string multiply(string num1, string num2) {

         string small ;

         string big;

         if( num1.size() < num2.size() ){

             small = num1;

             big = num2;

         }else if( num2.size() < num1.size() ){

             small = num2;

             big = num1;

         }else{

             small = num1;

             big = num2;

         }

         int n = small.size() ;

         vector<string> re;

         string::reverse_iterator it_s = small.rbegin() ;

         while( it_s != small.rend() ){

             string  s;

             int up = ;

             string::reverse_iterator it_b = big.rbegin() ;

             while( it_b != big.rend() ){

                 int m = (*it_s - '') * (*it_b - '') + up;

                 if(  m <  ){

                     s = std::to_string(m) + s;

                     up = ;

                 }else{

                     s = std::to_string( m% )  + s;

                     up = m/;

                 }

                 ++it_b;

             }

             if( up !=  ){

                 s = std::to_string( up ) + s;

             }

             re.push_back( s );

             ++it_s;

         }

         string zero;

         for( vector<string>::iterator it = re.begin() ; it != re.end() ; it++ ){

             *it += zero;

             zero += "";

         }

         string result = "" ;

         for( int i =  ; i < re.size() ; i++ ){

             result = binaryAdd( result , re[i] );

         }

         int q = ;

         for( string::iterator it = result.begin() ; it != result.end() ; ++it ){

             q += (*it - '');

         }

         if( q == )

             result = "";

         return result;

     }

     string binaryAdd( string s1 , string s2 ){

         string s;

         string::reverse_iterator it1 = s1.rbegin();

         string::reverse_iterator it2 = s2.rbegin();

         int up = ;

         while( it1 != s1.rend() && it2 != s2.rend() ){

             int a = (*it1 - '') + (*it2 - '') + up;

             if( a <  ){

                 s  = std::to_string(a) + s;

                 up = ;

             }else{

                 s = std::to_string( a -  ) + s;

                 up = ;

             }

             ++it1 ;

             ++it2 ;

         }

         while( it1 != s1.rend() ){

             if( *it1 - '' + up <  ){

                 s = std::to_string( *it1 - '' + up ) + s;

                 up = ;

             }else{

                 s = std::to_string( *it1 - '' + up -  ) + s;

                 up = ;

             }

             ++it1;

         }

         while( it2 != s2.rend() ){

             if( *it2 - '' + up <  ){

                 s = std::to_string( *it2 - '' + up ) + s;

                 up = ;

             }else{

                 s = std::to_string( *it2 - '' + up -  ) + s;

                 up = ;

             }

             ++it2;

         }

         if( up == ){

             s = std::to_string() + s;

         }

         return s;

     }