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:heavy_check_mark: verify/utilities/random_generators.test.cpp

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Code

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

#include "../../utilities/random.hpp"

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

#ifndef NDEBUG
namespace {

struct Dsu {
    std::vector<int> parent;

    explicit Dsu(int size) : parent(size, -1) {}

    int leader(int vertex) {
        if (parent[vertex] < 0) return vertex;
        return parent[vertex] = leader(parent[vertex]);
    }

    bool merge(int first, int second) {
        first = leader(first);
        second = leader(second);
        if (first == second) return false;
        if (parent[second] < parent[first]) std::swap(first, second);
        parent[first] += parent[second];
        parent[second] = first;
        return true;
    }
};

void test_basic_generators() {
    m1une::utilities::Random first(123456);
    m1une::utilities::Random second(123456);
    assert(first.sequence(100, -10, 20) == second.sequence(100, -10, 20));
    assert(first.string(100, "abc") == second.string(100, "abc"));
    assert(first.permutation(100) == second.permutation(100));
    assert(first.tree(100) == second.tree(100));
    assert(first.graph(100, 300) == second.graph(100, 300));

    m1une::utilities::Random random(998244353);
    auto sequence = random.sequence(1000, -7LL, 11LL);
    assert(sequence.size() == 1000);
    for (long long value : sequence) assert(-7 <= value && value <= 11);

    std::string text = random.string(1000, "xyz");
    assert(text.size() == 1000);
    for (char character : text) assert(character == 'x' || character == 'y' || character == 'z');

    std::vector<int> permutation = random.permutation(100, 10);
    std::sort(permutation.begin(), permutation.end());
    for (int i = 0; i < 100; i++) assert(permutation[i] == i + 10);
}

void test_trees() {
    m1une::utilities::Random random(123);
    assert(random.tree(0).empty());
    assert(random.tree(1).empty());
    for (int size = 2; size <= 200; size++) {
        auto edges = random.tree(size);
        assert(int(edges.size()) == size - 1);
        Dsu dsu(size);
        for (auto [from, to] : edges) {
            assert(0 <= from && from < size);
            assert(0 <= to && to < size);
            assert(from != to);
            assert(dsu.merge(from, to));
        }
        int root = dsu.leader(0);
        for (int vertex = 1; vertex < size; vertex++) assert(dsu.leader(vertex) == root);
    }
}

void test_graphs() {
    m1une::utilities::Random random(456);
    for (int size = 2; size <= 50; size++) {
        int maximum = size * (size - 1) / 2;
        int edge_count = std::min(maximum, size * 3);
        auto edges = random.graph(size, edge_count);
        assert(int(edges.size()) == edge_count);
        std::set<std::pair<int, int>> unique;
        for (auto [from, to] : edges) {
            assert(0 <= from && from < to && to < size);
            unique.emplace(from, to);
        }
        assert(int(unique.size()) == edge_count);
    }

    auto complete = random.graph(20, 190);
    assert(complete.size() == 190);
    std::set<std::pair<int, int>> complete_unique(complete.begin(), complete.end());
    assert(complete_unique.size() == 190);

    auto directed = random.directed_graph(20, 300);
    std::set<std::pair<int, int>> directed_unique;
    for (auto [from, to] : directed) {
        assert(0 <= from && from < 20);
        assert(0 <= to && to < 20);
        assert(from != to);
        directed_unique.emplace(from, to);
    }
    assert(directed_unique.size() == directed.size());

    m1une::utilities::RandomGraphOptions options;
    options.allow_self_loops = true;
    auto looped_complete = random.graph(5, 15, options);
    std::set<std::pair<int, int>> looped_unique;
    for (auto [from, to] : looped_complete) {
        assert(0 <= from && from <= to && to < 5);
        looped_unique.emplace(from, to);
    }
    assert(looped_unique.size() == 15);

    options.directed = true;
    auto directed_looped_complete = random.graph(5, 25, options);
    std::set<std::pair<int, int>> directed_looped_unique(
        directed_looped_complete.begin(), directed_looped_complete.end());
    assert(directed_looped_unique.size() == 25);

    options.allow_parallel_edges = true;
    auto multigraph = random.graph(3, 1000, options);
    assert(multigraph.size() == 1000);
    for (auto [from, to] : multigraph) {
        assert(0 <= from && from < 3);
        assert(0 <= to && to < 3);
    }
}

void test_weighted_graphs_and_dags() {
    m1une::utilities::Random random(789);

    auto weighted_tree = random.weighted_tree(100, -50LL, 70LL);
    assert(weighted_tree.size() == 99);
    Dsu dsu(100);
    for (auto [from, to, weight] : weighted_tree) {
        assert(-50 <= weight && weight <= 70);
        assert(dsu.merge(from, to));
    }

    auto weighted_graph = random.weighted_graph(50, 300, -20, 30);
    assert(weighted_graph.size() == 300);
    std::set<std::pair<int, int>> graph_edges;
    for (auto [from, to, weight] : weighted_graph) {
        assert(0 <= from && from < to && to < 50);
        assert(-20 <= weight && weight <= 30);
        graph_edges.emplace(from, to);
    }
    assert(graph_edges.size() == 300);

    for (int size = 2; size <= 80; size++) {
        int maximum = size * (size - 1) / 2;
        int edge_count = std::min(maximum, size * 4);
        auto edges = random.dag(size, edge_count);
        assert(int(edges.size()) == edge_count);

        std::vector<std::vector<int>> adjacency(size);
        std::vector<int> indegree(size);
        std::set<std::pair<int, int>> unique;
        for (auto [from, to] : edges) {
            assert(0 <= from && from < size);
            assert(0 <= to && to < size);
            assert(from != to);
            adjacency[from].push_back(to);
            indegree[to]++;
            unique.emplace(from, to);
        }
        assert(int(unique.size()) == edge_count);

        std::vector<int> queue;
        for (int vertex = 0; vertex < size; vertex++) {
            if (indegree[vertex] == 0) queue.push_back(vertex);
        }
        for (int head = 0; head < int(queue.size()); head++) {
            for (int next : adjacency[queue[head]]) {
                if (--indegree[next] == 0) queue.push_back(next);
            }
        }
        assert(int(queue.size()) == size);
    }

    auto weighted_dag = random.weighted_dag(100, 500, 1U, 100U);
    assert(weighted_dag.size() == 500);
    for (auto [from, to, weight] : weighted_dag) {
        assert(0 <= from && from < 100);
        assert(0 <= to && to < 100);
        assert(from != to);
        assert(1 <= weight && weight <= 100);
    }

    m1une::utilities::RandomGraphOptions parallel_options;
    parallel_options.allow_parallel_edges = true;
    auto parallel_dag = random.dag(2, 100, parallel_options);
    assert(parallel_dag.size() == 100);
    for (auto edge : parallel_dag) assert(edge == parallel_dag.front());

    auto parallel_weighted_dag =
        random.weighted_dag(2, 100, -3, 7, parallel_options);
    assert(parallel_weighted_dag.size() == 100);
    for (auto [from, to, weight] : parallel_weighted_dag) {
        assert(from == std::get<0>(parallel_weighted_dag.front()));
        assert(to == std::get<1>(parallel_weighted_dag.front()));
        assert(-3 <= weight && weight <= 7);
    }

    parallel_options.allow_self_loops = true;
    auto parallel_directed = random.directed_graph(2, 100, parallel_options);
    assert(parallel_directed.size() == 100);
    auto parallel_weighted_directed =
        random.weighted_directed_graph(2, 100, 0LL, 10LL, parallel_options);
    assert(parallel_weighted_directed.size() == 100);
}

}  // namespace
#endif

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

#ifndef NDEBUG
    test_basic_generators();
    test_trees();
    test_graphs();
    test_weighted_graphs_and_dags();
#endif

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
#line 1 "verify/utilities/random_generators.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "utilities/random.hpp"



#include <algorithm>
#include <cassert>
#include <chrono>
#include <concepts>
#include <cstdint>
#include <functional>
#include <numeric>
#include <queue>
#include <random>
#include <string>
#include <string_view>
#include <tuple>
#include <type_traits>
#include <unordered_set>
#include <utility>
#include <vector>

namespace m1une {
namespace utilities {

struct RandomGraphOptions {
    bool directed = false;
    bool allow_self_loops = false;
    bool allow_parallel_edges = false;
};

struct Random {
   private:
    std::mt19937_64 _engine;

    static unsigned long long chrono_seed() {
        return static_cast<unsigned long long>(
            std::chrono::steady_clock::now().time_since_epoch().count());
    }

    static std::uint64_t graph_edge_count(int vertex_count,
                                          const RandomGraphOptions& options) {
        std::uint64_t n = static_cast<unsigned int>(vertex_count);
        if (options.directed) {
            return options.allow_self_loops ? n * n : n * (n - 1);
        }
        return options.allow_self_loops ? n * (n + 1) / 2 : n * (n - 1) / 2;
    }

    static std::pair<int, int> decode_graph_edge(
        std::uint64_t index, int vertex_count,
        const RandomGraphOptions& options) {
        std::uint64_t n = static_cast<unsigned int>(vertex_count);
        if (options.directed) {
            std::uint64_t width = options.allow_self_loops ? n : n - 1;
            int from = int(index / width);
            int offset = int(index % width);
            int to = options.allow_self_loops || offset < from ? offset : offset + 1;
            return {from, to};
        }

        auto prefix = [&](std::uint64_t vertex) {
            if (options.allow_self_loops) {
                return vertex * (2 * n - vertex + 1) / 2;
            }
            return vertex * (2 * n - vertex - 1) / 2;
        };
        std::uint64_t low = 0;
        std::uint64_t high = n;
        while (low + 1 < high) {
            std::uint64_t middle = (low + high) / 2;
            if (prefix(middle) <= index) {
                low = middle;
            } else {
                high = middle;
            }
        }
        int from = int(low);
        int to = from + int(index - prefix(low)) +
                 (options.allow_self_loops ? 0 : 1);
        return {from, to};
    }

   public:
    Random() : _engine(chrono_seed()) {}
    explicit Random(unsigned long long seed) : _engine(seed) {}

    void seed(unsigned long long value) {
        _engine.seed(value);
    }

    std::mt19937_64& engine() {
        return _engine;
    }

    unsigned long long operator()() {
        return _engine();
    }

    long long uniform(long long l, long long r) {
        return std::uniform_int_distribution<long long>(l, r)(_engine);
    }

    unsigned long long uniform_unsigned(unsigned long long l, unsigned long long r) {
        return std::uniform_int_distribution<unsigned long long>(l, r)(_engine);
    }

    double real(double l = 0.0, double r = 1.0) {
        return std::uniform_real_distribution<double>(l, r)(_engine);
    }

    template <std::integral T>
    requires(!std::same_as<std::remove_cv_t<T>, bool>)
    std::vector<T> sequence(int size, T lower, T upper) {
        assert(0 <= size);
        assert(lower <= upper);
        if (size < 0 || upper < lower) return {};
        std::vector<T> result(size);
        if constexpr (std::signed_integral<T>) {
            std::uniform_int_distribution<long long> distribution(
                static_cast<long long>(lower), static_cast<long long>(upper));
            for (T& value : result) value = static_cast<T>(distribution(_engine));
        } else {
            std::uniform_int_distribution<unsigned long long> distribution(
                static_cast<unsigned long long>(lower),
                static_cast<unsigned long long>(upper));
            for (T& value : result) value = static_cast<T>(distribution(_engine));
        }
        return result;
    }

    std::string string(
        int length,
        std::string_view alphabet = "abcdefghijklmnopqrstuvwxyz") {
        assert(0 <= length);
        assert(length == 0 || !alphabet.empty());
        if (length < 0 || (0 < length && alphabet.empty())) return {};
        std::string result(length, '\0');
        for (char& character : result) {
            character = alphabet[uniform(0, int(alphabet.size()) - 1)];
        }
        return result;
    }

    std::vector<int> permutation(int size, int first = 0) {
        assert(0 <= size);
        if (size < 0) return {};
        std::vector<int> result(size);
        std::iota(result.begin(), result.end(), first);
        shuffle(result);
        return result;
    }

    // Returns the edges of a uniformly random labeled tree on [0, size).
    std::vector<std::pair<int, int>> tree(int size) {
        assert(0 <= size);
        if (size <= 1) return {};

        std::vector<int> prufer = sequence(size - 2, 0, size - 1);
        std::vector<int> degree(size, 1);
        for (int vertex : prufer) degree[vertex]++;
        std::priority_queue<int, std::vector<int>, std::greater<int>> leaves;
        for (int vertex = 0; vertex < size; vertex++) {
            if (degree[vertex] == 1) leaves.push(vertex);
        }

        std::vector<std::pair<int, int>> edges;
        edges.reserve(size - 1);
        for (int vertex : prufer) {
            int leaf = leaves.top();
            leaves.pop();
            edges.emplace_back(leaf, vertex);
            if (--degree[vertex] == 1) leaves.push(vertex);
        }
        int first = leaves.top();
        leaves.pop();
        edges.emplace_back(first, leaves.top());

        shuffle(edges);
        for (auto& [from, to] : edges) {
            if (uniform(0, 1)) std::swap(from, to);
        }
        return edges;
    }

    // Returns m random edges on [0, vertex_count). By default the result is
    // a simple undirected graph without self-loops.
    std::vector<std::pair<int, int>> graph(
        int vertex_count, int edge_count,
        RandomGraphOptions options = {}) {
        assert(0 <= vertex_count);
        assert(0 <= edge_count);
        if (vertex_count < 0 || edge_count < 0) return {};
        if (edge_count == 0) return {};
        assert(0 < vertex_count);
        if (vertex_count == 0) return {};
        if (!options.allow_self_loops) {
            assert(2 <= vertex_count || edge_count == 0);
            if (vertex_count < 2) return {};
        }

        std::vector<std::pair<int, int>> edges;
        edges.reserve(edge_count);
        if (options.allow_parallel_edges) {
            for (int edge = 0; edge < edge_count; edge++) {
                int from = int(uniform(0, vertex_count - 1));
                int to;
                if (options.allow_self_loops) {
                    to = int(uniform(0, vertex_count - 1));
                } else {
                    to = int(uniform(0, vertex_count - 2));
                    if (from <= to) to++;
                }
                if (!options.directed && to < from) std::swap(from, to);
                edges.emplace_back(from, to);
            }
            return edges;
        }

        std::uint64_t maximum = graph_edge_count(vertex_count, options);
        assert(static_cast<std::uint64_t>(edge_count) <= maximum);
        if (maximum < static_cast<std::uint64_t>(edge_count)) return {};

        std::unordered_set<std::uint64_t> selected;
        selected.reserve(static_cast<std::size_t>(edge_count) * 2 + 1);
        std::vector<std::uint64_t> indices;
        indices.reserve(edge_count);
        for (std::uint64_t current = maximum - edge_count;
             current < maximum; current++) {
            std::uint64_t candidate = uniform_unsigned(0, current);
            if (selected.contains(candidate)) candidate = current;
            selected.insert(candidate);
            indices.push_back(candidate);
        }
        for (std::uint64_t index : indices) {
            edges.push_back(decode_graph_edge(index, vertex_count, options));
        }
        return edges;
    }

    std::vector<std::pair<int, int>> directed_graph(
        int vertex_count, int edge_count,
        bool allow_self_loops = false) {
        RandomGraphOptions options;
        options.allow_self_loops = allow_self_loops;
        return directed_graph(vertex_count, edge_count, options);
    }

    std::vector<std::pair<int, int>> directed_graph(
        int vertex_count, int edge_count, RandomGraphOptions options) {
        options.directed = true;
        return graph(vertex_count, edge_count, options);
    }

    // Returns a directed acyclic graph. Vertices are randomly permuted before
    // every sampled edge is directed forward in that topological order.
    std::vector<std::pair<int, int>> dag(
        int vertex_count, int edge_count,
        RandomGraphOptions options = {}) {
        options.directed = false;
        options.allow_self_loops = false;
        std::vector<std::pair<int, int>> edges =
            graph(vertex_count, edge_count, options);
        std::vector<int> order = permutation(vertex_count);
        for (auto& [from, to] : edges) {
            from = order[from];
            to = order[to];
        }
        return edges;
    }

    template <std::integral Weight>
    requires(!std::same_as<std::remove_cv_t<Weight>, bool>)
    std::vector<std::tuple<int, int, Weight>> weighted_tree(
        int size, Weight lower, Weight upper) {
        std::vector<std::pair<int, int>> edges = tree(size);
        std::vector<Weight> weights = sequence(int(edges.size()), lower, upper);
        std::vector<std::tuple<int, int, Weight>> result;
        result.reserve(edges.size());
        for (int index = 0; index < int(edges.size()); index++) {
            result.emplace_back(edges[index].first, edges[index].second,
                                weights[index]);
        }
        return result;
    }

    template <std::integral Weight>
    requires(!std::same_as<std::remove_cv_t<Weight>, bool>)
    std::vector<std::tuple<int, int, Weight>> weighted_graph(
        int vertex_count, int edge_count, Weight lower, Weight upper,
        RandomGraphOptions options = {}) {
        std::vector<std::pair<int, int>> edges =
            graph(vertex_count, edge_count, options);
        std::vector<Weight> weights = sequence(int(edges.size()), lower, upper);
        std::vector<std::tuple<int, int, Weight>> result;
        result.reserve(edges.size());
        for (int index = 0; index < int(edges.size()); index++) {
            result.emplace_back(edges[index].first, edges[index].second,
                                weights[index]);
        }
        return result;
    }

    template <std::integral Weight>
    requires(!std::same_as<std::remove_cv_t<Weight>, bool>)
    std::vector<std::tuple<int, int, Weight>> weighted_directed_graph(
        int vertex_count, int edge_count, Weight lower, Weight upper,
        bool allow_self_loops = false) {
        RandomGraphOptions options;
        options.allow_self_loops = allow_self_loops;
        return weighted_directed_graph(vertex_count, edge_count, lower, upper,
                                       options);
    }

    template <std::integral Weight>
    requires(!std::same_as<std::remove_cv_t<Weight>, bool>)
    std::vector<std::tuple<int, int, Weight>> weighted_directed_graph(
        int vertex_count, int edge_count, Weight lower, Weight upper,
        RandomGraphOptions options) {
        options.directed = true;
        return weighted_graph(vertex_count, edge_count, lower, upper, options);
    }

    template <std::integral Weight>
    requires(!std::same_as<std::remove_cv_t<Weight>, bool>)
    std::vector<std::tuple<int, int, Weight>> weighted_dag(
        int vertex_count, int edge_count, Weight lower, Weight upper,
        RandomGraphOptions options = {}) {
        std::vector<std::pair<int, int>> edges =
            dag(vertex_count, edge_count, options);
        std::vector<Weight> weights = sequence(int(edges.size()), lower, upper);
        std::vector<std::tuple<int, int, Weight>> result;
        result.reserve(edges.size());
        for (int index = 0; index < int(edges.size()); index++) {
            result.emplace_back(edges[index].first, edges[index].second,
                                weights[index]);
        }
        return result;
    }

    template <typename T>
    void shuffle(std::vector<T>& v) {
        std::shuffle(v.begin(), v.end(), _engine);
    }

    template <typename Iterator>
    void shuffle(Iterator first, Iterator last) {
        std::shuffle(first, last, _engine);
    }

    template <typename T>
    const T& choice(const std::vector<T>& v) {
        return v[uniform(0, static_cast<long long>(v.size()) - 1)];
    }
};

}  // namespace utilities
}  // namespace m1une


#line 4 "verify/utilities/random_generators.test.cpp"

#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#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/utilities/random_generators.test.cpp"
#include <set>
#line 14 "verify/utilities/random_generators.test.cpp"

#ifndef NDEBUG
namespace {

struct Dsu {
    std::vector<int> parent;

    explicit Dsu(int size) : parent(size, -1) {}

    int leader(int vertex) {
        if (parent[vertex] < 0) return vertex;
        return parent[vertex] = leader(parent[vertex]);
    }

    bool merge(int first, int second) {
        first = leader(first);
        second = leader(second);
        if (first == second) return false;
        if (parent[second] < parent[first]) std::swap(first, second);
        parent[first] += parent[second];
        parent[second] = first;
        return true;
    }
};

void test_basic_generators() {
    m1une::utilities::Random first(123456);
    m1une::utilities::Random second(123456);
    assert(first.sequence(100, -10, 20) == second.sequence(100, -10, 20));
    assert(first.string(100, "abc") == second.string(100, "abc"));
    assert(first.permutation(100) == second.permutation(100));
    assert(first.tree(100) == second.tree(100));
    assert(first.graph(100, 300) == second.graph(100, 300));

    m1une::utilities::Random random(998244353);
    auto sequence = random.sequence(1000, -7LL, 11LL);
    assert(sequence.size() == 1000);
    for (long long value : sequence) assert(-7 <= value && value <= 11);

    std::string text = random.string(1000, "xyz");
    assert(text.size() == 1000);
    for (char character : text) assert(character == 'x' || character == 'y' || character == 'z');

    std::vector<int> permutation = random.permutation(100, 10);
    std::sort(permutation.begin(), permutation.end());
    for (int i = 0; i < 100; i++) assert(permutation[i] == i + 10);
}

void test_trees() {
    m1une::utilities::Random random(123);
    assert(random.tree(0).empty());
    assert(random.tree(1).empty());
    for (int size = 2; size <= 200; size++) {
        auto edges = random.tree(size);
        assert(int(edges.size()) == size - 1);
        Dsu dsu(size);
        for (auto [from, to] : edges) {
            assert(0 <= from && from < size);
            assert(0 <= to && to < size);
            assert(from != to);
            assert(dsu.merge(from, to));
        }
        int root = dsu.leader(0);
        for (int vertex = 1; vertex < size; vertex++) assert(dsu.leader(vertex) == root);
    }
}

void test_graphs() {
    m1une::utilities::Random random(456);
    for (int size = 2; size <= 50; size++) {
        int maximum = size * (size - 1) / 2;
        int edge_count = std::min(maximum, size * 3);
        auto edges = random.graph(size, edge_count);
        assert(int(edges.size()) == edge_count);
        std::set<std::pair<int, int>> unique;
        for (auto [from, to] : edges) {
            assert(0 <= from && from < to && to < size);
            unique.emplace(from, to);
        }
        assert(int(unique.size()) == edge_count);
    }

    auto complete = random.graph(20, 190);
    assert(complete.size() == 190);
    std::set<std::pair<int, int>> complete_unique(complete.begin(), complete.end());
    assert(complete_unique.size() == 190);

    auto directed = random.directed_graph(20, 300);
    std::set<std::pair<int, int>> directed_unique;
    for (auto [from, to] : directed) {
        assert(0 <= from && from < 20);
        assert(0 <= to && to < 20);
        assert(from != to);
        directed_unique.emplace(from, to);
    }
    assert(directed_unique.size() == directed.size());

    m1une::utilities::RandomGraphOptions options;
    options.allow_self_loops = true;
    auto looped_complete = random.graph(5, 15, options);
    std::set<std::pair<int, int>> looped_unique;
    for (auto [from, to] : looped_complete) {
        assert(0 <= from && from <= to && to < 5);
        looped_unique.emplace(from, to);
    }
    assert(looped_unique.size() == 15);

    options.directed = true;
    auto directed_looped_complete = random.graph(5, 25, options);
    std::set<std::pair<int, int>> directed_looped_unique(
        directed_looped_complete.begin(), directed_looped_complete.end());
    assert(directed_looped_unique.size() == 25);

    options.allow_parallel_edges = true;
    auto multigraph = random.graph(3, 1000, options);
    assert(multigraph.size() == 1000);
    for (auto [from, to] : multigraph) {
        assert(0 <= from && from < 3);
        assert(0 <= to && to < 3);
    }
}

void test_weighted_graphs_and_dags() {
    m1une::utilities::Random random(789);

    auto weighted_tree = random.weighted_tree(100, -50LL, 70LL);
    assert(weighted_tree.size() == 99);
    Dsu dsu(100);
    for (auto [from, to, weight] : weighted_tree) {
        assert(-50 <= weight && weight <= 70);
        assert(dsu.merge(from, to));
    }

    auto weighted_graph = random.weighted_graph(50, 300, -20, 30);
    assert(weighted_graph.size() == 300);
    std::set<std::pair<int, int>> graph_edges;
    for (auto [from, to, weight] : weighted_graph) {
        assert(0 <= from && from < to && to < 50);
        assert(-20 <= weight && weight <= 30);
        graph_edges.emplace(from, to);
    }
    assert(graph_edges.size() == 300);

    for (int size = 2; size <= 80; size++) {
        int maximum = size * (size - 1) / 2;
        int edge_count = std::min(maximum, size * 4);
        auto edges = random.dag(size, edge_count);
        assert(int(edges.size()) == edge_count);

        std::vector<std::vector<int>> adjacency(size);
        std::vector<int> indegree(size);
        std::set<std::pair<int, int>> unique;
        for (auto [from, to] : edges) {
            assert(0 <= from && from < size);
            assert(0 <= to && to < size);
            assert(from != to);
            adjacency[from].push_back(to);
            indegree[to]++;
            unique.emplace(from, to);
        }
        assert(int(unique.size()) == edge_count);

        std::vector<int> queue;
        for (int vertex = 0; vertex < size; vertex++) {
            if (indegree[vertex] == 0) queue.push_back(vertex);
        }
        for (int head = 0; head < int(queue.size()); head++) {
            for (int next : adjacency[queue[head]]) {
                if (--indegree[next] == 0) queue.push_back(next);
            }
        }
        assert(int(queue.size()) == size);
    }

    auto weighted_dag = random.weighted_dag(100, 500, 1U, 100U);
    assert(weighted_dag.size() == 500);
    for (auto [from, to, weight] : weighted_dag) {
        assert(0 <= from && from < 100);
        assert(0 <= to && to < 100);
        assert(from != to);
        assert(1 <= weight && weight <= 100);
    }

    m1une::utilities::RandomGraphOptions parallel_options;
    parallel_options.allow_parallel_edges = true;
    auto parallel_dag = random.dag(2, 100, parallel_options);
    assert(parallel_dag.size() == 100);
    for (auto edge : parallel_dag) assert(edge == parallel_dag.front());

    auto parallel_weighted_dag =
        random.weighted_dag(2, 100, -3, 7, parallel_options);
    assert(parallel_weighted_dag.size() == 100);
    for (auto [from, to, weight] : parallel_weighted_dag) {
        assert(from == std::get<0>(parallel_weighted_dag.front()));
        assert(to == std::get<1>(parallel_weighted_dag.front()));
        assert(-3 <= weight && weight <= 7);
    }

    parallel_options.allow_self_loops = true;
    auto parallel_directed = random.directed_graph(2, 100, parallel_options);
    assert(parallel_directed.size() == 100);
    auto parallel_weighted_directed =
        random.weighted_directed_graph(2, 100, 0LL, 10LL, parallel_options);
    assert(parallel_weighted_directed.size() == 100);
}

}  // namespace
#endif

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

#ifndef NDEBUG
    test_basic_generators();
    test_trees();
    test_graphs();
    test_weighted_graphs_and_dags();
#endif

    long long a, b;
    fast_input >> a >> b;
    fast_output << a + b << '\n';
}
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