
        std::uint32_t next = next_state(rng_state);
        int node = make_node(std::move(value), int(next), false, -1, -1);
        auto [l, r] = split_node(root, pos);
        return make_version(merge(merge(l, node), r), next);
    }

    PersistentDynamicMonoidArray insert(int pos, const std::vector<T>& v) const {
        assert(0 <= pos && pos <= size());
        if (v.empty()) return *this;
        std::uint32_t next = rng_state;
        int mid = build_from_vector(v, next);
        auto [l, r] = split_node(root, pos);
        return make_version(merge(merge(l, mid), r), next);
    }

    PersistentDynamicMonoidArray insert(int pos, std::vector<T>&& v) const {
        assert(0 <= pos && pos <= size());
        if (v.empty()) return *this;
        std::uint32_t next = rng_state;
        int mid = build_from_vector(std::move(v), next);
        auto [l, r] = split_node(root, pos);
        return make_version(merge(merge(l, mid), r), next);
    }

    PersistentDynamicMonoidArray insert(int pos, std::initializer_list<T> init) const {
        return insert(pos, std::vector<T>(init));
    }

    PersistentDynamicMonoidArray insert(int pos, const PersistentDynamicMonoidArray& other) const {
        assert(0 <= pos && pos <= size());
        if (other.empty()) return *this;
        int mid = import_node(other, other.root);
        auto [l, r] = split_node(root, pos);
        return make_version(merge(merge(l, mid), r), rng_state);
    }

    PersistentDynamicMonoidArray push_back(T value) const {
        return insert(size(), std::move(value));
    }

    PersistentDynamicMonoidArray push_front(T value) const {
        return insert(0, std::move(value));
    }

    PersistentDynamicMonoidArray append(const std::vector<T>& v) const {
        return insert(size(), v);
    }

    PersistentDynamicMonoidArray append(std::vector<T>&& v) const {
        return insert(size(), std::move(v));
    }

    PersistentDynamicMonoidArray append(const PersistentDynamicMonoidArray& other) const {
        return insert(size(), other);
    }

    PersistentDynamicMonoidArray erase(int pos) const {
        assert(0 <= pos && pos < size());
        auto [a, b] = split_node(root, pos);
        auto [mid, c] = split_node(b, 1);
        (void)mid;
        return make_version(merge(a, c), rng_state);
    }

    PersistentDynamicMonoidArray erase(int l, int r) const {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return *this;
        auto [a, b] = split_node(root, l);
        auto [mid, c] = split_node(b, r - l);
        (void)mid;
        return make_version(merge(a, c), rng_state);
    }

    PersistentDynamicMonoidArray pop_back() const {
        assert(!empty());
        return erase(size() - 1);
    }

    PersistentDynamicMonoidArray pop_front() const {
        assert(!empty());
        return erase(0);
    }

    T get(int pos) const {
        assert(0 <= pos && pos < size());
        return (*pool)[find_node(root, pos)].val;
    }

    T operator[](int pos) const {
        return get(pos);
    }

    T front() const {
        assert(!empty());
        return get(0);
    }

    T back() const {
        assert(!empty());
        return get(size() - 1);
    }

    PersistentDynamicMonoidArray set(int pos, T value) const {
        assert(0 <= pos && pos < size());
        return make_version(set_node(root, pos, std::move(value)), rng_state);
    }

    void set_inplace(int pos, T value) {
        assert(0 <= pos && pos < size());
        int next_root = set_node_inplace(root, pos, std::move(value));
        pool->replace(root, next_root);
        pool->discard_unreferenced();
    }

    PersistentDynamicMonoidArray reverse(int l, int r) const {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return *this;
        auto [a, b] = split_node(root, l);
        auto [mid, c] = split_node(b, r - l);
        return make_version(merge(merge(a, reversed_node(mid)), c), rng_state);
    }

    PersistentDynamicMonoidArray reverse() const {
        return make_version(reversed_node(root), rng_state);
    }

    PersistentDynamicMonoidArray rotate(int l, int m, int r) const {
        assert(0 <= l && l <= m && m <= r && r <= size());
        if (l == m || m == r) return *this;
        auto [a, b] = split_node(root, l);
        auto [c, d] = split_node(b, m - l);
        auto [e, f] = split_node(d, r - m);
        return make_version(merge(merge(a, e), merge(c, f)), rng_state);
    }

    T prod(int l, int r) const {
        assert(0 <= l && l <= r && r <= size());
        if (l == r) return Monoid::id();
        return prod_dfs(root, l, r, 0);
    }

    T all_prod() const {
        return root == -1 ? Monoid::id() : (*pool)[root].prod;
    }

    std::pair<PersistentDynamicMonoidArray, PersistentDynamicMonoidArray> split(int pos) const {
        assert(0 <= pos && pos <= size());
        auto [l, r] = split_node(root, pos);
        PersistentDynamicMonoidArray left(l, rng_state, pool);
        PersistentDynamicMonoidArray right(r, rng_state, pool);
        pool->discard_unreferenced();
        return {std::move(left), std::move(right)};
    }

    PersistentDynamicMonoidArray split_off(int pos) const {
        assert(0 <= pos && pos <= size());
        return make_version(split_node(root, pos).second, rng_state);
    }

    std::vector<T> to_vector() const {
        std::vector<T> res;
        res.reserve(size());
        dump_dfs(root, res);
        return res;
    }

    std::vector<T> to_vector(int l, int r) const {
        assert(0 <= l && l <= r && r <= size());
        std::vector<T> res;
        res.reserve(r - l);
        dump_range_dfs(root, l, r, 0, res);
        return res;
    }
};

}  // namespace ds
}  // namespace m1une


#line 4 "verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp"

#include <algorithm>
#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#line 9 "utilities/fast_io.hpp"
#include <cstdio>
#include <cstdlib>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#include <iterator>
#include <string>
#include <sys/stat.h>
#include <type_traits>
#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 8 "verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp"
#include <numeric>
#include <random>
#line 13 "verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp"

#line 1 "monoid/add.hpp"



namespace m1une {
namespace monoid {

// Monoid for addition (Range Sum).
template <typename T>
struct Add {
    using value_type = T;
    static constexpr bool commutative = true;

    // Returns the identity element for addition, which is 0.
    static constexpr T id() {
        return T(0);
    }

    // Returns the sum of a and b.
    static constexpr T op(const T& a, const T& b) {
        return a + b;
    }

    static constexpr T inv(const T& x) {
        return -x;
    }
};

}  // namespace monoid
}  // namespace m1une


#line 15 "verify/ds/dynamic_array/persistent_dynamic_monoid_array.test.cpp"

struct StringMonoid {
    using value_type = std::string;

    static std::string id() {
        return "";
    }

    static std::string op(const std::string& a, const std::string& b) {
        return a + b;
    }
};

std::string join(const std::vector<std::string>& a, int l, int r) {
    std::string res;
    for (int i = l; i < r; i++) res += a[i];
    return res;
}

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

    using Array = m1une::ds::PersistentDynamicMonoidArray<StringMonoid>;

    Array a = {"a", "b", "c", "d", "e"};
    Array b = a.insert(2, "X");
    Array c = b.reverse(1, 5);
    Array d = c.rotate(1, 3, 6);
    Array e = d.set(0, "Z");
    Array f = e.erase(2);

    assert(a.to_vector() == (std::vector<std::string>{"a", "b", "c", "d", "e"}));
    assert(b.to_vector() == (std::vector<std::string>{"a", "b", "X", "c", "d", "e"}));
    assert(c.to_vector() == (std::vector<std::string>{"a", "d", "c", "X", "b", "e"}));
    assert(d.to_vector() == (std::vector<std::string>{"a", "X", "b", "e", "d", "c"}));
    assert(e.to_vector() == (std::vector<std::string>{"Z", "X", "b", "e", "d", "c"}));
    assert(f.to_vector() == (std::vector<std::string>{"Z", "X", "e", "d", "c"}));
    assert(c.prod(0, c.size()) == "adcXbe");
    assert(c.prod(1, 5) == "dcXb");
    assert(f.all_prod() == "ZXedc");
    assert(f.get(2) == "e");
    assert(f.front() == "Z");
    assert(f.back() == "c");

    auto [left, right] = f.split(2);
    assert(left.to_vector() == (std::vector<std::string>{"Z", "X"}));
    assert(right.to_vector() == (std::vector<std::string>{"e", "d", "c"}));
    assert(left.append(right).to_vector() == f.to_vector());
    assert(f.split_off(3).to_vector() == (std::vector<std::string>{"d", "c"}));
    assert(f.clear().empty());

    std::mt19937 rng(1);
    std::vector<std::pair<Array, std::vector<std::string>>> versions;
    versions.push_back({Array(), {}});
    for (int step = 0; step < 300; step++) {
        int id = int(rng() % versions.size());
        Array cur = versions[id].first;
        std::vector<std::string> expected = versions[id].second;
        assert(cur.to_vector() == expected);

        Array next = cur;
        std::vector<std::string> next_expected = expected;
        int op = int(rng() % 8);
        if (op == 0 || next_expected.empty()) {
            int pos = int(rng() % (next_expected.size() + 1));
            std::string value(1, char('a' + int(rng() % 26)));
            next = cur.insert(pos, value);
            next_expected.insert(next_expected.begin() + pos, value);
        } else if (op == 1) {
            int pos = int(rng() % next_expected.size());
            next = cur.erase(pos);
            next_expected.erase(next_expected.begin() + pos);
        } else if (op == 2) {
            int l = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > r) std::swap(l, r);
            next = cur.erase(l, r);
            next_expected.erase(next_expected.begin() + l, next_expected.begin() + r);
        } else if (op == 3) {
            int pos = int(rng() % next_expected.size());
            std::string value(1, char('A' + int(rng() % 26)));
            next = cur.set(pos, value);
            next_expected[pos] = value;
        } else if (op == 4) {
            int l = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > r) std::swap(l, r);
            next = cur.reverse(l, r);
            std::reverse(next_expected.begin() + l, next_expected.begin() + r);
        } else if (op == 5) {
            int l = int(rng() % (next_expected.size() + 1));
            int m = int(rng() % (next_expected.size() + 1));
            int r = int(rng() % (next_expected.size() + 1));
            if (l > m) std::swap(l, m);
            if (m > r) std::swap(m, r);
            if (l > m) std::swap(l, m);
            next = cur.rotate(l, m, r);
            std::rotate(next_expected.begin() + l, next_expected.begin() + m, next_expected.begin() + r);
        } else if (op == 6 && next_expected.size() < 80) {
            int other_id = int(rng() % versions.size());
            next = cur.append(versions[other_id].first);
            next_expected.insert(next_expected.end(), versions[other_id].second.begin(), versions[other_id].second.end());
        } else {
            next = cur.reverse();
            std::reverse(next_expected.begin(), next_expected.end());
        }

        assert(cur.to_vector() == expected);
        assert(next.to_vector() == next_expected);
        assert(next.all_prod() == join(next_expected, 0, int(next_expected.size())));
        for (int l = 0; l <= int(next_expected.size()); l++) {
            for (int r = l; r <= int(next_expected.size()); r++) {
                assert(next.prod(l, r) == join(next_expected, l, r));
            }
        }
        if (!next_expected.empty()) {
            int pos = int(rng() % next_expected.size());
            assert(next[pos] == next_expected[pos]);
        }
        int split_pos = int(rng() % (next_expected.size() + 1));
        auto [prefix, suffix] = next.split(split_pos);
        assert(prefix.to_vector() == std::vector<std::string>(next_expected.begin(), next_expected.begin() + split_pos));
        assert(suffix.to_vector() == std::vector<std::string>(next_expected.begin() + split_pos, next_expected.end()));

        if (next_expected.size() <= 100) versions.push_back({next, next_expected});
    }

    int size, query_count;
    fast_input >> size >> query_count;
    std::vector<long long> values(size);
    for (long long& value : values) fast_input >> value;

    using SumArray =
        m1une::ds::PersistentDynamicMonoidArray<m1une::monoid::Add<long long>>;
    SumArray current(values);
    while (query_count--) {
        int type, left_index, right_index;
        fast_input >> type >> left_index >> right_index;
        if (type == 0) {
            current = current.reverse(left_index, right_index);
        } else {
            fast_output << current.prod(left_index, right_index) << '\n';
        }
    }
}
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