class BinaryString {
public:
    std::string value;

    BinaryString(const std::string& bin_str) : value(bin_str) {}

    // Overload the + operator
    BinaryString operator+(const BinaryString& other) const {
        std::string result = "";
        
        for (int i = 0; i<value.size(); i++) {
            if(value[i]=='1' || other.value[i]=='1'){
                result+="1";
            }
        }
        std::reverse(result.begin(), result.end());
        return BinaryString(result);
    }
};



vector<int> acmTeam(vector<string> topic) {
    int subjects = 0;
    int knowitalls = 0;
    std::vector<BinaryString> teams;
    std::transform(topic.begin(), topic.end(), std::back_inserter(teams), [](const std::string& s) { return BinaryString(s); });
    
    for(int i = 0; i<teams.size(); i++){
        for(int j = i+1; j<teams.size(); j++){
             BinaryString team_sum = teams[i] + teams[j];
             
             if(team_sum.value.size()>subjects){
                subjects = team_sum.value.size();
                knowitalls = 0;
             }
             
            if(team_sum.value.size()==subjects){
                knowitalls++;
             }
        }
    }
    
    
    return {subjects, knowitalls};
}