#include <cstdlib>   #include <cstdarg>   #include <cassert>   #include <cctype> // tolower   #include <ctime>   #include <cmath>      #include <iostream>   #include <sstream>   #include <fstream>   #include <iomanip>   #include <stdexcept>      #include <map>   #include <set>   #include <list>   #include <queue>   #include <vector>   #include <string>      #include <limits>   #include <utility>      #include <numeric>   #include <iterator>   #include <algorithm>   #include <functional>      /*    * g++ -g -std=c++11 -DBUG -D_GLIBCXX_DEBUG -Wall -Wfatal-errors -o cforce{,.cpp}    * g++ -g -DBUG -D_GLIBCXX_DEBUG -Wall -Wfatal-errors -o cforce{,.cpp}    *    * TODO:    *      C++ dataframe    *      stl11 -> c++11 standard template lib in c++98    *      overload >> for map and set, using (insert) iterator    *      chmod:: consider an algorithm stable to int64 overflow    *      shortest path algorithm    *      shortest path in a tree    *      maximum network flow    *      partial idx/iter sort    *      a prime number generator which traverses prime numbers w/ ++    *      a divisor generator which traverses divisors efficiently    *      Apply1st ?!    *      Apply2nd and bind2nd ?!    *          count_if ( a.begin(), a.end(), a.second < x )    *      Arbitrary-precision arithmetic / Big Integer / Fraction - rational num    *      tuple class --> cplusplus.com/reference/tuple    *      get<1>, get<2>, bind2nd ( foo ( get<2> pair ), val )    *      isin( const T & val, first, last )    *      fuinction composition in c++    *          blogea.bureau14.fr/index.php/2012/11/function-composition-in-c11/    *          cpp-next.com/archive/2010/11/expressive-c-fun-with-function-composition/    *      TimeWrapper -- accumulate time of a function call    *          stackoverflow.com/questions/879408    *      hash map -- possible hash value & obj % some_big_prime [ b272 ]    *          lower level can be a simple map to resolve hash collisions    *      add explicit everywhere necessary    *      bloom filters    *      heap -> how to update values in place / increase-key or decrease-key ... IterHeap ?!    *      median maintaince --> max_heap / min_heap    *      prim s min spaning tree alg. O ( m log n ) using heap contianing V - X vertices    *      kruskal algorithm minimum cost spanning tree with union find data structure    *      unique_ptr    *      hufman codes    *      simple arithmatic tests    *      longest common subsequence using seq. alignment type algorithm    *      longest common substring ( consequative subsequeance )    *      Graham scan; en.wikipedia.org/wiki/Graham_scan    */      /*    * @recepies    * ----------------------------------------------    * odd / even    *      transform ( x.begin(), x.end(), x.begin(), bind2nd( modulus<int>(), 2 ));    *      count_if ( x.begin(), x.end(), bind2nd( modulus < int > (), 2));    * Apply2nd    *      max_element ( m.begin(), m.end(), Apply2nd < string, int , less < int > > )    *      sort ( a.begin(), a.end(), Apply2nd < char, int , greater< int > > )    *      count_if ( m.begin(), m.end(), Apply2nd < string, int, modulus < int > > )    *      accumulate ( m.begin(), m.end(), 0.0, Apply2nd < int, double, plus < double > > )    *      accumulate ( m.begin( ), m.end( ), pair < int, double> ( 0 , 0.0 ) , operator+ < int, double > )    * abs_diff    *      adjacent_difference ( a.begin(), a.end(), adj_diff.begin( ), abs_diff < int > ( ) )    *      accumulate ( a.begin(), a.end(), 0, abs_diff < int > ( ) )    * erase    *      a.erase ( remove_if ( a.begin( ), a.end( ), bind2nd ( less < int >( ), 0 ) ), a.end( ) )    *      a.erase ( remove ( a.begin( ), a.end( ), b.begin( ), b.end( ) ), a.end ( ) )    * binding    *      bind2nd ( mem_fun_ref (& ClassName::m_func ), arg )  // binds the argument of the object    * iterator generators    *      generate_n ( back_inserter ( a ), n, rand );  // calls push_back    *      generate_n ( inserter( a, a.begin( ) + 5 ), 10, RandInt( 0 , 100 ) )  // calls insert    *      copy ( foo.begin( ), foo.end( ), insert_iterator < std::list < double > > ( bar, bar.begin( ) + 5 ))    * copy ( a.begin( ), a.end( ), ostream_iterator < double > ( cout,  ,   ))    * accumulate ( m.begin( ), m.end( ), pair < int, double> ( 0 , 0.0 ) , operator+ < int, double > )    * transform (numbers.begin(), numbers.end(), lengths.begin(), mem_fun_ref(&string::length));    */      /*    * @good read    * ----------------------------------------------    *  [ partial ] template specialization    *      cprogramming.com/tutorial/template_specialization.html    *  function composition    *      cpp-next.com/archive/2010/11/expressive-c-fun-with-function-composition    */      /*    * @prob set    * ----------------------------------------------    *  purification --> c330    */      /*    * @limits    * ----------------------------------------------    * int                  31    2.14e+09    * long int             31    2.14e+09    * unsigned             32    4.29e+09    * long unsigned        32    4.29e+09    * size_t               32    4.29e+09    * long long int        63    9.22e+18    * long long unsigned   64    1.84e+19    */      /*    * issues    * ----------------------------------------------    * stackoverflow.com/questions/10281809    * mem_fun -> func_obj ( pointer to instance, origanal argument )    * bind1st ( mem_fun ( & ClassName::m_func ), this )    // binds obj of the class    * bind1st takes  const T &  as the first argument    */      /*    *  typedef / define    * ----------------------------------------------    */      typedef          long long int  int64;   typedef unsigned long long int uint64;      #define DOUBLE_INF std::numeric_limits< double >::infinity()   #define DOUBLE_NAN std::numeric_limits< double >::quiet_NaN()      #define DECLARE( X )        typedef       shared_ptr < X >  X ## _shared_ptr;        typedef const shared_ptr < X >  X ## _const_shared_ptr;      #ifdef BUG       #define DEBUG(var) { std::cout << #var <<  :   << (var) << std::endl; }       #define EXPECT(expr) if ( ! (expr) ) std::cerr <<  Assertion              << #expr   failed at   << __FILE__ <<  :  << __LINE__ << std::endl;   #else       #define DEBUG(var)       #define EXPECT(expr)   #endif         #define DBG(v) std::copy( v.begin(), v.end(), std::ostream_iterator < typeof( *v.begin() )> ( std::cout,     ) )      /*    * http://rootdirectory.de/wiki/SSTR()    * usage:    *      SSTR(  x^2:   << x*x )    */   #define SSTR( val ) dynamic_cast< std::ostringstream & >( std::ostringstream() << std::dec << val ).str()         /* https://www.quora.com/C++-programming-language/What-are-some-cool-C++-tricks */   // template <typename T, size_t N>   // char (&ArraySizeHelper(T (&array)[N]))[N];   // #define arraysize(array) (sizeof(ArraySizeHelper(array)))      /*    * forward decleration    * ----------------------------------------------    */   class ScopeTimer;      /*    *  functional utils    * ----------------------------------------------    */      template < typename T >   struct abs_diff : std::binary_function < T, T, T >   {       typedef T value_type;          inline value_type operator( ) ( const value_type & x, const value_type & y ) const       {           return std::abs( x - y );       }   };      // template < class InputIterator, class T >   // class isin : public std::binary_function < InputIterator, InputIterator, bool >   // {   //     public:   //         typedef T value_type;   //   //         isin ( const InputIterator & first, const InputIterator & last ):   //             m_first ( first ), m_last ( last ) { }   //   //         bool operator ( ) ( const value_type & val ) const   //         {   //             return std::find ( m_first, m_last, val ) != m_last;   //         }   //     private:   //         const InputIterator m_first, m_last;   // }      template < typename value_type, typename cont_type >   class isin : public std::unary_function < value_type, bool >   {       public:           isin( const cont_type & vals ): m_vals ( vals ) { };              bool operator ( ) ( const value_type & x ) const           {               return std::find ( m_vals.begin( ), m_vals.end( ), x ) != m_vals.end( );           }          private:           const cont_type m_vals;   };      /*    * max_element, min_element, count_if ... on the 2nd element    * eg: max_element ( m.begin(), m.end(), Apply2nd < string, int , less < int > > )    */   template < class T1, class T2, class BinaryOperation >   class Apply2nd : std::binary_function < typename std::pair < T1, T2 >,                                           typename std::pair < T1, T2 >,                                           typename BinaryOperation::result_type >   {       public:           typedef T1 first_type;           typedef T2 second_type;              typedef typename BinaryOperation::result_type result_type;           typedef typename std::pair < first_type, second_type > value_type;              inline result_type operator( ) ( const value_type & x, const value_type & y ) const           {               return binary_op ( x.second , y.second );           }       private:           BinaryOperation binary_op;   };      /*    * algo utils    * ----------------------------------------------    */         /**    * count the number of inversions in a permutation; i.e. how many    * times two adjacent elements need to be swaped to sort the list;    * 3 5 2 4 1  -->  7    */   template < class InputIterator >   typename std::iterator_traits<InputIterator>::difference_type   count_inv ( InputIterator first, InputIterator last )   {       typedef typename std::iterator_traits<InputIterator>::difference_type difference_type;       typedef typename std::iterator_traits<InputIterator>::value_type value_type;          std::list < value_type > l; /* list of sorted values */       difference_type cnt = 0;          for ( difference_type n = 0; first != last; ++first, ++n )       {           /* count how many elements larger than *first appear before *first */           typename std::list < value_type >::iterator iter = l.begin( );           cnt += n;              for ( ; iter != l.end( ) && * iter <= * first; ++ iter, -- cnt )               ;           l.insert( iter, * first );       }          return cnt;   }      template < class ForwardIterator, class T >   inline void fill_inc_seq ( ForwardIterator first, ForwardIterator last, T val )   {       for ( ; first != last; ++first, ++val )           * first = val;   }      template <class ForwardIterator, class InputIterator >   ForwardIterator remove ( ForwardIterator first, ForwardIterator last, InputIterator begin, InputIterator end )   {       ForwardIterator result = first;          for ( ; first != last; ++ first )           if ( find ( begin, end, *first ) == end )           {               *result = *first;               ++result;           }          return result;   }      /* stackoverflow.com/questions/1577475 */   template < class RAIter, class Compare >   class ArgSortComp   {       public:           ArgSortComp ( const RAIter & first, Compare comp ):  m_first ( first ), m_comp( comp ) { }           inline bool operator() ( const size_t & i, const size_t & j ) const           {               return m_comp (  m_first[ i ] ,  m_first[ j ] );           }       private:           const RAIter & m_first;           const Compare m_comp;   };      /*!    * usage:    *      vector < size_t > idx;    *      argsort ( a.begin( ), a.end( ), idx, less < Type > ( ) );    */   template < class RAIter, class Compare >   void argsort ( const RAIter & first, const RAIter & last, std::vector < size_t > & idx, Compare comp )   {       const size_t n = last - first;       idx.resize ( n );          for ( size_t j = 0; j < n; ++ j )           idx[ j ] = j ;          std::sort ( idx.begin( ), idx.end( ), ArgSortComp< RAIter, Compare > ( first, comp ) );   }      template < class RAIter, class Compare >   class IterSortComp   {       public:           IterSortComp ( Compare comp ): m_comp ( comp ) { }           inline bool operator( ) ( const RAIter & i, const RAIter & j ) const           {               return m_comp ( * i, * j );           }       private:           const Compare m_comp;   };      /*!    * usage:    *      vector < list < Type >::const_iterator > idx;    *      itersort ( a.begin( ), a.end( ), idx, less < Type > ( ) );    */   template <class INIter, class RAIter, class Compare>   void itersort ( INIter first, INIter last, std::vector < RAIter > & idx, Compare comp )   {       /* alternatively: stackoverflow.com/questions/4307271 */       idx.resize ( std::distance ( first, last ) );       for ( typename std::vector < RAIter >::iterator j = idx.begin( ); first != last; ++ j, ++ first )           * j = first;          std::sort ( idx.begin( ), idx.end( ), IterSortComp< RAIter, Compare > (comp ) );   }         /*    *  string utils    * ----------------------------------------------    */      inline void erase ( std::string & str, const char & ch )   {       std::binder2nd < std::equal_to < char > > isch ( std::equal_to < char > ( ), ch );       std::string::iterator iter = std::remove_if ( str.begin(), str.end(), isch );       str.erase ( iter, str.end() );   }      inline void erase ( std::string & str, const std::string & chrs )   {       isin < char, std::string > isin_chrs ( chrs );       std::string::iterator iter = std::remove_if ( str.begin(), str.end(), isin_chrs );       str.erase ( iter, str.end() );   }      template < typename value_type>   inline std::string val2str ( const value_type & x )   {       std::ostringstream sout ( std::ios_base::out );       sout << x;       return sout.str();   }      template < typename value_type>   inline value_type str2val ( const std::string & str )   {       std::istringstream iss ( str, std::ios_base::in );       value_type val;          iss >> val;       return val;   }      std::vector< std::string > tokenize ( const std::string & str, const char & sep )   {       /*!        * outputs empty tokens and assumes str does not start with sep        * corner cases:        *      empty string, one char string,        *      string starting/ending with sep, all sep, end with two sep        */          std::vector < std::string > res;       std::string::const_iterator follow = str.begin( ),                                   lead   = str.begin( );          while ( true )       {           while ( lead != str.end() && * lead != sep )               ++ lead;              res.push_back ( std::string( follow, lead ) );              if ( lead != str.end ( ) )               follow = 1 + lead ++ ;           else               break;       }          return res;   }      /*!    * chunk a string into strings of size [ at most ] k    */   void chunk ( const std::string::const_iterator first,                const std::string::const_iterator last,                const size_t k,                const bool right_to_left,                std::list < std::string > & str_list )   {       str_list.clear( );          if ( right_to_left )           /* chunk from the end of the string */           for ( std::string::const_iterator i, j = last; j != first; j = i )           {               i = first + k < j ? j - k : first;               str_list.push_back ( std::string ( i, j ) );           }       else           /* chunk from the begining of the string */           for ( std::string::const_iterator i = first, j; i != last; i = j )           {               j = i + k < last ? i + k : last;               str_list.push_back ( std::string ( i, j ) );           }   }      /*!    * next lexicographically smallest string    * within char set a..z    */   std::string & operator++( std::string & s )   {       /* find the first char from right less than  z  */       std::string::reverse_iterator j = find_if( s.rbegin( ), s.rend( ),               std::bind2nd( std::less < char > ( ),  z  ));          if ( j != s.rend( ))       {           ++ *j;           std::fill( s.rbegin( ), j,  a  );       }       else           s.assign( s.length( ) + 1,  a  );          return s;   }      /*!    * getline ( cin, str )    *      requires ctrl-D    *      cin >> str; does not pass after space char    */         /*    *  number utils    * ----------------------------------------------    */         class BigInteger   {   #if ULONG_MAX <= 1 << 32       typedef long long unsigned val_type;   #else       typedef long unsigned val_type;   #endif       const static int WSIZE = 32;       const static val_type BASE = 1LL << WSIZE;       public:       private:           std::list < val_type > val;  /* val[ 0 ] is most significant */           bool pos;                    /* true if sign is positive     */   };      /**    * greatest common divisor - Euclid s alg.    */   template < typename value_type > inline   value_type gcd ( value_type a, value_type b )   {       return ! b ? a : gcd( b, a % b );          // if ( a < 0 )  a = -a ;       // if ( b < 0 )  b = -b ;       // if ( a < b )  std::swap ( a, b );          /* corner case: one of the values is zero */       // if ( ! b )   return a;          // for ( value_type r = a % b; r ; r = a % b )       // {       //     a = b;       //     b = r;       // }          // return b;   }         /**    * prime factorization    */   template < class T >   void prime_factors( T n, std::map < T, size_t > & fac )   {       for ( T k = 2; n > 1; ++ k )           if ( ! ( n % k ) )           {               size_t & ref = fac[ k ];               while ( ! ( n % k ) )               {                   ++ ref;                   n /= k;               }           }   }      /* abs diff - safe for unsigned types */   template < class T >   inline T absdiff( T a, T b )   {       return a < b ? b - a : a - b;   }         namespace   {       template < class T >       std::pair < T, T > __extgcd ( const T & x0, const T & y0,                                     const T & x1, const T & y1,                                     const T & r0, const T & r1 )       {           const T q  = r0 / r1;           const T r2 = r0 % r1;              if ( ! ( r1 % r2 ) )               return std::make_pair < T, T > ( x0 - q * x1, y0 - q * y1 );              const T x2 = x0 - q * x1;           const T y2 = y0 - q * y1;              return __extgcd ( x1, y1, x2, y2, r1, r2 );       }   }      /**    * extended euclidean algorithm: a x  +  b y = gcd( a, b)    * en.wikipedia.org/wiki/Extended_Euclidean_algorithm    */   template < class value_type > inline   std::pair < value_type, value_type > extgcd ( value_type a, value_type b )   {       return a % b           ? __extgcd < value_type > ( 1, 0, 0, 1, a, b )           : std::make_pair < value_type, value_type > ( 0, 1 );   }         /**    * modular multiplicative inverse    * en.wikipedia.org/wiki/Modular_multiplicative_inverse    */   template < class value_type > inline   value_type modinv ( value_type a, value_type m )   {       const std::pair < value_type, value_type > coef ( extgcd( a, m ) );          /* a needs to be coprime to the modulus, or the inverse won t exist */       if ( a * coef.first + m * coef.second != 1 )           throw std::runtime_error ( val2str( a ) +   is not coprime to   + val2str( m ));          /* return a pos num between 1 & m-1 */       return ( m + coef.first % m ) % m;   }      inline bool isnan ( const double & a )   {       return ! ( a == a );   }      template < typename value_type >   inline value_type mini ( int n, ... )   {       va_list vl;       va_start (vl, n);       value_type res = va_arg ( vl, value_type );          for ( int i = 1; i < n; ++i ) {           const value_type val = va_arg ( vl, value_type );           res = std::min ( res, val );       }          va_end( vl );       return res;   }      template < typename value_type >   inline value_type maxi ( int n, ... )   {       va_list vl;       va_start (vl, n);       value_type res = va_arg ( vl, value_type );          for ( int i = 1; i < n; ++i ) {           const value_type val = va_arg ( vl, value_type );           res = std::max ( res, val );       }          va_end( vl );       return res;   }      // XXX look this up how is this implemented   template < class T >   inline int sign ( const T & x )   {       if ( x == T() )           return 0;       else if ( x < T() )           return -1;       else           return 1;   }      /*    * change moduluos from n to m    */   std::string chmod ( std::string num, const unsigned n, const unsigned m )   {       const char * digit =  0123456789abcdefghijklmnopqrstuvwxyz ;       std::transform ( num.begin(), num.end(), num.begin(), tolower );          isin < char, std::string > is_alpha_num ( digit );       assert ( find_if ( num.begin( ), num.end( ), std::not1 ( is_alpha_num ) ) == num.end( ));          unsigned long long int val ( 0 );          if ( n == 10U )       {           std::istringstream iss ( num, std::ios_base::in );           iss >> val;       }       else           for ( std::string::const_iterator iter = num.begin( ); iter != num.end( ); ++ iter )               val = val * n + (  a  <= *iter ? *iter -  a  + 10U : *iter -  0 );          if ( m == 10U )       {           std::ostringstream sout ( std::ios_base::out );           sout << val;           return sout.str ( );       }       else       {           std::string res;           for ( ; val ; val /= m )               res.push_back( digit [ val % m ] );              return res.length( ) ? std::string( res.rbegin( ), res.rend( )) :  0 ;       }   }      template < class value_type >  /* a^n mod m */   value_type powmod ( value_type a, const value_type & n, const value_type & m )   {       if ( a == 1 || ! n )           return m != 1 ? 1 : 0;          value_type res = 1;       for ( value_type k = 1; k <= n; a = a * a % m, k = k << 1 )           if ( k & n )               res =  ( res * a ) % m;          return res;   }      /*    * Fermat pseudoprime test    * www.math.umbc.edu/~campbell/Computers/Python/numbthy.py    * NOTE: since return type is bool, and powmod may break for ints,    *       the argument is always casted to long long    */   inline bool is_pseudo_prime ( const long long & a )   {       /* all the primes less than 1000 ( 168 primes )*/       const long long p [ ] = { 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,                                 79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,                                 163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,                                 241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,                                 337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,                                 431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,                                 521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,                                 617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,                                 719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,                                 823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,                                 929,937,941,947,953,967,971,977,983,991,997 };          const size_t n = sizeof( p ) / sizeof ( p[ 0 ] );          if ( a < p[ n - 1 ] + 1)           return std::binary_search ( p, p + n , a );          if ( std::find_if ( p, p + n, std::not1 ( std::bind1st ( std::modulus< long long >( ), a ))) != p + n )           return false;          const size_t k = a <    9006401LL ? 3 :                        a <   10403641LL ? 4 :                        a <   42702661LL ? 5 :                        a < 1112103541LL ? 6 : 7;          for ( size_t j = 0; j < k; ++ j )           if ( powmod ( p[ j ], a - 1, a ) != 1 )               return false;          return true;   }         /*    * returns a sorted vector of all primes less than or equal to n    * maximum adj diff of all primes less than 1e5 is 72 ( 114 for 1e6 )    */   template < typename value_type >   std::vector < value_type > get_primes ( const value_type n )   {   #ifdef BUG       ScopeTimer scope_timer (  std::vector < value_type > get_primes ( const value_type n )  );   #endif          typedef typename std::vector < value_type >::iterator iterator;       std::vector < value_type > primes;          for ( value_type k = 2 ; k <= n; ++ k )           if ( is_pseudo_prime ( k ) )           {               const value_type sqrt_k = 1 + static_cast < value_type > ( sqrt ( k + 1 ) );               iterator iend = upper_bound ( primes.begin( ), primes.end( ), sqrt_k );                  if ( find_if ( primes.begin( ), iend, std::not1 ( std::bind1st ( std::modulus< value_type >( ), k ) ) ) != iend )                   continue;                  primes.push_back ( k );           }          return primes;   }      template < class T >   inline std::list < std::pair < T, size_t > > get_prime_fact ( T a )   {       std::list < std::pair < T, size_t > > fac;          for ( T k = 2; a > 1; ++ k )           if ( ! ( a % k ) )  // no need to check if k is prime           {               size_t m = 0;               for ( ; ! ( a % k ) ; ++m, a/= k )                   ;                  fac.push_back ( std::pair < T, size_t > ( k, m ) );           }       return fac;   }         template < class T >   T n_choose_k ( T n, T k )   {       if ( k > n )           return 0;          const T lb = std::min ( k, n - k ) + 1;       const T ub = n - lb + 1;          T res = 1, j = 2;       while ( n > ub && j < lb)       {           res *= n--;           while ( j < lb and ! (res % j) )               res /= j++;       }          while ( n > ub )           res *= n--;          return res;   }         /**    * median calculator, using two heaps    */   template < class InputIter >   inline std::pair < typename InputIter::value_type, typename InputIter::value_type >   median ( InputIter first, InputIter last )   {       typedef typename InputIter::value_type      value_type;       typedef std::pair< value_type, value_type > result_type;          /*        * max_heap:        *      - the lower half of the elements        *      - the biggest of such elements is on the top        */       std::vector < value_type > max_heap, min_heap;          /*        * comp argument to heap algorithm should provide        *  strict weak ordering ; in particular        *      std::not2 ( std::less < value_type > )        * does not have such a strict weak ordering;        */       std::less    < value_type > max_heap_comp;       std::greater < value_type > min_heap_comp;          if ( first == last )  /* corner case: empty vector */           throw std::runtime_error (  median of an empty vector is undefined!  );          InputIter iter = first;       max_heap.push_back ( * iter );          for ( ++iter ; iter != last; ++ iter )           if ( * iter < max_heap.front() )           {               max_heap.push_back ( * iter );               std::push_heap ( max_heap.begin(), max_heap.end(), max_heap_comp );                  if ( min_heap.size() + 1 < max_heap.size() )               {                   /* max_heap has got too large */                   min_heap.push_back( max_heap.front() );                   std::push_heap( min_heap.begin(), min_heap.end(), min_heap_comp );                      std::pop_heap( max_heap.begin(), max_heap.end(), max_heap_comp );                   max_heap.pop_back();               }           }           else           {               min_heap.push_back ( * iter );               std::push_heap ( min_heap.begin(), min_heap.end(), min_heap_comp );                  if ( max_heap.size() + 1 < min_heap.size() )               {                   /* min_heap has got too large */                   max_heap.push_back( min_heap.front() );                   std::push_heap( max_heap.begin(), max_heap.end(), max_heap_comp );                      std::pop_heap( min_heap.begin(), min_heap.end(), min_heap_comp );                   min_heap.pop_back();               }           }          DEBUG( max_heap );       DEBUG( min_heap );          return min_heap.empty( )  /* corner case: ++first = last */           ? result_type ( *first, *first )           : result_type ( max_heap.size() < min_heap.size() ? min_heap.front() : max_heap.front(),                           min_heap.size() < max_heap.size() ? max_heap.front() : min_heap.front() );   }      /*    * geometry util    * ----------------------------------------------    */      struct xyPoint   {       double x, y;       xyPoint ( const double & a = .0, const double & b = .0 ): x ( a ), y( b ) { };   };         struct xyCircle   {       xyPoint center;       double radius;   };      std::ostream & operator<< ( std::ostream & out, const xyPoint & p )   {       out <<  (  << p.x <<  ,   << p.y <<  ) ;       return out;   }      std::istream & operator>> ( std::istream & ist, xyPoint & p )   {       ist >> p.x >> p.y;       return ist;   }      std::ostream & operator<< ( std::ostream & out, const xyCircle & o )   {       out <<  {(  << o.center.x <<  ,   << o.center.y <<  )   << o.radius <<  } ;       return out;   }      std::istream & operator>> ( std::istream & ist, xyCircle & o )   {       ist >> o.center.x >> o.center.y >> o.radius;       return ist;   }      inline double cartesian_dist ( const xyPoint & a, const xyPoint & b )   {       const double d = a.x - b.x;       const double e = a.y - b.y;       return std::sqrt ( d * d + e * e );   }      class xyLine   {       public:           xyLine ( const xyPoint & , const xyPoint & );           xyLine ( const double slope, const double intercept );              /*            *  signed  orthogonal distance; the sign is useful            * to compare which side of the line the point is            */           inline double orth_dist ( const xyPoint & ) const;       private:           double m_slope;           double m_intercept;           double m_normfac;   /* normalization factor for orth_dist calc */              bool   m_vertical;  /* if the line is verticcal                */           double m_xcross;    /* x axis cross point for vertical line    */   };      xyLine::xyLine ( const xyPoint & a, const xyPoint & b )   {       if ( a.x == b.x )  /* vertical line */       {           m_vertical  = true;           m_xcross    = a.x;              m_intercept = DOUBLE_NAN;           m_slope     = DOUBLE_INF;           m_normfac   = DOUBLE_NAN;       }       else       {           m_vertical  = false;           m_xcross    = DOUBLE_NAN;              m_slope     = ( b.y - a.y ) / ( b.x - a.x );           m_intercept = a.y - m_slope * a.x;           m_normfac   = std::sqrt ( m_slope * m_slope + 1.0 );       }   }      xyLine::xyLine ( const double slope, const double intercept ):       m_slope ( slope ),  m_intercept ( intercept )   {        m_vertical = false;        m_xcross   = DOUBLE_NAN;        m_normfac  = std::sqrt ( m_slope * m_slope + 1.0 );   }      double xyLine::orth_dist ( const xyPoint & o ) const /*  signed  orthogonal distance */   {       if ( m_vertical )           return o.x - m_xcross;       else           return ( m_slope * o.x - o.y + m_intercept ) / m_normfac;   }      inline double triangle_area ( const xyPoint & a, const xyPoint & b, const xyPoint & c )   {       const xyLine l ( a, b );       const double h = std::abs ( l.orth_dist ( c ) );       const double e = cartesian_dist ( a, b );       return h * e;   }      /*    *  operator<< overrides    * ----------------------------------------------    */      namespace   {       /* helper function to output containers */       template < typename T >       std::ostream & __output ( std::ostream & out, const T & a )       {           typedef typename T::const_iterator const_iterator;           out <<  {  ;              // does not work for  pair  value type           // std::copy ( a.begin( ), a.end( ), std::ostream_iterator < typename T::value_type > ( std::cout,  ,   ));              for ( const_iterator iter = a.begin(); iter != a.end(); ++ iter )                out << ( iter != a.begin( ) ?  ,   :    ) << *iter ;              return out <<   } ;       }   }      template < typename key_type, typename value_type >   std::ostream & operator<< ( std::ostream & out, const std::pair < key_type, value_type > & p)   {       out <<  (  << p.first <<  ,   << p.second <<  ) ;       return out;   }      template < typename key_type, typename value_type, typename comp >   std::ostream & operator<< ( std::ostream & out, const std::map < key_type, value_type, comp > & m )   {       return __output ( out, m );   }      template < typename value_type >   std::ostream & operator<< ( std::ostream & out, const std::set < value_type > & s )   {       return __output ( out, s );   }      template < typename value_type >   std::ostream & operator<< ( std::ostream & out, const std::vector < value_type > & a )   {       return __output ( out, a );   }      template < typename value_type >   std::ostream & operator<< ( std::ostream & out, const std::list < value_type > & a )   {       return __output ( out, a );   }      template < typename value_type >   std::ostream & operator<< ( std::ostream & out, const std::vector < std::vector < value_type > > & a )   {       typedef typename std::vector < std::vector < value_type > >::const_iterator const_iterator;          for ( const_iterator iter = a.begin( ); iter != a.end( ); ++ iter )           out <<   n  << *iter ;          return out;   }      /*    *  operator>> overrides    * ----------------------------------------------    */      template < typename key_type, typename value_type >   std::istream & operator>> ( std::istream & in, std::pair < key_type, value_type > & p)   {       in >> p.first >> p.second;       return in;   }      template < typename value_type >   std::istream & operator>> ( std::istream & in, std::vector < value_type > & a )   {       typedef typename std::vector < value_type >::iterator iterator;          if ( ! a.size( ) )       {           size_t n;           in >> n;           a.resize( n );       }          for ( iterator iter = a.begin(); iter != a.end(); ++ iter )           in >> * iter;          return in;   }      /*    *  readin quick utilities    * ----------------------------------------------    */      // template < typename value_type >   // inline void readin ( std::vector < value_type > & a, size_t n = 0, std::istream & in = std::cin )   // {   //     // if ( ! n ) std::cin >> n;   //     if ( ! n ) in >> n ;   //     a.resize ( n );   //     // std::cin >> a;   //     in >> a;   // }      // XXX consider removing   // template < typename key_type, typename value_type >   // inline void readin (std::vector < std::pair < key_type , value_type > > & a, size_t n = 0 )   // {   //     if ( !n ) std::cin >> n;   //     a.resize( n );   //     std::cin >> a;   // }      /*    *  pair utility    * ----------------------------------------------    */      /*    * accumulate ( m.begin( ), m.end( ), pair < int, double> ( 0 , 0.0 ) , operator+ < int, double > );    * stackoverflow.com/questions/18640152    */   template < typename T1, typename T2 >   inline std::pair < T1, T2 > operator+ ( const std::pair < T1, T2 > & a, const std::pair < T1, T2 > & b )   {       return std::make_pair < T1, T2 > ( a.first + b.first, a.second + b.second );   }      template < typename T1, typename T2 >   inline std::pair < T1, T2 > operator- ( const std::pair < T1, T2 > & a, const std::pair < T1, T2 > & b )   {       return std::make_pair < T1, T2 > ( a.first - b.first, a.second - b.second );   }      // template < class T1, class T2, class BinaryOperation >   // class Apply2nd : std::binary_function < typename std::pair < T1, T2 >,   //                                         typename std::pair < T1, T2 >,   //                                         typename BinaryOperation::result_type >      namespace   {       /*!        * helper template to do the work        */       template < size_t J, class T1, class T2 >       struct Get;          template < class T1, class T2 >       struct Get < 0, T1, T2 >       {           typedef typename std::pair < T1, T2 >::first_type result_type;              static       result_type & elm (       std::pair < T1, T2 > & pr ) { return pr.first; }           static const result_type & elm ( const std::pair < T1, T2 > & pr ) { return pr.first; }       };          template < class T1, class T2 >       struct Get < 1, T1, T2 >       {           typedef typename std::pair < T1, T2 >::second_type result_type;              static       result_type & elm (       std::pair < T1, T2 > & pr ) { return pr.second; }           static const result_type & elm ( const std::pair < T1, T2 > & pr ) { return pr.second; }       };   }      template < size_t J, class T1, class T2 >   typename Get< J, T1, T2 >::result_type & get ( std::pair< T1, T2 > & pr )   {       return Get < J, T1, T2 >::elm( pr );   }      template < size_t J, class T1, class T2 >   const typename Get< J, T1, T2 >::result_type & get ( const std::pair< T1, T2 > & pr )   {       return Get < J, T1, T2 >::elm( pr );   }      /*    * graph utils    * ----------------------------------------------    */      /*    * Dijkstra :: single-source shortest path problem for    * a graph with non-negative edge path costs, producing    * a shortest path tree    * en.wikipedia.org/wiki/Dijkstra s_algorithm    */   template < typename DistType >   void Dijekstra ( const size_t & source,                    const std::vector < std::list < size_t > > & adj,          // adjacency list                    const std::vector < std::vector < DistType > > & edge_len, // pair-wise distance for adjacent nodes                    std::vector < DistType > & dist,  // distance from the source                    std::vector < size_t > prev )     // previous node in the shortest path tree   {       // TODO   }      // TODO http://en.wikipedia.org/wiki/Shortest_path_problem   // TODO Graph class, Weighted graph, ...      /*    *  maximum cardinality matching in a bipartite graph    *        G = G1 ∪ G2 ∪ {NIL}    *  where G1 and G2 are partition of graph and NIL is a special null vertex    *  https://en.wikipedia.org/wiki/Hopcroft-Karp_algorithm    */   class HopcroftKarp   {       public:           HopcroftKarp ( const std::vector < std::list < size_t > > & adj,                          const std::vector < bool > & tag );              size_t get_npair ( ) { return npair; };           std::map < size_t, size_t > get_map ( );          private:           bool mf_breadth_first_search ( );  // breadth first search from unpaired nodes in G1           bool mf_depth_first_search ( const size_t v ); // dfs w/ toggeling augmenting paths              const std::vector < std::list < size_t > > & m_adj;  // adjacency list for each node           const std::vector < bool > & m_tag;  // binary tag distinguishing partitions              size_t npair;           const size_t NIL;  // special null vertex           const size_t INF;  // practically infinity distance              std::vector < size_t > m_g1;    // set of nodes with tag = true           std::vector < size_t > m_dist;  // dist from unpaired vertices in G1           std::vector < size_t > m_pair;   };         std::map < size_t, size_t > HopcroftKarp::get_map ( )   {       std::map < size_t, size_t > m;          for ( size_t j = 0; j < m_pair.size( ); ++ j )           if ( m_pair[ j ] != NIL  && m_tag[ j ])               m[ j ] = m_pair[ j ];          return m;   }         HopcroftKarp::HopcroftKarp ( const std::vector < std::list < size_t > > & adj,                                const std::vector < bool > & tag ):       m_adj ( adj ),       m_tag ( tag ),       npair ( 0 ),       NIL ( adj.size( )),       INF ( adj.size( ) + 1 ),       m_dist ( std::vector < size_t > ( adj.size( ) + 1, INF)),       m_pair ( std::vector < size_t > ( adj.size( ), NIL ))  // initially everything is paired with nil   {       assert ( m_adj.size() == m_tag.size() );          for ( size_t j = 0; j < tag.size( ); ++ j )           if ( tag[ j ] )               m_g1.push_back ( j );          while ( mf_breadth_first_search ( ) )           for ( std::vector < size_t >::const_iterator v = m_g1.begin( ); v != m_g1.end( ); ++ v )               if ( m_pair[ *v ] == NIL && mf_depth_first_search ( *v ) )                   ++ npair;   }      bool HopcroftKarp::mf_breadth_first_search( )   {       /* only nodes from g1 are queued */       std::queue < size_t > bfs_queue;          /* initialize queue with all unpaired nodes from g1 */       for ( std::vector < size_t >::const_iterator v = m_g1.begin( ); v != m_g1.end( ); ++v )           if ( m_pair[ *v ] == NIL )           {               m_dist[ *v ] = 0;               bfs_queue.push ( *v );           }           else               m_dist[ *v ] = INF;          m_dist[ NIL ] = INF;          /* find all the shortest augmenting paths to node nil */       while ( ! bfs_queue.empty() )       {           const size_t v = bfs_queue.front( );           bfs_queue.pop ( );              if ( m_dist[ v ] < m_dist[ NIL ] )               for ( std::list < size_t >::const_iterator u = m_adj[ v ].begin( ); u != m_adj[ v ].end( ); ++ u )                   if ( m_dist[ m_pair[ * u ] ] == INF )                   {                       m_dist[ m_pair[ * u ] ] = m_dist[ v ] + 1;                       bfs_queue.push ( m_pair[ * u ] );                   }       }          return m_dist[ NIL ] != INF;   }         bool HopcroftKarp::mf_depth_first_search( const size_t v )   {       if ( v == NIL )           return true;       else       {           for ( std::list < size_t >::const_iterator u = m_adj[ v ].begin( ); u != m_adj[ v ].end( ); ++ u )               if ( m_dist[ m_pair[ *u ] ] == m_dist[ v ] + 1  && mf_depth_first_search( m_pair[ *u ] ))               {                   /*                    * there is an augmenting path to nil from m_pair[ *u ]                    * and hence there is an augmenting path from v to u and                    * u to to nil; therefore v and u can be paired together                    */                   m_pair [ *u ] = v;                   m_pair [  v ] = *u;                   return true;               }           m_dist[ v ] = INF;           return false;       }   }      /*    *  data-structure utility    * ----------------------------------------------    */      template < class T, class Comp = std::less< T > >   class Heap  /* less< T > --> max-heap */   {       typedef T value_type;       typedef typename std::vector < value_type >::size_type size_type;       public:           /*            * stackoverflow.com/questions/10387751            * possible work-around: a memebr pointer to m_val            *            * TODO: static/friend heapify ( val, & heap )  XXX O( n ) ?!            */           Heap ( ): m_val ( std::vector < value_type > ( ) ) , m_comp ( Comp( ) ){ }              template < class InputIter >           Heap ( InputIter first, InputIter last ):               m_val ( std::vector < value_type > ( ) ) , m_comp( Comp( ) )           {               for ( ; first != last ; ++ first )                   m_val.push_back ( * first );                  std::make_heap( m_val.begin( ), m_val.end( ), m_comp );           }              /*!            * to avoid destroying heap property, front( )            * should always return a  const  reference            */           inline const value_type & front( ) const { return m_val.front( ); }           inline bool empty( ) const { return m_val.empty( ); }           inline size_type size( ) const { return m_val.size( );  }              inline void push ( const value_type & a )           {               m_val.push_back( a );               std::push_heap( m_val.begin( ), m_val.end( ), m_comp );           }           inline void pop( )           {               std::pop_heap ( m_val.begin( ), m_val.end( ), m_comp );               m_val.pop_back( );           }              // inline void swap( Heap< T, Comp> & other ) { m_val.swap( other.m_val ) };           // void sort( ) { std::sort_heap ( m_val.begin( ), m_val.end( ), m_comp ); }           // template < class X, class Y >           // friend std::ostream & operator<<( std::ostream & out, const Heap < X, Y> & heap );       private:           std::vector < value_type > m_val;           const Comp m_comp;   };      /*    * boost.org/doc/libs/1_54_0/libs/smart_ptr/shared_ptr.htm    */   template < class Type >   class shared_ptr   {       typedef Type value_type;       public:           explicit shared_ptr ( value_type * p = NULL ) : ptr ( p ), count ( new size_t ( 1U ) ) { }           shared_ptr ( const shared_ptr < value_type > & sp ): ptr ( sp.ptr ), count ( sp.count ) { ++ * count; }           ~ shared_ptr ( ) { release( ); }              bool operator== ( const shared_ptr < value_type > & sp ) { return ptr == sp.ptr; }           bool operator!= ( const shared_ptr < value_type > & sp ) { return ptr != sp.ptr; }              shared_ptr < value_type > & operator= ( const shared_ptr < value_type > & sp )           {               if ( this != & sp && ptr != sp.ptr )               {                   release( );                   ptr   = sp.ptr;                   count = sp.count;                   ++ * count;               }               return * this;           }              value_type * operator-> ( ) { return ptr ; }           value_type & operator* ( ) { return *ptr ; }           const value_type * operator-> ( ) const { return ptr ; }           const value_type & operator* ( ) const { return *ptr; }              void swap ( shared_ptr < value_type > & sp )           {               if ( this != &sp && ptr != sp.ptr )               {                   std::swap ( ptr, sp.ptr );                   std::swap ( count, sp.count );               }           }          private:           void release ( )           {               /* stackoverflow.com/questions/615355 */               -- * count;               if ( ! * count )               {                   delete count;                   delete ptr;                   count = NULL;                   ptr   = NULL;               }           }           value_type * ptr;           size_t     * count;   };      /*!    * union find data structure with    *      - lazy unions    *      - union by rank    *      - path compression    */   class UnionFind   {       public:           UnionFind( const size_t n ):               parent ( std::vector < size_t > ( n ) ),   /* initialize each node as its own   */               rank   ( std::vector < size_t > ( n, 0 ))  /* parent and set all the ranks to 0 */           {               for ( size_t j = 0; j < n; ++ j )                   parent[ j ] = j ;           }              inline size_t find( const size_t s )           {               /*                * perform path compresion and add shortcut                * if parent[ s ] is not a root node                */               const size_t p = parent[ s ];               return parent[ p ] == p ? p : parent[ s ] = find( p ) ;           }              inline void lazy_union ( size_t i, size_t j )           {               /* unions should be done on root nodes */               i = find( i );               j = find( j );                  if ( i != j )               {                   if ( rank [ i ] < rank[ j ] )                       parent[ i ] = j;                   else                   {                       parent[ j ] = i;                       rank[ i ]  += rank[ i ] == rank[ j ];                   }               }           }       private:           std::vector < size_t > parent;           std::vector < size_t > rank;   };         // TODO XXX   // template < class NumType >   // unsigned num_hash_func ( const NumType & a )   // {   //     // XXX what will happen in case of overflow?   //     return static_cast < unsigned > ( a % 9973 ) % 9973 ;   // }      /*    * XXX: HashMap: map< Key, T > data [ 9973 ]    * data [ num_hash_func ( key ) ][ key ]    */         /*    *  testing util    * ----------------------------------------------    */      // TODO add a preprocessor which automatically includes the funciton name, or __line__   // and disables if not in debug mode   /* prints the life length of the object when it goes out of scope */   class ScopeTimer   {       public:           ScopeTimer ( const std::string & msg =    ): tic ( clock ( )), m_msg( msg ) { };              ~ ScopeTimer ( )           {               const clock_t toc = clock();               const uint64 dt   = 1000L * ( toc - tic ) / CLOCKS_PER_SEC;                  const uint64 mil = dt % 1000L;               const uint64 sec = ( dt / 1000L ) % 60L;               const uint64 min = ( dt / 60000L ) % 60L;               const uint64 hrs = ( dt / 3600000L );                  std::cout <<   n  << m_msg <<   n telapsed time:  ;                  if ( hrs )  std::cout << hrs <<   hrs,  ;               if ( min )  std::cout << min <<   min,  ;               if ( sec )  std::cout << sec <<   sec,  ;               std::cout << mil <<   mil-sec n ;           }          private:           typedef unsigned long long int  uint64;           const clock_t tic;           const std::string m_msg;   };      class RandInt   {       public:           RandInt ( int a = 0, int b = 100 ): m ( a ), f ( static_cast < double > ( b - a ) / RAND_MAX ) { }           inline int operator() ( ) { return m + std::ceil ( f * rand( ) ); }       private:           const int m;           const double f;   };         class RandDouble   {       public:           RandDouble ( double a = 0.0, double b = 1.0 ): m ( a ), f ( ( b - a ) / RAND_MAX ) { }           inline double operator() ( ) { return m + f * rand( ); }       private:           const double m, f;   };      class Noisy   {       public:           Noisy ( std::string str ): msg ( str )           {               std::cout <<   Noisy (   << msg <<   ) t@   << this << std::endl;           }           ~Noisy ( )           {               std::cout <<  ~Noisy (   << msg <<   ) t@   << this << std::endl;           }           void beep ( )           {               std::cout <<   beep (   << msg <<   ) t@   << this << std::endl;           }           void beep ( ) const           {               std::cout <<   const beep (   << msg <<   ) t@   << this << std::endl;           }       private:           const std::string msg;   };      DECLARE ( Noisy );         /*    * ----------------------------------------------    * ----------------------------------------------    */      /*    * -- @@@ -------------------------------------------------    */      using namespace std;         // struct Comp   // {   //     // bool operator() ( const pair < int, int > & x, const pair < int, int > & y )   //     // {   //     //     return abs( x.first ) + abs( x.second ) < abs( y.first ) + abs( y.second );   //     // }   //   //     // bool operator( ) ( const xyCircle & a, const xyCircle & b )   //     // {   //     //     return a.radius < b.radius;   //     // }   //     //   //     bool operator( ) ( const pair < size_t, size_t > & pr, const size_t & x )   //     {   //         return pr.second < x;   //     }   // };      void probA()   {       vector <size_t> a;       cin >> a;       sort( a.begin(), a.end() );       copy ( a.begin( ), a.end( ), ostream_iterator < size_t > ( cout,     ));   }      size_t probB( )   {       size_t n;          string str;       cin >> n >> str;          // const size_t n = str.size();          const size_t INF = n + 2;       vector < size_t > ldist( n ), rdist( n);          rdist[ 0 ] = str[ 0 ] ==  R  ? 0 : INF;       for ( size_t j = 1; j < n; ++ j )           switch ( str[ j ] )           {               case  R :                   rdist[ j ] = 0;                   break;               case  L :                   rdist[ j ] = INF;                   break;               case  . :                   rdist[ j ] = 1 + rdist[ j - 1 ];                   break;           }          ldist[ n - 1 ] = str[ n - 1 ] ==  L  ? 0 : INF;       for ( size_t j = n - 1; j > 0; -- j )           switch ( str[ j - 1] )           {               case  L :                   ldist[ j - 1] = 0;                   break;               case  R :                   ldist[ j - 1] = INF;                   break;               case  . :                   ldist[ j - 1] = 1 + ldist[ j ];                   break;           }          DEBUG( ldist );       DEBUG( rdist );          size_t cnt = 0;       for ( size_t j = 0; j < n; ++ j )           if ( ( INF <= ldist[j]  && INF <= rdist[j] ) || ldist[ j ] == rdist[ j ] )               ++ cnt;          return cnt;   }         int main ( const int argc, char * argv [ ])   {          cout << probB();          // c79( );       // cout << c343( );       // cout << setprecision( 10 )          return EXIT_SUCCESS;   }         /**    *   mislav.uniqpath.com/2011/12/vim-revisited/    * set encoding=utf-8    * %s/ (. {60,70 } ) / 1 r/gc    * %s/ / /gc    * %s/10 ([0-9] {1,2 } )/10^ 1/gc    */