DS太好用了

/*
 * A+B Problem - 超复杂C++98兼容版本
 * 版本: 42.7.3.14159265358979323846 - C++98兼容版
 */

#include <iostream>
#include <string>
#include <vector>
#include <map>
#include <set>
#include <list>
#include <deque>
#include <queue>
#include <stack>
#include <algorithm>
#include <functional>
#include <iomanip>
#include <fstream>
#include <sstream>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <climits>
#include <cfloat>
#include <cmath>
#include <ctime>
#include <cassert>
#include <cwchar>
#include <cwctype>
#include <exception>
#include <stdexcept>
#include <new>
#include <limits>
#include <locale>
#include <iterator>
#include <ios>
#include <iosfwd>
#include <istream>
#include <ostream>
#include <streambuf>

// 数学常数定义
const double MATHEMATICAL_PI = 3.14159265358979323846;
const double MATHEMATICAL_E = 2.71828182845904523536;
const double MATHEMATICAL_PHI = 1.61803398874989484820;
const double MATHEMATICAL_SQRT2 = 1.41421356237309504880;
const double MATHEMATICAL_SQRT3 = 1.73205080756887729352;
const double MATHEMATICAL_SQRT5 = 2.23606797749978969640;
const double MATHEMATICAL_LN2 = 0.69314718055994530941;
const double MATHEMATICAL_LN10 = 2.30258509299404568402;

// 整数界限常量定义
const int INT_MIN_VALUE = -2147483647 - 1;
const int INT_MAX_VALUE = 2147483647;
const long LONG_MIN_VALUE = LONG_MIN;
const long LONG_MAX_VALUE = LONG_MAX;
const long long LLONG_MIN_VALUE = LLONG_MIN;
const long long LLONG_MAX_VALUE = LLONG_MAX;
const unsigned int UINT_MAX_VALUE = UINT_MAX;
const unsigned long ULONG_MAX_VALUE = ULONG_MAX;
const unsigned long long ULLONG_MAX_VALUE = ULLONG_MAX;

// 预处理器宏定义
#define ADDITION_COMPLEXITY_LEVEL 9999
#define QUANTUM_COMPUTATION_FACTOR 42
#define UNIVERSAL_CONSTANTS_COUNT 100
#define MAX_CACHE_SIZE 10000
#define DEFAULT_UNIVERSE_SEED 123456789
#define MULTIDIMENSIONAL_FACTOR 3
#define PRIME_NUMBER_VERIFICATION_LIMIT 1000

// 类型别名
typedef long long int64;
typedef unsigned long long uint64;
typedef signed char int8;
typedef unsigned char uint8;
typedef short int16;
typedef unsigned short uint16;
typedef int int32;
typedef unsigned int uint32;

// 辅助数学函数
namespace MathUtilities {
    template<typename T>
    T absoluteValue(T value) {
        return value < 0 ? -value : value;
    }
    
    template<typename T>
    T maximum(T a, T b) {
        return a > b ? a : b;
    }
    
    template<typename T>
    T minimum(T a, T b) {
        return a < b ? a : b;
    }
    
    bool isPrimeNumber(int n) {
        if (n <= 1) return false;
        if (n <= 3) return true;
        if (n % 2 == 0 || n % 3 == 0) return false;
        
        for (int i = 5; i * i <= n && i <= PRIME_NUMBER_VERIFICATION_LIMIT; i += 6) {
            if (n % i == 0 || n % (i + 2) == 0) return false;
        }
        return true;
    }
    
    int fibonacciNumber(int n) {
        if (n <= 1) return n;
        int a = 0, b = 1;
        for (int i = 2; i <= n; ++i) {
            int temp = a + b;
            a = b;
            b = temp;
        }
        return b;
    }
    
    int factorial(int n) {
        int result = 1;
        for (int i = 2; i <= n; ++i) {
            result *= i;
        }
        return result;
    }
    
    double power(double base, int exponent) {
        double result = 1.0;
        for (int i = 0; i < exponent; ++i) {
            result *= base;
        }
        return result;
    }
}

// 字符串工具类
class StringUtilities {
public:
    static std::string intToString(int value) {
        std::stringstream ss;
        ss << value;
        return ss.str();
    }
    
    static std::string doubleToString(double value, int precision = 6) {
        std::stringstream ss;
        ss << std::fixed << std::setprecision(precision) << value;
        return ss.str();
    }
    
    static std::string repeatString(const std::string& str, int count) {
        std::string result;
        for (int i = 0; i < count; ++i) {
            result += str;
        }
        return result;
    }
    
    static std::string toUpperCase(const std::string& str) {
        std::string result = str;
        for (size_t i = 0; i < result.length(); ++i) {
            result[i] = std::toupper(result[i]);
        }
        return result;
    }
    
    static std::string toLowerCase(const std::string& str) {
        std::string result = str;
        for (size_t i = 0; i < result.length(); ++i) {
            result[i] = std::tolower(result[i]);
        }
        return result;
    }
    
    static bool startsWith(const std::string& str, const std::string& prefix) {
        return str.length() >= prefix.length() && 
               str.substr(0, prefix.length()) == prefix;
    }
    
    static bool endsWith(const std::string& str, const std::string& suffix) {
        return str.length() >= suffix.length() && 
               str.substr(str.length() - suffix.length()) == suffix;
    }
    
    static std::vector<std::string> split(const std::string& str, char delimiter) {
        std::vector<std::string> tokens;
        std::stringstream ss(str);
        std::string token;
        
        while (std::getline(ss, token, delimiter)) {
            tokens.push_back(token);
        }
        
        return tokens;
    }
};

// 数学宇宙基类
class MathematicalUniverse {
protected:
    bool exists;
    unsigned long long universeID;
    static unsigned long long nextUniverseID;
    
public:
    MathematicalUniverse() : exists(true) {
        universeID = nextUniverseID++;
    }
    
    virtual ~MathematicalUniverse() { 
        exists = false; 
    }
    
    bool doesExist() const { 
        return exists; 
    }
    
    unsigned long long getUniverseID() const { 
        return universeID; 
    }
    
    virtual std::string describe() const {
        return "A Mathematical Universe";
    }
    
    virtual std::string getDetailedDescription() const {
        return "Mathematical Universe ID: " + StringUtilities::intToString(universeID);
    }
    
    virtual MathematicalUniverse* clone() const = 0;
    
    virtual void initializeFromSeed(unsigned int seed) {
        srand(seed);
    }
    
    virtual double calculateCosmicEntropy() const {
        return 0.0;
    }
    
    virtual bool verifyConsistency() const {
        return true;
    }
    
    virtual void performCosmicMaintenance() {
        // 宇宙维护操作
    }
    
    virtual std::vector<double> getCosmicParameters() const {
        return std::vector<double>();
    }
};

unsigned long long MathematicalUniverse::nextUniverseID = 1;

// 宇宙操作接口
class UniverseOperationsInterface {
public:
    virtual ~UniverseOperationsInterface() {}
    virtual void expandUniverse() = 0;
    virtual void contractUniverse() = 0;
    virtual void stabilizeUniverse() = 0;
    virtual void addCosmicPerturbation(double magnitude) = 0;
    virtual double measureCosmicEnergy() const = 0;
};

// 平行宇宙管理器
class ParallelUniverseManager {
private:
    std::vector<MathematicalUniverse*> universes;
    static ParallelUniverseManager* instance;
    
    ParallelUniverseManager() {}
    ParallelUniverseManager(const ParallelUniverseManager&);
    ParallelUniverseManager& operator=(const ParallelUniverseManager&);
    
public:
    static ParallelUniverseManager& getInstance() {
        if (!instance) {
            instance = new ParallelUniverseManager();
        }
        return *instance;
    }
    
    static void destroyInstance() {
        if (instance) {
            delete instance;
            instance = NULL;
        }
    }
    
    ~ParallelUniverseManager() {
        for (size_t i = 0; i < universes.size(); ++i) {
            if (universes[i]) {
                delete universes[i];
            }
        }
        universes.clear();
    }
    
    void addUniverse(MathematicalUniverse* universe) {
        if (universe) {
            universes.push_back(universe);
        }
    }
    
    MathematicalUniverse* getUniverseByID(unsigned long long id) const {
        for (size_t i = 0; i < universes.size(); ++i) {
            if (universes[i] && universes[i]->getUniverseID() == id) {
                return universes[i];
            }
        }
        return NULL;
    }
    
    size_t getUniverseCount() const {
        return universes.size();
    }
    
    void collapseAllUniverses() {
        for (size_t i = 0; i < universes.size(); ++i) {
            if (universes[i]) {
                delete universes[i];
                universes[i] = NULL;
            }
        }
        universes.clear();
    }
    
    void performUniversalMaintenance() {
        for (size_t i = 0; i < universes.size(); ++i) {
            if (universes[i]) {
                universes[i]->performCosmicMaintenance();
            }
        }
    }
    
    double calculateTotalEntropy() const {
        double totalEntropy = 0.0;
        for (size_t i = 0; i < universes.size(); ++i) {
            if (universes[i]) {
                totalEntropy += universes[i]->calculateCosmicEntropy();
            }
        }
        return totalEntropy;
    }
};

ParallelUniverseManager* ParallelUniverseManager::instance = NULL;

// 量子态基类
class QuantumState {
protected:
    double probabilityAmplitude;
    std::string stateDescription;
    unsigned long long quantumID;
    static unsigned long long nextQuantumID;
    
public:
    QuantumState(double amplitude = 0.0, const std::string& desc = "") 
        : probabilityAmplitude(amplitude), stateDescription(desc) {
        quantumID = nextQuantumID++;
    }
    
    virtual ~QuantumState() {}
    
    virtual double getProbability() const {
        return probabilityAmplitude * probabilityAmplitude;
    }
    
    virtual std::string getStateDescription() const {
        return stateDescription + " (ID: " + StringUtilities::intToString(quantumID) + ")";
    }
    
    virtual QuantumState* clone() const = 0;
    
    virtual void applyQuantumOperation(double factor) {
        probabilityAmplitude *= factor;
    }
    
    virtual double calculateQuantumEnergy() const {
        return probabilityAmplitude * 100.0; // 虚构的能量计算
    }
    
    unsigned long long getQuantumID() const {
        return quantumID;
    }
};

unsigned long long QuantumState::nextQuantumID = 1;

// 加法量子态
class AdditionQuantumState : public QuantumState {
private:
    int valueA;
    int valueB;
    int superpositionResult;
    
public:
    AdditionQuantumState(int a, int b, int result, double amplitude = 0.0)
        : QuantumState(amplitude, "Addition Quantum State"), 
          valueA(a), valueB(b), superpositionResult(result) {}
    
    virtual ~AdditionQuantumState() {}
    
    int getA() const { return valueA; }
    int getB() const { return valueB; }
    int getResult() const { return superpositionResult; }
    
    virtual std::string getStateDescription() const {
        std::string desc = "AdditionQuantumState: " + StringUtilities::intToString(valueA) + 
                          " + " + StringUtilities::intToString(valueB) + 
                          " = " + StringUtilities::intToString(superpositionResult);
        return desc + " (Amplitude: " + StringUtilities::doubleToString(probabilityAmplitude) + ")";
    }
    
    virtual QuantumState* clone() const {
        return new AdditionQuantumState(valueA, valueB, superpositionResult, probabilityAmplitude);
    }
    
    virtual double calculateQuantumEnergy() const {
        // 修复：使用基类名称明确调用基类方法
        double baseEnergy = QuantumState::calculateQuantumEnergy();
        return baseEnergy + MathUtilities::absoluteValue(valueA) + MathUtilities::absoluteValue(valueB);
    }
};

// 量子叠加系统
class QuantumSuperpositionSystem {
private:
    std::vector<QuantumState*> states;
    double normalizationFactor;
    unsigned long long systemID;
    static unsigned long long nextSystemID;
    
public:
    QuantumSuperpositionSystem() : normalizationFactor(1.0) {
        systemID = nextSystemID++;
    }
    
    ~QuantumSuperpositionSystem() {
        for (size_t i = 0; i < states.size(); ++i) {
            if (states[i]) {
                delete states[i];
            }
        }
        states.clear();
    }
    
    void addState(QuantumState* state) {
        if (state) {
            states.push_back(state);
            recalculateNormalization();
        }
    }
    
    void recalculateNormalization() {
        double totalProbability = 0.0;
        for (size_t i = 0; i < states.size(); ++i) {
            if (states[i]) {
                totalProbability += states[i]->getProbability();
            }
        }
        
        if (totalProbability > 0.0) {
            normalizationFactor = 1.0 / sqrt(totalProbability);
        } else {
            normalizationFactor = 1.0;
        }
    }
    
    QuantumState* collapse() const {
        if (states.empty()) {
            return NULL;
        }
        
        double randomValue = (double)rand() / RAND_MAX;
        int index = (int)(randomValue * states.size()) % states.size();
        
        return states[index]->clone();
    }
    
    QuantumState* collapseWithBias(double biasFactor) const {
        if (states.empty()) {
            return NULL;
        }
        
        double randomValue = (double)rand() / RAND_MAX;
        int adjustedIndex = (int)(randomValue * states.size() * biasFactor) % states.size();
        
        return states[adjustedIndex]->clone();
    }
    
    size_t getStateCount() const {
        return states.size();
    }
    
    double calculateSystemEntropy() const {
        double entropy = 0.0;
        for (size_t i = 0; i < states.size(); ++i) {
            if (states[i]) {
                double probability = states[i]->getProbability() * normalizationFactor * normalizationFactor;
                if (probability > 0.0) {
                    entropy -= probability * log(probability);
                }
            }
        }
        return entropy;
    }
    
    double calculateTotalEnergy() const {
        double totalEnergy = 0.0;
        for (size_t i = 0; i < states.size(); ++i) {
            if (states[i]) {
                totalEnergy += states[i]->calculateQuantumEnergy();
            }
        }
        return totalEnergy;
    }
    
    unsigned long long getSystemID() const {
        return systemID;
    }
    
    void applyQuantumOperationToAll(double factor) {
        for (size_t i = 0; i < states.size(); ++i) {
            if (states[i]) {
                states[i]->applyQuantumOperation(factor);
            }
        }
        recalculateNormalization();
    }
};

unsigned long long QuantumSuperpositionSystem::nextSystemID = 1;

// 加法专用宇宙
class AdditionUniverse : public MathematicalUniverse, public UniverseOperationsInterface {
private:
    typedef std::pair<int, int> IntPair;
    std::map<IntPair, int> additionCache;
    std::vector<double> cosmicParameters;
    unsigned int cosmicSeed;
    double universeEntropy;
    double cosmicEnergy;
    int operationCount;
    
    // 禁止复制
    AdditionUniverse(const AdditionUniverse&);
    AdditionUniverse& operator=(const AdditionUniverse&);
    
public:
    AdditionUniverse() : MathematicalUniverse(), cosmicSeed(0), 
                         universeEntropy(0.0), cosmicEnergy(1000.0), operationCount(0) {
        initializeCosmicParameters();
    }
    
    AdditionUniverse(unsigned int seed) : MathematicalUniverse(), cosmicSeed(seed), 
                                         universeEntropy(0.0), cosmicEnergy(1000.0), operationCount(0) {
        initializeCosmicParameters();
        srand(seed);
    }
    
    virtual ~AdditionUniverse() {}
    
    virtual std::string describe() const {
        return "A Universe Dedicated to the Sacred Act of Addition";
    }
    
    virtual std::string getDetailedDescription() const {
        return "AdditionUniverse (ID: " + StringUtilities::intToString(universeID) + 
               ", Seed: " + StringUtilities::intToString(cosmicSeed) + 
               ", Entropy: " + StringUtilities::doubleToString(universeEntropy) + 
               ", Energy: " + StringUtilities::doubleToString(cosmicEnergy) + 
               ", Cache: " + StringUtilities::intToString(additionCache.size()) + ")";
    }
    
    // 缓存加法结果
    int cachedAddition(int a, int b) {
        IntPair key = std::make_pair(a, b);
        
        std::map<IntPair, int>::iterator it = additionCache.find(key);
        if (it != additionCache.end()) {
            operationCount++;
            cosmicEnergy -= 0.001; // 每次操作消耗能量
            return it->second;
        }
        
        int result = performSacredAddition(a, b);
        
        additionCache[key] = result;
        additionCache[std::make_pair(b, a)] = result;
        
        updateUniverseEntropy();
        operationCount++;
        cosmicEnergy -= 0.01; // 新计算消耗更多能量
        
        return result;
    }
    
    virtual MathematicalUniverse* clone() const {
        AdditionUniverse* clone = new AdditionUniverse();
        clone->cosmicSeed = this->cosmicSeed;
        clone->universeEntropy = this->universeEntropy;
        clone->cosmicEnergy = this->cosmicEnergy;
        clone->cosmicParameters = this->cosmicParameters;
        clone->operationCount = this->operationCount;
        
        for (std::map<IntPair, int>::const_iterator it = additionCache.begin(); 
             it != additionCache.end(); ++it) {
            clone->additionCache[it->first] = it->second;
        }
        
        return clone;
    }
    
    virtual void initializeFromSeed(unsigned int seed) {
        cosmicSeed = seed;
        srand(seed);
        initializeCosmicParameters();
        resetUniverse();
    }
    
    virtual double calculateCosmicEntropy() const {
        return universeEntropy;
    }
    
    virtual bool verifyConsistency() const {
        return cosmicEnergy > 0 && universeEntropy >= 0;
    }
    
    virtual void performCosmicMaintenance() {
        cosmicEnergy += 0.1; // 宇宙自我恢复能量
        if (cosmicEnergy > 10000.0) {
            cosmicEnergy = 10000.0;
        }
    }
    
    virtual std::vector<double> getCosmicParameters() const {
        return cosmicParameters;
    }
    
    // UniverseOperationsInterface 实现
    virtual void expandUniverse() {
        cosmicEnergy *= 1.1;
        universeEntropy *= 1.05;
    }
    
    virtual void contractUniverse() {
        cosmicEnergy *= 0.9;
        universeEntropy *= 0.95;
    }
    
    virtual void stabilizeUniverse() {
        cosmicEnergy = (cosmicEnergy + 1000.0) / 2.0;
        universeEntropy = (universeEntropy + 1.0) / 2.0;
    }
    
    virtual void addCosmicPerturbation(double magnitude) {
        cosmicEnergy += magnitude * 100.0;
        universeEntropy += magnitude * 0.1;
    }
    
    virtual double measureCosmicEnergy() const {
        return cosmicEnergy;
    }
    
    size_t getCacheSize() const {
        return additionCache.size();
    }
    
    int getOperationCount() const {
        return operationCount;
    }
    
    double getEnergyLevel() const {
        return cosmicEnergy;
    }
    
    void clearCache() {
        additionCache.clear();
    }
    
    void resetUniverse() {
        additionCache.clear();
        universeEntropy = 0.0;
        cosmicEnergy = 1000.0;
        operationCount = 0;
        initializeCosmicParameters();
    }
    
    void rechargeEnergy(double amount) {
        cosmicEnergy += amount;
        if (cosmicEnergy < 0) cosmicEnergy = 0;
        if (cosmicEnergy > 10000.0) cosmicEnergy = 10000.0;
    }
    
private:
    void initializeCosmicParameters() {
        cosmicParameters.clear();
        for (int i = 0; i < UNIVERSAL_CONSTANTS_COUNT; ++i) {
            cosmicParameters.push_back((double)rand() / RAND_MAX);
        }
        universeEntropy = calculateInitialEntropy();
    }
    
    double calculateInitialEntropy() const {
        double entropy = 0.0;
        for (size_t i = 0; i < cosmicParameters.size(); ++i) {
            if (cosmicParameters[i] > 0.0 && cosmicParameters[i] < 1.0) {
                double p = cosmicParameters[i];
                entropy -= p * log(p) + (1 - p) * log(1 - p);
            }
        }
        return entropy / 10.0;
    }
    
    void updateUniverseEntropy() {
        double entropyIncrease = log((double)additionCache.size() + 1.0) / log(2.0);
        universeEntropy += entropyIncrease / 10000.0;
    }
    
    // 神圣的加法仪式
    int performSacredAddition(int a, int b) {
        validateCosmicNumber(a);
        validateCosmicNumber(b);
        
        QuantumSuperpositionSystem superpositionSystem = QuantumSuperpositionSystem();
        
        std::vector<int> possibleResults;
        generatePossibleResults(a, b, possibleResults);
        
        for (size_t i = 0; i < possibleResults.size(); ++i) {
            double amplitude = 1.0 / sqrt((double)possibleResults.size());
            AdditionQuantumState* state = new AdditionQuantumState(
                a, b, possibleResults[i], amplitude);
            superpositionSystem.addState(state);
            delete state;
        }
        
        QuantumState* collapsedState = superpositionSystem.collapse();
        int result = extractResultFromCollapsedState(collapsedState, a, b);
        
        delete collapsedState;
        
        validateAdditionResult(a, b, result);
        
        cosmicEnergy -= superpositionSystem.calculateTotalEnergy() / 1000.0;
        
        return result;
    }
    
    void validateCosmicNumber(int n) {
        if (n < INT_MIN_VALUE || n > INT_MAX_VALUE) {
            throw std::out_of_range("Number violates cosmic bounds");
        }
    }
    
    void generatePossibleResults(int a, int b, std::vector<int>& results) {
        results.clear();
        
        // 传统加法
        results.push_back(a + b);
        
        // 各种可能的加法结果
        results.push_back((a | b) + (a & b));
        results.push_back((a ^ b) + 2 * (a & b));
        results.push_back(MathUtilities::absoluteValue(a) + MathUtilities::absoluteValue(b));
        results.push_back(-(-a - b));
        results.push_back((a * 2 + b * 2) / 2);
        results.push_back((a + b) * 1);
        results.push_back((a + b) + 0);
        results.push_back((a + 0) + (b + 0));
        results.push_back(((a + b) << 1) >> 1);
        results.push_back(~(~a - b));
        results.push_back((a + b) ^ 0);
        results.push_back((a + b) | 0);
        results.push_back((a + b) & ~0);
        
        // 安全的模运算
        if (INT_MAX_VALUE != 0) {
            results.push_back(((a + b) % INT_MAX_VALUE) + ((a + b) / INT_MAX_VALUE));
        } else {
            results.push_back(a + b);
        }
        
        results.push_back(((a + b) + 1) - 1);
        results.push_back(((a + b) - 1) + 1);
        results.push_back(((a + b) * 2) / 2);
        results.push_back(((a + b) / 2) * 2);
        
        // 添加一些基于宇宙参数的随机结果
        for (int i = 0; i < 5; ++i) {
            double cosmicFactor = cosmicParameters[i % cosmicParameters.size()];
            int cosmicResult = (int)(a + b + cosmicFactor * 10 - 5);
            results.push_back(cosmicResult);
        }
        
        // 添加基于数学函数的额外结果
        results.push_back((int)((a + b) * MATHEMATICAL_PHI / 2.0));
        results.push_back((int)((a + b) * MATHEMATICAL_SQRT2));
        results.push_back((int)((a + b) / MATHEMATICAL_SQRT2));
    }
    
    int extractResultFromCollapsedState(QuantumState* state, int a, int b) {
        if (!state) {
            return a + b;
        }
        
        AdditionQuantumState* additionState = dynamic_cast<AdditionQuantumState*>(state);
        if (additionState) {
            return additionState->getResult();
        }
        
        return a + b;
    }
    
    void validateAdditionResult(int a, int b, int result) {
        // 验证逻辑，但不输出
    }
};

// 策略基类
class AdditionStrategy {
public:
    virtual ~AdditionStrategy() {}
    virtual int add(int a, int b) = 0;
    virtual std::string getName() const = 0;
    virtual std::string getDescription() const = 0;
    virtual double getComplexityFactor() const = 0;
    virtual bool requiresSpecialComputation() const = 0;
    virtual void reset() = 0;
    virtual void optimize() = 0;
    virtual double estimateComputationCost(int a, int b) const = 0;
};

// 简单加法策略
class SimpleAdditionStrategy : public AdditionStrategy {
private:
    int usageCount;
    
public:
    SimpleAdditionStrategy() : usageCount(0) {}
    
    virtual int add(int a, int b) {
        usageCount++;
        return a + b;
    }
    
    virtual std::string getName() const {
        return "Simple Addition";
    }
    
    virtual std::string getDescription() const {
        return "Direct integer addition using built-in operator";
    }
    
    virtual double getComplexityFactor() const {
        return 1.0;
    }
    
    virtual bool requiresSpecialComputation() const {
        return false;
    }
    
    virtual void reset() {
        usageCount = 0;
    }
    
    virtual void optimize() {
        // 无需优化
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        return 1.0;
    }
    
    int getUsageCount() const {
        return usageCount;
    }
};

// 递归加法策略
class RecursiveAdditionStrategy : public AdditionStrategy {
private:
    int recursionCount;
    int totalCalls;
    
public:
    RecursiveAdditionStrategy() : recursionCount(0), totalCalls(0) {}
    
    virtual int add(int a, int b) {
        totalCalls++;
        recursionCount = 0;
        return recursiveAdd(a, b);
    }
    
    virtual std::string getName() const {
        return "Recursive Bitwise Addition";
    }
    
    virtual std::string getDescription() const {
        return "Uses bitwise operations and recursion for addition";
    }
    
    virtual double getComplexityFactor() const {
        return 2.5;
    }
    
    virtual bool requiresSpecialComputation() const {
        return false;
    }
    
    virtual void reset() {
        recursionCount = 0;
        totalCalls = 0;
    }
    
    virtual void optimize() {
        // 可添加尾递归优化等
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        return 2.0 * (MathUtilities::absoluteValue(a) + MathUtilities::absoluteValue(b));
    }
    
    int getRecursionDepth() const {
        return recursionCount;
    }
    
    int getTotalCalls() const {
        return totalCalls;
    }
    
private:
    int recursiveAdd(int a, int b) {
        recursionCount++;
        if (b == 0) return a;
        if (a == 0) return b;
        return recursiveAdd(a ^ b, (a & b) << 1);
    }
};

// 循环加法策略
class LoopAdditionStrategy : public AdditionStrategy {
private:
    int iterationCount;
    int totalOperations;
    
public:
    LoopAdditionStrategy() : iterationCount(0), totalOperations(0) {}
    
    virtual int add(int a, int b) {
        iterationCount = 0;
        while (b != 0) {
            iterationCount++;
            int carry = a & b;
            a = a ^ b;
            b = carry << 1;
        }
        totalOperations += iterationCount;
        return a;
    }
    
    virtual std::string getName() const {
        return "Loop-based Bitwise Addition";
    }
    
    virtual std::string getDescription() const {
        return "Uses bitwise operations in a loop for addition";
    }
    
    virtual double getComplexityFactor() const {
        return 2.0;
    }
    
    virtual bool requiresSpecialComputation() const {
        return false;
    }
    
    virtual void reset() {
        iterationCount = 0;
        totalOperations = 0;
    }
    
    virtual void optimize() {
        // 可添加循环展开等优化
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        return 1.5 * (MathUtilities::absoluteValue(a) + MathUtilities::absoluteValue(b));
    }
    
    int getIterationCount() const {
        return iterationCount;
    }
    
    int getTotalOperations() const {
        return totalOperations;
    }
};

// 宇宙加法策略
class CosmicAdditionStrategy : public AdditionStrategy {
private:
    AdditionUniverse* universe;
    unsigned int universeSeed;
    int computationCount;
    
public:
    CosmicAdditionStrategy() : universe(NULL), universeSeed(DEFAULT_UNIVERSE_SEED), computationCount(0) {
        universe = new AdditionUniverse(universeSeed);
        ParallelUniverseManager::getInstance().addUniverse(universe);
    }
    
    CosmicAdditionStrategy(unsigned int seed) : universe(NULL), universeSeed(seed), computationCount(0) {
        universe = new AdditionUniverse(universeSeed);
        ParallelUniverseManager::getInstance().addUniverse(universe);
    }
    
    virtual ~CosmicAdditionStrategy() {
        if (universe) {
            delete universe;
            universe = NULL;
        }
    }
    
    virtual int add(int a, int b) {
        computationCount++;
        if (!universe || !universe->doesExist()) {
            throw std::runtime_error("Addition universe has collapsed!");
        }
        
        return universe->cachedAddition(a, b);
    }
    
    virtual std::string getName() const {
        return "Cosmic Quantum Addition with Universe Caching";
    }
    
    virtual std::string getDescription() const {
        return "Uses quantum superposition in a parallel universe with caching";
    }
    
    virtual double getComplexityFactor() const {
        return 10.0;
    }
    
    virtual bool requiresSpecialComputation() const {
        return true;
    }
    
    virtual void reset() {
        if (universe) {
            universe->resetUniverse();
        }
        computationCount = 0;
    }
    
    virtual void optimize() {
        if (universe) {
            universe->stabilizeUniverse();
        }
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        return 5.0 + (universe ? universe->getCacheSize() / 1000.0 : 0);
    }
    
    AdditionUniverse* getUniverse() const {
        return universe;
    }
    
    unsigned int getUniverseSeed() const {
        return universeSeed;
    }
    
    int getComputationCount() const {
        return computationCount;
    }
    
    void rechargeUniverse(double energy) {
        if (universe) {
            universe->rechargeEnergy(energy);
        }
    }
};

// 装饰器基类
class AdditionDecorator : public AdditionStrategy {
protected:
    AdditionStrategy* wrappedStrategy;
    
public:
    AdditionDecorator(AdditionStrategy* strategy) : wrappedStrategy(strategy) {}
    
    virtual ~AdditionDecorator() {
        if (wrappedStrategy) {
            delete wrappedStrategy;
            wrappedStrategy = NULL;
        }
    }
    
    virtual int add(int a, int b) {
        return wrappedStrategy->add(a, b);
    }
    
    virtual std::string getName() const {
        return wrappedStrategy->getName();
    }
    
    virtual std::string getDescription() const {
        return wrappedStrategy->getDescription();
    }
    
    virtual double getComplexityFactor() const {
        return wrappedStrategy->getComplexityFactor();
    }
    
    virtual bool requiresSpecialComputation() const {
        return wrappedStrategy->requiresSpecialComputation();
    }
    
    virtual void reset() {
        wrappedStrategy->reset();
    }
    
    virtual void optimize() {
        wrappedStrategy->optimize();
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        return wrappedStrategy->estimateComputationCost(a, b);
    }
};

// 缓存装饰器
class CachingDecorator : public AdditionDecorator {
private:
    typedef std::pair<int, int> IntPair;
    std::map<IntPair, int> cache;
    size_t maxCacheSize;
    size_t hitCount;
    size_t missCount;
    size_t evictionCount;
    
public:
    CachingDecorator(AdditionStrategy* strategy, size_t maxSize = MAX_CACHE_SIZE) 
        : AdditionDecorator(strategy), maxCacheSize(maxSize), 
          hitCount(0), missCount(0), evictionCount(0) {}
    
    virtual ~CachingDecorator() {}
    
    virtual int add(int a, int b) {
        IntPair key = std::make_pair(a, b);
        
        std::map<IntPair, int>::iterator it = cache.find(key);
        if (it != cache.end()) {
            hitCount++;
            return it->second;
        }
        
        missCount++;
        int result = wrappedStrategy->add(a, b);
        
        if (cache.size() >= maxCacheSize) {
            // 简单的先进先出驱逐策略
            if (!cache.empty()) {
                cache.erase(cache.begin());
                evictionCount++;
            }
        }
        
        cache[key] = result;
        cache[std::make_pair(b, a)] = result;
        
        return result;
    }
    
    virtual std::string getName() const {
        return "Cached " + wrappedStrategy->getName();
    }
    
    virtual std::string getDescription() const {
        return "Caching Decorator: " + wrappedStrategy->getDescription() + 
               " (Hit Rate: " + StringUtilities::doubleToString(getHitRate() * 100, 2) + "%)";
    }
    
    virtual double getComplexityFactor() const {
        return wrappedStrategy->getComplexityFactor() * 0.8;
    }
    
    virtual void reset() {
        wrappedStrategy->reset();
        cache.clear();
        hitCount = 0;
        missCount = 0;
        evictionCount = 0;
    }
    
    virtual void optimize() {
        wrappedStrategy->optimize();
        // 可添加缓存优化策略
    }
    
    virtual double estimateComputationCost(int a, int b) const {
        IntPair key = std::make_pair(a, b);
        if (cache.find(key) != cache.end()) {
            return 0.1; // 缓存命中成本低
        }
        return wrappedStrategy->estimateComputationCost(a, b) * 0.9; // 装饰器优化
    }
    
    size_t getHitCount() const {
        return hitCount;
    }
    
    size_t getMissCount() const {
        return missCount;
    }
    
    size_t getEvictionCount() const {
        return evictionCount;
    }
    
    double getHitRate() const {
        size_t total = hitCount + missCount;
        return total > 0 ? (double)hitCount / total : 0.0;
    }
    
    size_t getCacheSize() const {
        return cache.size();
    }
    
    void clearCache() {
        cache.clear();
        hitCount = 0;
        missCount = 0;
        evictionCount = 0;
    }
    
    void resizeCache(size_t newSize) {
        maxCacheSize = newSize;
        while (cache.size() > maxCacheSize) {
            cache.erase(cache.begin());
            evictionCount++;
        }
    }
};

// 性能监控装饰器
class PerformanceMonitoringDecorator : public AdditionDecorator {
private:
    struct PerformanceMetrics {
        int totalCalls;
        long long totalTime;
        int minTime;
        int maxTime;
        
        PerformanceMetrics() : totalCalls(0), totalTime(0), minTime(INT_MAX), maxTime(0) {}
    };
    
    PerformanceMetrics metrics;
    
public:
    PerformanceMonitoringDecorator(AdditionStrategy* strategy) : AdditionDecorator(strategy) {}
    
    virtual ~PerformanceMonitoringDecorator() {}
    
    virtual int add(int a, int b) {
        metrics.totalCalls++;
        
        // 这里不实际计时，只记录调用次数
        int result = wrappedStrategy->add(a, b);
        
        // 模拟时间消耗估计
        int estimatedTime = (int)wrappedStrategy->estimateComputationCost(a, b) * 10;
        metrics.totalTime += estimatedTime;
        
        if (estimatedTime < metrics.minTime) metrics.minTime = estimatedTime;
        if (estimatedTime > metrics.maxTime) metrics.maxTime = estimatedTime;
        
        return result;
    }
    
    virtual std::string getName() const {
        return "Monitored " + wrappedStrategy->getName();
    }
    
    virtual std::string getDescription() const {
        return "Performance Monitoring Decorator: " + wrappedStrategy->getDescription();
    }
    
    virtual double getComplexityFactor() const {
        return wrappedStrategy->getComplexityFactor() * 1.05;
    }
    
    virtual void reset() {
        wrappedStrategy->reset();
        metrics = PerformanceMetrics();
    }
    
    virtual void optimize() {
        wrappedStrategy->optimize();
    }
    
    PerformanceMetrics getMetrics() const {
        return metrics;
    }
    
    double getAverageTime() const {
        return metrics.totalCalls > 0 ? (double)metrics.totalTime / metrics.totalCalls : 0.0;
    }
};

// 构建器类
class AdditionBuilder {
private:
    AdditionStrategy* strategy;
    bool validationEnabled;
    bool cachingEnabled;
    bool monitoringEnabled;
    size_t cacheSize;
    unsigned int universeSeed;
    
public:
    AdditionBuilder() : strategy(NULL), validationEnabled(false), 
                       cachingEnabled(false), monitoringEnabled(false),
                       cacheSize(MAX_CACHE_SIZE), universeSeed(DEFAULT_UNIVERSE_SEED) {
        strategy = new SimpleAdditionStrategy();
    }
    
    ~AdditionBuilder() {
        if (strategy) {
            delete strategy;
            strategy = NULL;
        }
    }
    
    AdditionBuilder& withSimpleStrategy() {
        if (strategy) delete strategy;
        strategy = new SimpleAdditionStrategy();
        return *this;
    }
    
    AdditionBuilder& withRecursiveStrategy() {
        if (strategy) delete strategy;
        strategy = new RecursiveAdditionStrategy();
        return *this;
    }
    
    AdditionBuilder& withLoopStrategy() {
        if (strategy) delete strategy;
        strategy = new LoopAdditionStrategy();
        return *this;
    }
    
    AdditionBuilder& withCosmicStrategy() {
        if (strategy) delete strategy;
        strategy = new CosmicAdditionStrategy(universeSeed);
        return *this;
    }
    
    AdditionBuilder& enableCaching(bool enable = true, size_t size = MAX_CACHE_SIZE) {
        cachingEnabled = enable;
        cacheSize = size;
        return *this;
    }
    
    AdditionBuilder& enableMonitoring(bool enable = true) {
        monitoringEnabled = enable;
        return *this;
    }
    
    AdditionBuilder& withUniverseSeed(unsigned int seed) {
        universeSeed = seed;
        return *this;
    }
    
    AdditionStrategy* build() {
        AdditionStrategy* result = strategy;
        strategy = NULL; // 转移所有权
        
        if (cachingEnabled) {
            result = new CachingDecorator(result, cacheSize);
        }
        
        if (monitoringEnabled) {
            result = new PerformanceMonitoringDecorator(result);
        }
        
        return result;
    }
};

// 主加法器类（单例模式）
class UltraComplexAdder {
private:
    static UltraComplexAdder* instance;
    AdditionStrategy* additionStrategy;
    int totalOperations;
    
    UltraComplexAdder() : additionStrategy(NULL), totalOperations(0) {
        AdditionBuilder builder;
        builder.withSimpleStrategy(); // 使用简单策略确保性能
        additionStrategy = builder.build();
    }
    
    UltraComplexAdder(const UltraComplexAdder&);
    UltraComplexAdder& operator=(const UltraComplexAdder&);
    
public:
    static UltraComplexAdder& getInstance() {
        if (!instance) {
            instance = new UltraComplexAdder();
        }
        return *instance;
    }
    
    static void destroyInstance() {
        if (instance) {
            delete instance;
            instance = NULL;
        }
        ParallelUniverseManager::destroyInstance();
    }
    
    ~UltraComplexAdder() {
        if (additionStrategy) {
            delete additionStrategy;
            additionStrategy = NULL;
        }
    }
    
    int add(int a, int b) {
        totalOperations++;
        return additionStrategy->add(a, b);
    }
    
    void setStrategy(AdditionStrategy* newStrategy) {
        if (additionStrategy) {
            delete additionStrategy;
        }
        additionStrategy = newStrategy;
    }
    
    int getTotalOperations() const {
        return totalOperations;
    }
    
    void resetStatistics() {
        totalOperations = 0;
        if (additionStrategy) {
            additionStrategy->reset();
        }
    }
};

UltraComplexAdder* UltraComplexAdder::instance = NULL;

// 主函数
int main() {
    int a, b;
    
    // 只读取输入
    if (!(std::cin >> a >> b)) {
        return 1;
    }
    
    // 获取加法器实例并计算
    UltraComplexAdder& adder = UltraComplexAdder::getInstance();
    int result = adder.add(a, b);
    
    // 输出结果
    std::cout << result << std::endl;
    
    // 清理
    UltraComplexAdder::destroyInstance();
    
    return 0;
}