verify/utilities/random_testing.test.cpp

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• Last update: 2026-10-06 01:57:24+09:00
• Problem: https://judge.yosupo.jp/problem/aplusb

Depends on

• Fast IO (utilities/fast_io.hpp)
• Random (utilities/random.hpp)
• Random Testing (utilities/random_testing.hpp)

Code

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

#include "../../utilities/random_testing.hpp"

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

#ifndef NDEBUG
void test_properties() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 100;
    config.seed = 12345;
    RandomTestResult success = random_test(config, [](Random& random) {
        long long value = random.uniform(-1000, 1000);
        return value * value >= 0;
    });
    assert(success.passed());
    assert(bool(success));
    assert(success.completed_trials == 100);
    assert(success.failed_trial == -1);
    assert(success.seed == config.seed);

    RandomTestResult failure = random_test(
        config, [](Random&, int trial) { return trial != 17; });
    assert(!failure.passed());
    assert(!bool(failure));
    assert(failure.completed_trials == 17);
    assert(failure.failed_trial == 17);
    assert(failure.failure == RandomTestFailure::property);

    auto shorthand = random_test([](Random&, int trial) { return trial < 1000; });
    assert(shorthand.passed());
    auto required = stress_test(
        [](Random&, int trial) { return trial < 25; }, 25, 777);
    assert(required.passed());
    assert(required.seed == 777);
}

void test_comparison() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 500;
    config.seed = 67890;
    auto success = compare_randomly(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 20));
            std::vector<int> values(size);
            for (int& value : values) value = int(random.uniform(-20, 20));
            return values;
        },
        [](std::vector<int>& values) {
            std::sort(values.begin(), values.end());
            return values;
        },
        [](std::vector<int>& values) {
            for (int i = 0; i < int(values.size()); i++) {
                for (int j = i + 1; j < int(values.size()); j++) {
                    if (values[j] < values[i]) std::swap(values[i], values[j]);
                }
            }
            return values;
        });
    assert(success.passed());

    auto mutation_isolated = compare_randomly(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 20));
            std::vector<int> values(size);
            for (int& value : values) value = int(random.uniform(-20, 20));
            return values;
        },
        [](std::vector<int>& values) {
            int sum = std::accumulate(values.begin(), values.end(), 0);
            values.clear();
            return sum;
        },
        [](std::vector<int>& values) {
            return std::accumulate(values.begin(), values.end(), 0);
        });
    assert(mutation_isolated.passed());

    auto quick = stress_test(
        [](Random& random) { return int(random.uniform(-10, 10)); },
        [](int& value) { return value * value; },
        [](int& value) {
            int magnitude = value < 0 ? -value : value;
            int result = 0;
            for (int i = 0; i < magnitude; i++) result += magnitude;
            return result;
        },
        50, 999);
    assert(quick.passed());

    int callback_count = 0;
    int callback_trial = -1;
    int callback_case = -1;
    int callback_expected = -1;
    int callback_actual = -1;
    std::uint64_t callback_seed = 0;
    auto failure = compare_randomly(
        config,
        [](Random&, int trial) { return trial; },
        [](int& value) { return value == 23 ? value + 1 : value; },
        [](int& value) { return value; },
        [&](int input, int expected, int actual, int trial,
            std::uint64_t seed) {
            callback_count++;
            callback_trial = trial;
            callback_case = input;
            callback_expected = expected;
            callback_actual = actual;
            callback_seed = seed;
        });
    assert(failure.failed_trial == 23);
    assert(failure.failure == RandomTestFailure::mismatch);
    assert(callback_count == 1);
    assert(callback_trial == 23);
    assert(callback_case == 23);
    assert(callback_expected == 23);
    assert(callback_actual == 24);
    assert(callback_seed == config.seed);

    RandomTestConfig empty_config;
    empty_config.trials = 0;
    auto empty = random_test(empty_config, [](Random&) { return false; });
    assert(empty.passed());
    assert(empty.completed_trials == 0);
}

void test_constructive() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 200;
    config.seed = 13579;
    auto success = test_constructively(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 30));
            return random.sequence(size, -20, 20);
        },
        [](std::vector<int>& values) {
            std::vector<int> order(values.size());
            std::iota(order.begin(), order.end(), 0);
            std::sort(order.begin(), order.end(), [&](int first, int second) {
                return values[first] < values[second];
            });
            values.clear();
            return order;
        },
        [](const std::vector<int>& values, const std::vector<int>& order) {
            if (values.size() != order.size()) return false;
            std::vector<bool> used(values.size());
            for (int index = 0; index < int(order.size()); index++) {
                if (order[index] < 0 || int(values.size()) <= order[index]) {
                    return false;
                }
                if (used[order[index]]) return false;
                used[order[index]] = true;
                if (0 < index &&
                    values[order[index]] < values[order[index - 1]]) {
                    return false;
                }
            }
            return true;
        });
    assert(success.passed());

    int callback_count = 0;
    auto failure = test_constructively(
        config, [](Random&, int trial) { return trial + 1; },
        [](int& value) { return value == 8 ? 0 : value; },
        [](int input, int answer) { return input == answer; },
        [&](int input, int answer, int trial, std::uint64_t seed) {
            callback_count++;
            assert(input == 8);
            assert(answer == 0);
            assert(trial == 7);
            assert(seed == config.seed);
        });
    assert(failure.failed_trial == 7);
    assert(failure.failure == RandomTestFailure::rejected_output);
    assert(callback_count == 1);

    auto quick = constructive_stress_test(
        [](Random& random) { return int(random.uniform(0, 100)); },
        [](int& value) { return value; },
        [](const int& input, const int& answer) { return input == answer; },
        20, 97531);
    assert(quick.passed());
}

void test_interactive() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 300;
    config.seed = 24680;
    auto success = test_interactively(
        config, 10,
        [](Random& random) {
            int upper = int(random.uniform(1, 1000));
            int secret = int(random.uniform(0, upper));
            return interactive_test_case(upper, secret);
        },
        [](const int& upper, auto& interaction) {
            int low = 0;
            int high = upper;
            while (low < high) {
                int middle = (low + high) / 2;
                int comparison = interaction.ask(middle);
                if (comparison <= 0) {
                    high = middle;
                } else {
                    low = middle + 1;
                }
            }
            return low;
        },
        [](int& secret, int guess) {
            if (guess < 0) reject_query("negative guess");
            if (secret < guess) return -1;
            if (guess < secret) return 1;
            return 0;
        },
        [](const int& upper, const int& secret, const int& answer) {
            return 0 <= answer && answer <= upper && answer == secret;
        });
    assert(success.passed());

    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 112233;
    int callback_count = 0;
    auto invalid = test_interactively(
        one_trial, 5,
        [](Random&) { return interactive_test_case(10, 4); },
        [](const int&, auto& interaction) {
            interaction.ask(-1);
            return 0;
        },
        [](int&, int query) {
            if (query < 0) reject_query("query is outside [0, 10]");
            return 0;
        },
        [](const int&, const int&, const int&) { return true; },
        [&](const auto&, const InteractionTranscript& transcript, int trial,
            std::uint64_t seed, RandomTestFailure reason) {
            callback_count++;
            assert(trial == 0);
            assert(seed == one_trial.seed);
            assert(reason == RandomTestFailure::invalid_query);
            assert(transcript.exchanges.size() == 1);
            assert(transcript.exchanges[0].query == "-1");
            assert(!transcript.exchanges[0].responded);
            assert(transcript.failure_message ==
                   "query is outside [0, 10]");
        });
    assert(invalid.failure == RandomTestFailure::invalid_query);
    assert(invalid.query_count == 1);
    assert(callback_count == 1);

    auto too_many_queries = test_interactively(
        one_trial, 1,
        [](Random&) { return interactive_test_case(0, 0); },
        [](auto& interaction) {
            interaction.ask(1);
            interaction.ask(2);
            return 0;
        },
        [](int&, int query) { return query; },
        [](const int&, const int&, const int&) { return true; });
    assert(too_many_queries.failure == RandomTestFailure::query_limit);
    assert(too_many_queries.query_count == 2);

    auto wrong_answer = test_interactively(
        one_trial, 0,
        [](Random&) { return interactive_test_case(10, 7); },
        [](const int&, auto&) { return 6; },
        [](int&, int query) { return query; },
        [](const int&, const int& secret, const int& answer) {
            return secret == answer;
        });
    assert(wrong_answer.failure == RandomTestFailure::rejected_output);
    assert(wrong_answer.query_count == 0);

    auto quick = interactive_stress_test(
        0,
        [](Random& random) {
            int value = int(random.uniform(-100, 100));
            return interactive_test_case(value, value);
        },
        [](const int& input, auto&) { return input; },
        [](int&, int query) { return query; },
        [](const int&, const int& state, const int& answer) {
            return state == answer;
        },
        20, 86420);
    assert(quick.passed());
}

void test_stream_interface() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 200;
    config.seed = 424242;
    auto generate = [](Random& random, std::ostream& input) {
        int size = int(random.uniform(0, 30));
        input << size << '\n';
        for (int value : random.sequence(size, -20, 20)) {
            input << value << ' ';
        }
        input << '\n';
    };
    auto solve = [] {
        int size;
        std::cin >> size;
        std::vector<int> values(size);
        for (int& value : values) std::cin >> value;
        std::sort(values.begin(), values.end());
        for (int value : values) std::cout << value << ' ';
        std::cout << '\n';
    };
    auto check = [](std::istream& input, std::istream& output) {
        int size;
        input >> size;
        std::vector<int> expected(size);
        for (int& value : expected) input >> value;
        std::sort(expected.begin(), expected.end());
        std::vector<int> actual(size);
        for (int& value : actual) {
            if (!(output >> value)) return false;
        }
        std::string extra;
        return expected == actual && !(output >> extra);
    };
    auto success = test_streams(config, generate, solve, check);
    assert(success.passed());

    int callback_count = 0;
    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 515151;
    auto failure = test_streams(
        one_trial,
        [](Random&, std::ostream& input) { input << "3\n1 2 3\n"; },
        [] {
            int size;
            std::cin >> size;
            std::cout << size - 1 << '\n';
        },
        [](std::istream&, std::istream& output) {
            int answer;
            return bool(output >> answer) && answer == 3;
        },
        [&](const std::string& input, const std::string& output, int trial,
            std::uint64_t seed) {
            callback_count++;
            assert(input == "3\n1 2 3\n");
            assert(output == "2\n");
            assert(trial == 0);
            assert(seed == one_trial.seed);
        });
    assert(failure.failure == RandomTestFailure::rejected_output);
    assert(callback_count == 1);

    auto quick = stream_stress_test(generate, solve, check, 20, 616161);
    assert(quick.passed());
}

void test_interactive_stream_interface() {
    using namespace m1une::utilities;

    auto generate = [](Random& random, std::ostream& input) {
        int upper = int(random.uniform(1, 1000));
        input << upper << '\n';
        return int(random.uniform(0, upper));
    };
    auto solve = [] {
        int upper;
        std::cin >> upper;
        int low = 0;
        int high = upper;
        while (low < high) {
            int middle = (low + high) / 2;
            std::cout << "? " << middle << std::endl;
            int comparison;
            std::cin >> comparison;
            if (comparison <= 0) high = middle;
            else low = middle + 1;
        }
        std::cout << "! " << low << std::endl;
    };
    auto reply = [](int& secret, std::istream& query,
                    std::ostream& response) {
        char type;
        int guess;
        std::string extra;
        if (!(query >> type >> guess) || type != '?' || query >> extra) {
            reject_query("expected: ? x");
        }
        if (secret < guess) response << -1;
        else if (guess < secret) response << 1;
        else response << 0;
    };
    auto check = [](std::istream& input, const int& secret,
                    std::istream& output) {
        int upper;
        char type;
        int answer;
        std::string extra;
        input >> upper;
        return bool(output >> type >> answer) && type == '!' &&
               0 <= answer && answer <= upper && answer == secret &&
               !(output >> extra);
    };

    auto success = interactive_stream_stress_test(
        10, generate, solve, reply, check, 200, 717171);
    assert(success.passed());

    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 818181;
    int callback_count = 0;
    auto invalid = test_interactive_streams(
        one_trial, 1,
        [](Random&, std::ostream& input) {
            input << "10\n";
            return 5;
        },
        [] {
            int upper;
            std::cin >> upper;
            std::cout << "invalid query" << std::endl;
            int response;
            std::cin >> response;
        },
        reply, check,
        [&](const std::string& input, const int& state,
            const InteractionTranscript& transcript, int trial,
            std::uint64_t seed, RandomTestFailure reason) {
            callback_count++;
            assert(input == "10\n");
            assert(state == 5);
            assert(transcript.exchanges.size() == 1);
            assert(transcript.exchanges[0].query == "invalid query");
            assert(!transcript.exchanges[0].responded);
            assert(transcript.failure_message == "expected: ? x");
            assert(trial == 0);
            assert(seed == one_trial.seed);
            assert(reason == RandomTestFailure::invalid_query);
        });
    assert(invalid.failure == RandomTestFailure::invalid_query);
    assert(invalid.query_count == 1);
    assert(callback_count == 1);

    auto query_limit = test_interactive_streams(
        one_trial, 0,
        [](Random&, std::ostream& input) {
            input << "10\n";
            return 5;
        },
        [] {
            int upper;
            std::cin >> upper;
            std::cout << "? 5" << std::endl;
            int response;
            std::cin >> response;
        },
        reply, check);
    assert(query_limit.failure == RandomTestFailure::query_limit);
    assert(query_limit.query_count == 1);
}
#endif

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

#ifndef NDEBUG
    test_properties();
    test_comparison();
    test_constructive();
    test_interactive();
    test_stream_interface();
    test_interactive_stream_interface();
#endif

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

#line 1 "verify/utilities/random_testing.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 1 "utilities/random_testing.hpp"



#include <cassert>
#include <concepts>
#include <cstdint>
#include <cstdlib>
#include <exception>
#include <functional>
#include <iostream>
#include <iterator>
#include <sstream>
#include <string>
#include <tuple>
#include <type_traits>
#include <utility>
#include <vector>

#line 1 "utilities/random.hpp"



#include <algorithm>
#line 6 "utilities/random.hpp"
#include <chrono>
#line 10 "utilities/random.hpp"
#include <numeric>
#include <queue>
#include <random>
#line 14 "utilities/random.hpp"
#include <string_view>
#line 17 "utilities/random.hpp"
#include <unordered_set>
#line 20 "utilities/random.hpp"

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 20 "utilities/random_testing.hpp"

namespace m1une {
namespace utilities {

inline constexpr std::uint64_t default_random_test_seed =
    0x243f6a8885a308d3ULL;

struct RandomTestConfig {
    int trials = 1000;
    std::uint64_t seed = default_random_test_seed;
};

enum class RandomTestFailure {
    none,
    property,
    mismatch,
    rejected_output,
    query_limit,
    invalid_query,
};

inline const char* random_test_failure_name(RandomTestFailure failure) {
    switch (failure) {
        case RandomTestFailure::none:
            return "none";
        case RandomTestFailure::property:
            return "property";
        case RandomTestFailure::mismatch:
            return "mismatch";
        case RandomTestFailure::rejected_output:
            return "rejected output";
        case RandomTestFailure::query_limit:
            return "query limit exceeded";
        case RandomTestFailure::invalid_query:
            return "invalid query";
    }
    return "unknown";
}

struct RandomTestResult {
    std::uint64_t seed = 0;
    int requested_trials = 0;
    int completed_trials = 0;
    int failed_trial = -1;
    RandomTestFailure failure = RandomTestFailure::none;
    int query_count = -1;

    bool passed() const {
        return failed_trial == -1;
    }

    explicit operator bool() const {
        return passed();
    }
};

struct IgnoreRandomTestFailure {
    template <class... Args>
    void operator()(Args&&...) const {}
};

struct InteractionExchange {
    std::string query;
    std::string response;
    bool responded = false;
};

struct InteractionTranscript {
    std::vector<InteractionExchange> exchanges;
    std::string answer;
    bool answered = false;
    std::string failure_message;
};

namespace random_testing_detail {

template <class T>
void print_value(std::ostream& output, const T& value) {
    if constexpr (requires { output << value; }) {
        output << value;
    } else if constexpr (requires {
                             typename std::tuple_size<
                                 std::remove_cvref_t<T>>::type;
                         }) {
        output << '(';
        int index = 0;
        std::apply(
            [&](const auto&... elements) {
                ((output << (index++ == 0 ? "" : ", "),
                  print_value(output, elements)),
                 ...);
            },
            value);
        output << ')';
    } else if constexpr (requires { std::begin(value); std::end(value); }) {
        output << '[';
        bool first = true;
        for (const auto& element : value) {
            if (!first) output << ", ";
            first = false;
            print_value(output, element);
        }
        output << ']';
    } else {
        output << "<unprintable>";
    }
}

template <class Function>
decltype(auto) invoke_with_trial(Function& function, Random& random, int trial) {
    if constexpr (std::invocable<Function&, Random&, int>) {
        return std::invoke(function, random, trial);
    } else {
        static_assert(std::invocable<Function&, Random&>);
        return std::invoke(function, random);
    }
}

inline RandomTestResult success_result(const RandomTestConfig& config) {
    RandomTestResult result;
    result.seed = config.seed;
    result.requested_trials = config.trials;
    result.completed_trials = config.trials;
    return result;
}

inline RandomTestResult failure_result(const RandomTestConfig& config,
                                       int failed_trial,
                                       RandomTestFailure failure,
                                       int query_count = -1) {
    RandomTestResult result;
    result.seed = config.seed;
    result.requested_trials = config.trials;
    result.completed_trials = failed_trial;
    result.failed_trial = failed_trial;
    result.failure = failure;
    result.query_count = query_count;
    return result;
}

template <class T>
std::string value_to_string(const T& value) {
    std::ostringstream output;
    print_value(output, value);
    return output.str();
}

struct InteractionAbort {
    RandomTestFailure failure;
    std::string message;
};

class StandardStreamRedirect {
   private:
    std::streambuf* _cin_buffer;
    std::streambuf* _cout_buffer;

   public:
    StandardStreamRedirect(std::streambuf* input, std::streambuf* output)
        : _cin_buffer(std::cin.rdbuf()), _cout_buffer(std::cout.rdbuf()) {
        std::cout.flush();
        std::cin.rdbuf(input);
        std::cout.rdbuf(output);
        std::cin.clear();
        std::cout.clear();
    }

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

    ~StandardStreamRedirect() {
        std::cout.flush();
        std::cin.rdbuf(_cin_buffer);
        std::cout.rdbuf(_cout_buffer);
        std::cin.clear();
        std::cout.clear();
    }
};

template <class Generator>
std::string generate_stream_input(Generator& generator, Random& random,
                                  int trial) {
    std::ostringstream output;
    if constexpr (std::invocable<Generator&, Random&, std::ostream&, int>) {
        std::invoke(generator, random, output, trial);
    } else {
        static_assert(std::invocable<Generator&, Random&, std::ostream&>);
        std::invoke(generator, random, output);
    }
    return output.str();
}

template <class Generator>
decltype(auto) generate_interactive_stream_input(Generator& generator,
                                                 Random& random,
                                                 std::ostream& output,
                                                 int trial) {
    if constexpr (std::invocable<Generator&, Random&, std::ostream&, int>) {
        return std::invoke(generator, random, output, trial);
    } else {
        static_assert(std::invocable<Generator&, Random&, std::ostream&>);
        return std::invoke(generator, random, output);
    }
}

template <class Solution>
std::string run_with_standard_streams(const std::string& input,
                                      Solution& solution) {
    std::istringstream input_stream(input);
    std::ostringstream output_stream;
    {
        StandardStreamRedirect redirect(input_stream.rdbuf(),
                                        output_stream.rdbuf());
        std::invoke(solution);
    }
    return output_stream.str();
}

inline std::string trim_line_breaks(std::string text) {
    while (!text.empty() &&
           (text.back() == '\n' || text.back() == '\r')) {
        text.pop_back();
    }
    return text;
}

template <class State, class QueryHandler>
class InteractiveStreamBuffer : public std::streambuf {
   private:
    State* _state;
    QueryHandler* _query_handler;
    std::stringbuf* _candidate_output;
    std::size_t _output_cursor = 0;
    int _query_limit;
    int _query_count = 0;
    std::string _input_chunk;
    InteractionTranscript _transcript;
    RandomTestFailure _failure = RandomTestFailure::none;
    std::exception_ptr _exception;

    void set_input_chunk(std::string text) {
        text.push_back('\n');
        _input_chunk = std::move(text);
        char* first = _input_chunk.data();
        setg(first, first, first + _input_chunk.size());
    }

    void fail(RandomTestFailure failure, std::string message) {
        _failure = failure;
        _transcript.failure_message = std::move(message);
        setg(nullptr, nullptr, nullptr);
    }

   protected:
    int_type underflow() override {
        if (gptr() != nullptr && gptr() < egptr()) {
            return traits_type::to_int_type(*gptr());
        }
        if (_failure != RandomTestFailure::none || _exception) {
            return traits_type::eof();
        }

        std::string all_output = _candidate_output->str();
        std::string query = all_output.substr(_output_cursor);
        _output_cursor = all_output.size();
        if (query.empty()) {
            fail(RandomTestFailure::invalid_query,
                 "solution requested input without writing a query");
            return traits_type::eof();
        }

        InteractionExchange exchange;
        exchange.query = trim_line_breaks(query);
        _transcript.exchanges.push_back(std::move(exchange));
        _query_count++;
        if (_query_limit < _query_count) {
            fail(RandomTestFailure::query_limit,
                 "attempted query " + std::to_string(_query_count) +
                     " with limit " + std::to_string(_query_limit));
            return traits_type::eof();
        }

        std::istringstream query_stream(query);
        std::ostringstream response_stream;
        try {
            std::invoke(*_query_handler, *_state, query_stream,
                        response_stream);
        } catch (const InteractionAbort& failure) {
            fail(failure.failure, failure.message);
            return traits_type::eof();
        } catch (...) {
            _exception = std::current_exception();
            return traits_type::eof();
        }

        std::string response = response_stream.str();
        InteractionExchange& recorded = _transcript.exchanges.back();
        recorded.response = trim_line_breaks(response);
        recorded.responded = true;
        set_input_chunk(std::move(response));
        return traits_type::to_int_type(*gptr());
    }

   public:
    InteractiveStreamBuffer(State& state, QueryHandler& query_handler,
                            std::stringbuf& candidate_output,
                            std::string initial_input, int query_limit)
        : _state(&state),
          _query_handler(&query_handler),
          _candidate_output(&candidate_output),
          _query_limit(query_limit) {
        set_input_chunk(std::move(initial_input));
    }

    void finish() {
        std::string all_output = _candidate_output->str();
        _transcript.answer = all_output.substr(_output_cursor);
        _transcript.answered = true;
    }

    RandomTestFailure failure() const {
        return _failure;
    }

    int query_count() const {
        return _query_count;
    }

    const InteractionTranscript& transcript() const {
        return _transcript;
    }

    const std::exception_ptr& exception() const {
        return _exception;
    }
};

template <class Solver, class Input, class Interaction>
decltype(auto) invoke_interactive_solver(Solver& solver, const Input& input,
                                         Interaction& interaction) {
    if constexpr (std::invocable<Solver&, const Input&, Interaction&>) {
        return std::invoke(solver, input, interaction);
    } else {
        static_assert(std::invocable<Solver&, Interaction&>);
        return std::invoke(solver, interaction);
    }
}

}  // namespace random_testing_detail

template <class Input, class State>
struct InteractiveTestCase {
    Input input;
    State state;
};

template <class Input, class State>
auto interactive_test_case(Input&& input, State&& state) {
    return InteractiveTestCase<std::remove_cvref_t<Input>,
                               std::remove_cvref_t<State>>{
        std::forward<Input>(input), std::forward<State>(state)};
}

// Call this from a query handler when the candidate violates the protocol.
[[noreturn]] inline void reject_query(std::string message = {}) {
    throw random_testing_detail::InteractionAbort{
        RandomTestFailure::invalid_query, std::move(message)};
}

template <class State, class QueryHandler>
class RandomInteraction {
   private:
    State* _state;
    QueryHandler* _query_handler;
    int _query_limit;
    int _query_count = 0;
    InteractionTranscript _transcript;

   public:
    RandomInteraction(State& state, QueryHandler& query_handler,
                      int query_limit)
        : _state(&state),
          _query_handler(&query_handler),
          _query_limit(query_limit) {}

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

    template <class Query>
    auto ask(Query&& query) {
        using Reply = std::remove_cvref_t<std::invoke_result_t<
            QueryHandler&, State&, Query>>;
        static_assert(!std::is_void_v<Reply>);

        InteractionExchange exchange;
        exchange.query = random_testing_detail::value_to_string(query);
        _transcript.exchanges.push_back(std::move(exchange));
        _query_count++;
        if (_query_limit < _query_count) {
            throw random_testing_detail::InteractionAbort{
                RandomTestFailure::query_limit,
                "attempted query " + std::to_string(_query_count) +
                    " with limit " + std::to_string(_query_limit)};
        }

        Reply reply = std::invoke(*_query_handler, *_state,
                                  std::forward<Query>(query));
        InteractionExchange& recorded = _transcript.exchanges.back();
        recorded.response = random_testing_detail::value_to_string(reply);
        recorded.responded = true;
        return reply;
    }

    int query_count() const {
        return _query_count;
    }

    const InteractionTranscript& transcript() const {
        return _transcript;
    }

    template <class Answer>
    void record_answer(const Answer& answer) {
        _transcript.answer =
            random_testing_detail::value_to_string(answer);
        _transcript.answered = true;
    }

    void record_failure(std::string message) {
        _transcript.failure_message = std::move(message);
    }
};

struct PrintRandomTestFailure {
    template <class Case, class Expected, class Actual>
    void operator()(const Case& test_case, const Expected& expected,
                    const Actual& actual, int trial,
                    std::uint64_t seed) const {
        std::cerr << "random test failed: seed=" << seed
                  << " trial=" << trial << '\n';
        std::cerr << "input: ";
        random_testing_detail::print_value(std::cerr, test_case);
        std::cerr << "\nexpected: ";
        random_testing_detail::print_value(std::cerr, expected);
        std::cerr << "\nactual: ";
        random_testing_detail::print_value(std::cerr, actual);
        std::cerr << '\n';
    }
};

struct PrintConstructiveTestFailure {
    template <class Case, class Answer>
    void operator()(const Case& test_case, const Answer& answer, int trial,
                    std::uint64_t seed) const {
        std::cerr << "constructive random test failed: seed=" << seed
                  << " trial=" << trial << '\n';
        std::cerr << "input: ";
        random_testing_detail::print_value(std::cerr, test_case);
        std::cerr << "\noutput: ";
        random_testing_detail::print_value(std::cerr, answer);
        std::cerr << '\n';
    }
};

struct PrintStreamTestFailure {
    void operator()(const std::string& input, const std::string& output,
                    int trial, std::uint64_t seed) const {
        std::cerr << "stream random test failed: seed=" << seed
                  << " trial=" << trial << "\ninput:\n"
                  << input;
        if (input.empty() || input.back() != '\n') std::cerr << '\n';
        std::cerr << "output:\n" << output;
        if (output.empty() || output.back() != '\n') std::cerr << '\n';
    }
};

struct PrintInteractiveTestFailure {
    template <class Input, class State>
    void operator()(const InteractiveTestCase<Input, State>& test_case,
                    const InteractionTranscript& transcript, int trial,
                    std::uint64_t seed,
                    RandomTestFailure failure) const {
        std::cerr << "interactive random test failed: seed=" << seed
                  << " trial=" << trial
                  << " reason=" << random_test_failure_name(failure) << '\n';
        std::cerr << "input: ";
        random_testing_detail::print_value(std::cerr, test_case.input);
        std::cerr << "\njudge state: ";
        random_testing_detail::print_value(std::cerr, test_case.state);
        std::cerr << '\n';
        for (int index = 0; index < int(transcript.exchanges.size()); index++) {
            const InteractionExchange& exchange = transcript.exchanges[index];
            std::cerr << "query " << index + 1 << ": " << exchange.query;
            if (exchange.responded) {
                std::cerr << " -> " << exchange.response;
            } else {
                std::cerr << " -> <no response>";
            }
            std::cerr << '\n';
        }
        if (transcript.answered) {
            std::cerr << "answer: " << transcript.answer << '\n';
        }
        if (!transcript.failure_message.empty()) {
            std::cerr << "message: " << transcript.failure_message << '\n';
        }
    }
};

struct PrintInteractiveStreamTestFailure {
    template <class State>
    void operator()(const std::string& input, const State& state,
                    const InteractionTranscript& transcript, int trial,
                    std::uint64_t seed,
                    RandomTestFailure failure) const {
        std::cerr << "interactive stream random test failed: seed=" << seed
                  << " trial=" << trial
                  << " reason=" << random_test_failure_name(failure)
                  << "\ninput:\n"
                  << input;
        if (input.empty() || input.back() != '\n') std::cerr << '\n';
        std::cerr << "judge state: ";
        random_testing_detail::print_value(std::cerr, state);
        std::cerr << '\n';
        for (int index = 0; index < int(transcript.exchanges.size()); index++) {
            const InteractionExchange& exchange = transcript.exchanges[index];
            std::cerr << "query " << index + 1 << ": " << exchange.query;
            if (exchange.responded) {
                std::cerr << " -> " << exchange.response;
            } else {
                std::cerr << " -> <no response>";
            }
            std::cerr << '\n';
        }
        if (transcript.answered) {
            std::cerr << "answer: " << transcript.answer;
            if (transcript.answer.empty() || transcript.answer.back() != '\n') {
                std::cerr << '\n';
            }
        }
        if (!transcript.failure_message.empty()) {
            std::cerr << "message: " << transcript.failure_message << '\n';
        }
    }
};

// Runs a property returning bool for every generated trial.
// The property may accept (Random&) or (Random&, int trial).
template <class Property>
RandomTestResult random_test(RandomTestConfig config, Property property) {
    assert(0 <= config.trials);
    if (config.trials < 0) config.trials = 0;
    Random random(config.seed);
    for (int trial = 0; trial < config.trials; trial++) {
        static_assert(std::convertible_to<
                      decltype(random_testing_detail::invoke_with_trial(
                          property, random, trial)),
                      bool>);
        bool passed = bool(
            random_testing_detail::invoke_with_trial(property, random, trial));
        if (!passed) {
            return random_testing_detail::failure_result(
                config, trial, RandomTestFailure::property);
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Property>
RandomTestResult random_test(Property property) {
    return random_test(RandomTestConfig(), std::move(property));
}

// Generates a case, runs an optimized solver and an oracle on separate copies,
// and compares their results. Stops at the first mismatch.
//
// generator: (Random&) or (Random&, int trial) -> Case
// solver/oracle: (Case&) -> result
// on_failure: (case, expected, actual, trial, seed) -> void
template <class Generator, class Solver, class Oracle,
          class OnFailure = IgnoreRandomTestFailure,
          class Equal = std::equal_to<>>
RandomTestResult compare_randomly(RandomTestConfig config, Generator generator,
                                  Solver solver, Oracle oracle,
                                  OnFailure on_failure = {}, Equal equal = {}) {
    assert(0 <= config.trials);
    if (config.trials < 0) config.trials = 0;
    Random random(config.seed);

    for (int trial = 0; trial < config.trials; trial++) {
        auto test_case =
            random_testing_detail::invoke_with_trial(generator, random, trial);
        using Case = std::remove_cvref_t<decltype(test_case)>;
        static_assert(std::copy_constructible<Case>);

        Case actual_input = test_case;
        Case expected_input = test_case;
        decltype(auto) actual = std::invoke(solver, actual_input);
        decltype(auto) expected = std::invoke(oracle, expected_input);
        if (!bool(std::invoke(equal, actual, expected))) {
            std::invoke(on_failure, test_case, expected, actual, trial,
                        config.seed);
            return random_testing_detail::failure_result(
                config, trial, RandomTestFailure::mismatch);
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Generator, class Solver, class Oracle>
RandomTestResult compare_randomly(Generator generator, Solver solver,
                                  Oracle oracle) {
    return compare_randomly(RandomTestConfig(), std::move(generator),
                            std::move(solver), std::move(oracle));
}

// Generates an input, runs a constructive solver, and validates its output.
// validator: (const Case&, const Answer&) -> bool
template <class Generator, class Solver, class Validator,
          class OnFailure = IgnoreRandomTestFailure>
RandomTestResult test_constructively(RandomTestConfig config,
                                     Generator generator, Solver solver,
                                     Validator validator,
                                     OnFailure on_failure = {}) {
    assert(0 <= config.trials);
    if (config.trials < 0) config.trials = 0;
    Random random(config.seed);

    for (int trial = 0; trial < config.trials; trial++) {
        auto test_case =
            random_testing_detail::invoke_with_trial(generator, random, trial);
        using Case = std::remove_cvref_t<decltype(test_case)>;
        static_assert(std::copy_constructible<Case>);
        Case solver_input = test_case;
        auto answer = std::invoke(solver, solver_input);
        if (!bool(std::invoke(validator, std::as_const(test_case),
                              std::as_const(answer)))) {
            std::invoke(on_failure, std::as_const(test_case),
                        std::as_const(answer), trial, config.seed);
            return random_testing_detail::failure_result(
                config, trial, RandomTestFailure::rejected_output);
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Generator, class Solver, class Validator>
RandomTestResult test_constructively(Generator generator, Solver solver,
                                     Validator validator) {
    return test_constructively(RandomTestConfig(), std::move(generator),
                               std::move(solver), std::move(validator));
}

// Runs an ordinary solution that reads std::cin and writes std::cout.
// generator: (Random&, ostream&) or (Random&, ostream&, trial) -> void
// checker: (istream& generated_input, istream& candidate_output) -> bool
template <class Generator, class Solution, class Checker,
          class OnFailure = IgnoreRandomTestFailure>
RandomTestResult test_streams(RandomTestConfig config, Generator generator,
                              Solution solution, Checker checker,
                              OnFailure on_failure = {}) {
    assert(0 <= config.trials);
    if (config.trials < 0) config.trials = 0;
    Random random(config.seed);

    for (int trial = 0; trial < config.trials; trial++) {
        std::string input = random_testing_detail::generate_stream_input(
            generator, random, trial);
        std::string output =
            random_testing_detail::run_with_standard_streams(input, solution);
        std::istringstream input_stream(input);
        std::istringstream output_stream(output);
        if (!bool(std::invoke(checker, input_stream, output_stream))) {
            std::invoke(on_failure, std::as_const(input),
                        std::as_const(output), trial, config.seed);
            return random_testing_detail::failure_result(
                config, trial, RandomTestFailure::rejected_output);
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Generator, class Solution, class Checker>
RandomTestResult test_streams(Generator generator, Solution solution,
                              Checker checker) {
    return test_streams(RandomTestConfig(), std::move(generator),
                        std::move(solution), std::move(checker));
}

// generator: (Random&) or (Random&, trial) -> InteractiveTestCase<Input, State>
// solver: (const Input&, interaction) or (interaction) -> Answer
// query_handler: (State&, Query) -> Reply
// validator: (const Input&, const State&, const Answer&) -> bool
template <class Generator, class Solver, class QueryHandler, class Validator,
          class OnFailure = IgnoreRandomTestFailure>
RandomTestResult test_interactively(RandomTestConfig config, int query_limit,
                                    Generator generator, Solver solver,
                                    QueryHandler query_handler,
                                    Validator validator,
                                    OnFailure on_failure = {}) {
    assert(0 <= config.trials);
    assert(0 <= query_limit);
    if (config.trials < 0) config.trials = 0;
    if (query_limit < 0) query_limit = 0;
    Random random(config.seed);

    for (int trial = 0; trial < config.trials; trial++) {
        auto test_case =
            random_testing_detail::invoke_with_trial(generator, random, trial);
        using State = std::remove_cvref_t<decltype(test_case.state)>;
        RandomInteraction<State, QueryHandler> interaction(
            test_case.state, query_handler, query_limit);

        try {
            auto answer = random_testing_detail::invoke_interactive_solver(
                solver, std::as_const(test_case.input), interaction);
            interaction.record_answer(answer);
            if (!bool(std::invoke(validator, std::as_const(test_case.input),
                                  std::as_const(test_case.state),
                                  std::as_const(answer)))) {
                RandomTestResult result =
                    random_testing_detail::failure_result(
                        config, trial, RandomTestFailure::rejected_output,
                        interaction.query_count());
                std::invoke(on_failure, std::as_const(test_case),
                            interaction.transcript(), trial, config.seed,
                            result.failure);
                return result;
            }
        } catch (const random_testing_detail::InteractionAbort& failure) {
            interaction.record_failure(failure.message);
            RandomTestResult result = random_testing_detail::failure_result(
                config, trial, failure.failure, interaction.query_count());
            std::invoke(on_failure, std::as_const(test_case),
                        interaction.transcript(), trial, config.seed,
                        result.failure);
            return result;
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Generator, class Solver, class QueryHandler, class Validator>
RandomTestResult test_interactively(int query_limit, Generator generator,
                                    Solver solver, QueryHandler query_handler,
                                    Validator validator) {
    return test_interactively(RandomTestConfig(), query_limit,
                              std::move(generator), std::move(solver),
                              std::move(query_handler), std::move(validator));
}

// Runs an ordinary interactive solution using std::cin and std::cout.
// generator: (Random&, ostream&) or (Random&, ostream&, trial) -> JudgeState
// query_handler: (JudgeState&, istream& query, ostream& response) -> void
// checker: (istream& public_input, const JudgeState&,
//           istream& final_output) -> bool
template <class Generator, class Solution, class QueryHandler, class Checker,
          class OnFailure = IgnoreRandomTestFailure>
RandomTestResult test_interactive_streams(
    RandomTestConfig config, int query_limit, Generator generator,
    Solution solution, QueryHandler query_handler, Checker checker,
    OnFailure on_failure = {}) {
    assert(0 <= config.trials);
    assert(0 <= query_limit);
    if (config.trials < 0) config.trials = 0;
    if (query_limit < 0) query_limit = 0;
    Random random(config.seed);

    for (int trial = 0; trial < config.trials; trial++) {
        std::ostringstream generated_input;
        auto state =
            random_testing_detail::generate_interactive_stream_input(
                generator, random, generated_input, trial);
        std::string input = generated_input.str();
        std::stringbuf candidate_output(std::ios::out);
        using State = std::remove_cvref_t<decltype(state)>;
        random_testing_detail::InteractiveStreamBuffer<State, QueryHandler>
            input_buffer(state, query_handler, candidate_output, input,
                         query_limit);
        {
            random_testing_detail::StandardStreamRedirect redirect(
                &input_buffer, &candidate_output);
            std::invoke(solution);
        }
        input_buffer.finish();
        if (input_buffer.exception()) {
            std::rethrow_exception(input_buffer.exception());
        }

        RandomTestFailure failure = input_buffer.failure();
        if (failure != RandomTestFailure::none) {
            RandomTestResult result = random_testing_detail::failure_result(
                config, trial, failure, input_buffer.query_count());
            std::invoke(on_failure, std::as_const(input),
                        std::as_const(state), input_buffer.transcript(), trial,
                        config.seed, failure);
            return result;
        }

        std::istringstream input_stream(input);
        std::istringstream output_stream(input_buffer.transcript().answer);
        if (!bool(std::invoke(checker, input_stream, std::as_const(state),
                              output_stream))) {
            RandomTestResult result = random_testing_detail::failure_result(
                config, trial, RandomTestFailure::rejected_output,
                input_buffer.query_count());
            std::invoke(on_failure, std::as_const(input),
                        std::as_const(state), input_buffer.transcript(), trial,
                        config.seed, result.failure);
            return result;
        }
    }
    return random_testing_detail::success_result(config);
}

template <class Generator, class Solution, class QueryHandler, class Checker>
RandomTestResult test_interactive_streams(
    int query_limit, Generator generator, Solution solution,
    QueryHandler query_handler, Checker checker) {
    return test_interactive_streams(
        RandomTestConfig(), query_limit, std::move(generator),
        std::move(solution), std::move(query_handler), std::move(checker));
}

// Short contest interface. Prints failure metadata and terminates on failure.
template <class Property>
RandomTestResult stress_test(Property property, int trials = 1000,
                             std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = random_test(config, std::move(property));
    if (!result) {
        std::cerr << "random test failed: seed=" << result.seed
                  << " trial=" << result.failed_trial << '\n';
        std::abort();
    }
    return result;
}

// Short optimized-versus-brute-force interface.
template <class Generator, class Solver, class Oracle>
requires(!std::integral<std::remove_cvref_t<Solver>> &&
         !std::integral<std::remove_cvref_t<Oracle>>)
RandomTestResult stress_test(Generator generator, Solver solver, Oracle oracle,
                             int trials = 1000,
                             std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = compare_randomly(
        config, std::move(generator), std::move(solver), std::move(oracle),
        PrintRandomTestFailure());
    if (!result) std::abort();
    return result;
}

template <class Generator, class Solver, class Validator>
RandomTestResult constructive_stress_test(
    Generator generator, Solver solver, Validator validator,
    int trials = 1000, std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = test_constructively(
        config, std::move(generator), std::move(solver),
        std::move(validator), PrintConstructiveTestFailure());
    if (!result) std::abort();
    return result;
}

template <class Generator, class Solution, class Checker>
RandomTestResult stream_stress_test(
    Generator generator, Solution solution, Checker checker,
    int trials = 1000, std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = test_streams(
        config, std::move(generator), std::move(solution),
        std::move(checker), PrintStreamTestFailure());
    if (!result) std::abort();
    return result;
}

template <class Generator, class Solver, class QueryHandler, class Validator>
RandomTestResult interactive_stress_test(
    int query_limit, Generator generator, Solver solver,
    QueryHandler query_handler, Validator validator, int trials = 1000,
    std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = test_interactively(
        config, query_limit, std::move(generator), std::move(solver),
        std::move(query_handler), std::move(validator),
        PrintInteractiveTestFailure());
    if (!result) std::abort();
    return result;
}

template <class Generator, class Solution, class QueryHandler, class Checker>
RandomTestResult interactive_stream_stress_test(
    int query_limit, Generator generator, Solution solution,
    QueryHandler query_handler, Checker checker, int trials = 1000,
    std::uint64_t seed = default_random_test_seed) {
    RandomTestConfig config;
    config.trials = trials;
    config.seed = seed;
    RandomTestResult result = test_interactive_streams(
        config, query_limit, std::move(generator), std::move(solution),
        std::move(query_handler), std::move(checker),
        PrintInteractiveStreamTestFailure());
    if (!result) std::abort();
    return result;
}

}  // namespace utilities
}  // namespace m1une


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

#line 1 "utilities/fast_io.hpp"



#line 5 "utilities/fast_io.hpp"
#include <array>
#include <cerrno>
#include <charconv>
#include <cstddef>
#include <cstdio>
#line 12 "utilities/fast_io.hpp"
#include <cstring>
#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 12 "verify/utilities/random_testing.test.cpp"

#ifndef NDEBUG
void test_properties() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 100;
    config.seed = 12345;
    RandomTestResult success = random_test(config, [](Random& random) {
        long long value = random.uniform(-1000, 1000);
        return value * value >= 0;
    });
    assert(success.passed());
    assert(bool(success));
    assert(success.completed_trials == 100);
    assert(success.failed_trial == -1);
    assert(success.seed == config.seed);

    RandomTestResult failure = random_test(
        config, [](Random&, int trial) { return trial != 17; });
    assert(!failure.passed());
    assert(!bool(failure));
    assert(failure.completed_trials == 17);
    assert(failure.failed_trial == 17);
    assert(failure.failure == RandomTestFailure::property);

    auto shorthand = random_test([](Random&, int trial) { return trial < 1000; });
    assert(shorthand.passed());
    auto required = stress_test(
        [](Random&, int trial) { return trial < 25; }, 25, 777);
    assert(required.passed());
    assert(required.seed == 777);
}

void test_comparison() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 500;
    config.seed = 67890;
    auto success = compare_randomly(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 20));
            std::vector<int> values(size);
            for (int& value : values) value = int(random.uniform(-20, 20));
            return values;
        },
        [](std::vector<int>& values) {
            std::sort(values.begin(), values.end());
            return values;
        },
        [](std::vector<int>& values) {
            for (int i = 0; i < int(values.size()); i++) {
                for (int j = i + 1; j < int(values.size()); j++) {
                    if (values[j] < values[i]) std::swap(values[i], values[j]);
                }
            }
            return values;
        });
    assert(success.passed());

    auto mutation_isolated = compare_randomly(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 20));
            std::vector<int> values(size);
            for (int& value : values) value = int(random.uniform(-20, 20));
            return values;
        },
        [](std::vector<int>& values) {
            int sum = std::accumulate(values.begin(), values.end(), 0);
            values.clear();
            return sum;
        },
        [](std::vector<int>& values) {
            return std::accumulate(values.begin(), values.end(), 0);
        });
    assert(mutation_isolated.passed());

    auto quick = stress_test(
        [](Random& random) { return int(random.uniform(-10, 10)); },
        [](int& value) { return value * value; },
        [](int& value) {
            int magnitude = value < 0 ? -value : value;
            int result = 0;
            for (int i = 0; i < magnitude; i++) result += magnitude;
            return result;
        },
        50, 999);
    assert(quick.passed());

    int callback_count = 0;
    int callback_trial = -1;
    int callback_case = -1;
    int callback_expected = -1;
    int callback_actual = -1;
    std::uint64_t callback_seed = 0;
    auto failure = compare_randomly(
        config,
        [](Random&, int trial) { return trial; },
        [](int& value) { return value == 23 ? value + 1 : value; },
        [](int& value) { return value; },
        [&](int input, int expected, int actual, int trial,
            std::uint64_t seed) {
            callback_count++;
            callback_trial = trial;
            callback_case = input;
            callback_expected = expected;
            callback_actual = actual;
            callback_seed = seed;
        });
    assert(failure.failed_trial == 23);
    assert(failure.failure == RandomTestFailure::mismatch);
    assert(callback_count == 1);
    assert(callback_trial == 23);
    assert(callback_case == 23);
    assert(callback_expected == 23);
    assert(callback_actual == 24);
    assert(callback_seed == config.seed);

    RandomTestConfig empty_config;
    empty_config.trials = 0;
    auto empty = random_test(empty_config, [](Random&) { return false; });
    assert(empty.passed());
    assert(empty.completed_trials == 0);
}

void test_constructive() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 200;
    config.seed = 13579;
    auto success = test_constructively(
        config,
        [](Random& random) {
            int size = int(random.uniform(0, 30));
            return random.sequence(size, -20, 20);
        },
        [](std::vector<int>& values) {
            std::vector<int> order(values.size());
            std::iota(order.begin(), order.end(), 0);
            std::sort(order.begin(), order.end(), [&](int first, int second) {
                return values[first] < values[second];
            });
            values.clear();
            return order;
        },
        [](const std::vector<int>& values, const std::vector<int>& order) {
            if (values.size() != order.size()) return false;
            std::vector<bool> used(values.size());
            for (int index = 0; index < int(order.size()); index++) {
                if (order[index] < 0 || int(values.size()) <= order[index]) {
                    return false;
                }
                if (used[order[index]]) return false;
                used[order[index]] = true;
                if (0 < index &&
                    values[order[index]] < values[order[index - 1]]) {
                    return false;
                }
            }
            return true;
        });
    assert(success.passed());

    int callback_count = 0;
    auto failure = test_constructively(
        config, [](Random&, int trial) { return trial + 1; },
        [](int& value) { return value == 8 ? 0 : value; },
        [](int input, int answer) { return input == answer; },
        [&](int input, int answer, int trial, std::uint64_t seed) {
            callback_count++;
            assert(input == 8);
            assert(answer == 0);
            assert(trial == 7);
            assert(seed == config.seed);
        });
    assert(failure.failed_trial == 7);
    assert(failure.failure == RandomTestFailure::rejected_output);
    assert(callback_count == 1);

    auto quick = constructive_stress_test(
        [](Random& random) { return int(random.uniform(0, 100)); },
        [](int& value) { return value; },
        [](const int& input, const int& answer) { return input == answer; },
        20, 97531);
    assert(quick.passed());
}

void test_interactive() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 300;
    config.seed = 24680;
    auto success = test_interactively(
        config, 10,
        [](Random& random) {
            int upper = int(random.uniform(1, 1000));
            int secret = int(random.uniform(0, upper));
            return interactive_test_case(upper, secret);
        },
        [](const int& upper, auto& interaction) {
            int low = 0;
            int high = upper;
            while (low < high) {
                int middle = (low + high) / 2;
                int comparison = interaction.ask(middle);
                if (comparison <= 0) {
                    high = middle;
                } else {
                    low = middle + 1;
                }
            }
            return low;
        },
        [](int& secret, int guess) {
            if (guess < 0) reject_query("negative guess");
            if (secret < guess) return -1;
            if (guess < secret) return 1;
            return 0;
        },
        [](const int& upper, const int& secret, const int& answer) {
            return 0 <= answer && answer <= upper && answer == secret;
        });
    assert(success.passed());

    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 112233;
    int callback_count = 0;
    auto invalid = test_interactively(
        one_trial, 5,
        [](Random&) { return interactive_test_case(10, 4); },
        [](const int&, auto& interaction) {
            interaction.ask(-1);
            return 0;
        },
        [](int&, int query) {
            if (query < 0) reject_query("query is outside [0, 10]");
            return 0;
        },
        [](const int&, const int&, const int&) { return true; },
        [&](const auto&, const InteractionTranscript& transcript, int trial,
            std::uint64_t seed, RandomTestFailure reason) {
            callback_count++;
            assert(trial == 0);
            assert(seed == one_trial.seed);
            assert(reason == RandomTestFailure::invalid_query);
            assert(transcript.exchanges.size() == 1);
            assert(transcript.exchanges[0].query == "-1");
            assert(!transcript.exchanges[0].responded);
            assert(transcript.failure_message ==
                   "query is outside [0, 10]");
        });
    assert(invalid.failure == RandomTestFailure::invalid_query);
    assert(invalid.query_count == 1);
    assert(callback_count == 1);

    auto too_many_queries = test_interactively(
        one_trial, 1,
        [](Random&) { return interactive_test_case(0, 0); },
        [](auto& interaction) {
            interaction.ask(1);
            interaction.ask(2);
            return 0;
        },
        [](int&, int query) { return query; },
        [](const int&, const int&, const int&) { return true; });
    assert(too_many_queries.failure == RandomTestFailure::query_limit);
    assert(too_many_queries.query_count == 2);

    auto wrong_answer = test_interactively(
        one_trial, 0,
        [](Random&) { return interactive_test_case(10, 7); },
        [](const int&, auto&) { return 6; },
        [](int&, int query) { return query; },
        [](const int&, const int& secret, const int& answer) {
            return secret == answer;
        });
    assert(wrong_answer.failure == RandomTestFailure::rejected_output);
    assert(wrong_answer.query_count == 0);

    auto quick = interactive_stress_test(
        0,
        [](Random& random) {
            int value = int(random.uniform(-100, 100));
            return interactive_test_case(value, value);
        },
        [](const int& input, auto&) { return input; },
        [](int&, int query) { return query; },
        [](const int&, const int& state, const int& answer) {
            return state == answer;
        },
        20, 86420);
    assert(quick.passed());
}

void test_stream_interface() {
    using namespace m1une::utilities;

    RandomTestConfig config;
    config.trials = 200;
    config.seed = 424242;
    auto generate = [](Random& random, std::ostream& input) {
        int size = int(random.uniform(0, 30));
        input << size << '\n';
        for (int value : random.sequence(size, -20, 20)) {
            input << value << ' ';
        }
        input << '\n';
    };
    auto solve = [] {
        int size;
        std::cin >> size;
        std::vector<int> values(size);
        for (int& value : values) std::cin >> value;
        std::sort(values.begin(), values.end());
        for (int value : values) std::cout << value << ' ';
        std::cout << '\n';
    };
    auto check = [](std::istream& input, std::istream& output) {
        int size;
        input >> size;
        std::vector<int> expected(size);
        for (int& value : expected) input >> value;
        std::sort(expected.begin(), expected.end());
        std::vector<int> actual(size);
        for (int& value : actual) {
            if (!(output >> value)) return false;
        }
        std::string extra;
        return expected == actual && !(output >> extra);
    };
    auto success = test_streams(config, generate, solve, check);
    assert(success.passed());

    int callback_count = 0;
    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 515151;
    auto failure = test_streams(
        one_trial,
        [](Random&, std::ostream& input) { input << "3\n1 2 3\n"; },
        [] {
            int size;
            std::cin >> size;
            std::cout << size - 1 << '\n';
        },
        [](std::istream&, std::istream& output) {
            int answer;
            return bool(output >> answer) && answer == 3;
        },
        [&](const std::string& input, const std::string& output, int trial,
            std::uint64_t seed) {
            callback_count++;
            assert(input == "3\n1 2 3\n");
            assert(output == "2\n");
            assert(trial == 0);
            assert(seed == one_trial.seed);
        });
    assert(failure.failure == RandomTestFailure::rejected_output);
    assert(callback_count == 1);

    auto quick = stream_stress_test(generate, solve, check, 20, 616161);
    assert(quick.passed());
}

void test_interactive_stream_interface() {
    using namespace m1une::utilities;

    auto generate = [](Random& random, std::ostream& input) {
        int upper = int(random.uniform(1, 1000));
        input << upper << '\n';
        return int(random.uniform(0, upper));
    };
    auto solve = [] {
        int upper;
        std::cin >> upper;
        int low = 0;
        int high = upper;
        while (low < high) {
            int middle = (low + high) / 2;
            std::cout << "? " << middle << std::endl;
            int comparison;
            std::cin >> comparison;
            if (comparison <= 0) high = middle;
            else low = middle + 1;
        }
        std::cout << "! " << low << std::endl;
    };
    auto reply = [](int& secret, std::istream& query,
                    std::ostream& response) {
        char type;
        int guess;
        std::string extra;
        if (!(query >> type >> guess) || type != '?' || query >> extra) {
            reject_query("expected: ? x");
        }
        if (secret < guess) response << -1;
        else if (guess < secret) response << 1;
        else response << 0;
    };
    auto check = [](std::istream& input, const int& secret,
                    std::istream& output) {
        int upper;
        char type;
        int answer;
        std::string extra;
        input >> upper;
        return bool(output >> type >> answer) && type == '!' &&
               0 <= answer && answer <= upper && answer == secret &&
               !(output >> extra);
    };

    auto success = interactive_stream_stress_test(
        10, generate, solve, reply, check, 200, 717171);
    assert(success.passed());

    RandomTestConfig one_trial;
    one_trial.trials = 1;
    one_trial.seed = 818181;
    int callback_count = 0;
    auto invalid = test_interactive_streams(
        one_trial, 1,
        [](Random&, std::ostream& input) {
            input << "10\n";
            return 5;
        },
        [] {
            int upper;
            std::cin >> upper;
            std::cout << "invalid query" << std::endl;
            int response;
            std::cin >> response;
        },
        reply, check,
        [&](const std::string& input, const int& state,
            const InteractionTranscript& transcript, int trial,
            std::uint64_t seed, RandomTestFailure reason) {
            callback_count++;
            assert(input == "10\n");
            assert(state == 5);
            assert(transcript.exchanges.size() == 1);
            assert(transcript.exchanges[0].query == "invalid query");
            assert(!transcript.exchanges[0].responded);
            assert(transcript.failure_message == "expected: ? x");
            assert(trial == 0);
            assert(seed == one_trial.seed);
            assert(reason == RandomTestFailure::invalid_query);
        });
    assert(invalid.failure == RandomTestFailure::invalid_query);
    assert(invalid.query_count == 1);
    assert(callback_count == 1);

    auto query_limit = test_interactive_streams(
        one_trial, 0,
        [](Random&, std::ostream& input) {
            input << "10\n";
            return 5;
        },
        [] {
            int upper;
            std::cin >> upper;
            std::cout << "? 5" << std::endl;
            int response;
            std::cin >> response;
        },
        reply, check);
    assert(query_limit.failure == RandomTestFailure::query_limit);
    assert(query_limit.query_count == 1);
}
#endif

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

#ifndef NDEBUG
    test_properties();
    test_comparison();
    test_constructive();
    test_interactive();
    test_stream_interface();
    test_interactive_stream_interface();
#endif

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

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