Assertion failure at vho_lower.cxx:2183 in pathscale

gistfile1.txt

namespace std { }
namespace __std_alias = std;
namespace NStl { }
namespace NStlPriv {
  using namespace NStl;
}
namespace stlport = NStl;



namespace _STL = NStl;
namespace __rw {


extern "C++" {

template <bool __b>
struct __rw_compile_assert;

template<>
struct __rw_compile_assert<true> { enum { _C_ok }; };





void
__rw_assert_fail (const char*, const char*, int, const char*)
    __attribute__ ((nothrow)) __attribute__ ((noreturn));
}

}
namespace std {
}

























extern "C" {



typedef unsigned char __u_char;
typedef unsigned short int __u_short;
typedef unsigned int __u_int;
typedef unsigned long int __u_long;


typedef signed char __int8_t;
typedef unsigned char __uint8_t;
typedef signed short int __int16_t;
typedef unsigned short int __uint16_t;
typedef signed int __int32_t;
typedef unsigned int __uint32_t;

typedef signed long int __int64_t;
typedef unsigned long int __uint64_t;







typedef long int __quad_t;
typedef unsigned long int __u_quad_t;


typedef unsigned long int __dev_t;
typedef unsigned int __uid_t;
typedef unsigned int __gid_t;
typedef unsigned long int __ino_t;
typedef unsigned long int __ino64_t;
typedef unsigned int __mode_t;
typedef unsigned long int __nlink_t;
typedef long int __off_t;
typedef long int __off64_t;
typedef int __pid_t;
typedef struct { int __val[2]; } __fsid_t;
typedef long int __clock_t;
typedef unsigned long int __rlim_t;
typedef unsigned long int __rlim64_t;
typedef unsigned int __id_t;
typedef long int __time_t;
typedef unsigned int __useconds_t;
typedef long int __suseconds_t;

typedef int __daddr_t;
typedef long int __swblk_t;
typedef int __key_t;


typedef int __clockid_t;


typedef void * __timer_t;


typedef long int __blksize_t;




typedef long int __blkcnt_t;
typedef long int __blkcnt64_t;


typedef unsigned long int __fsblkcnt_t;
typedef unsigned long int __fsblkcnt64_t;


typedef unsigned long int __fsfilcnt_t;
typedef unsigned long int __fsfilcnt64_t;

typedef long int __ssize_t;



typedef __off64_t __loff_t;
typedef __quad_t *__qaddr_t;
typedef char *__caddr_t;


typedef long int __intptr_t;


typedef unsigned int __socklen_t;



typedef __u_char u_char;
typedef __u_short u_short;
typedef __u_int u_int;
typedef __u_long u_long;
typedef __quad_t quad_t;
typedef __u_quad_t u_quad_t;
typedef __fsid_t fsid_t;




typedef __loff_t loff_t;





typedef __ino64_t ino_t;




typedef __ino64_t ino64_t;




typedef __dev_t dev_t;




typedef __gid_t gid_t;




typedef __mode_t mode_t;




typedef __nlink_t nlink_t;




typedef __uid_t uid_t;







typedef __off64_t off_t;




typedef __off64_t off64_t;




typedef __pid_t pid_t;





typedef __id_t id_t;




typedef __ssize_t ssize_t;





typedef __daddr_t daddr_t;
typedef __caddr_t caddr_t;





typedef __key_t key_t;


typedef __clock_t clock_t;





typedef __time_t time_t;



typedef __clockid_t clockid_t;
typedef __timer_t timer_t;








typedef __useconds_t useconds_t;



typedef __suseconds_t suseconds_t;





typedef long unsigned int size_t;






typedef unsigned long int ulong;
typedef unsigned short int ushort;
typedef unsigned int uint;
typedef int int8_t __attribute__ ((__mode__ (__QI__)));
typedef int int16_t __attribute__ ((__mode__ (__HI__)));
typedef int int32_t __attribute__ ((__mode__ (__SI__)));
typedef int int64_t __attribute__ ((__mode__ (__DI__)));


typedef unsigned int u_int8_t __attribute__ ((__mode__ (__QI__)));
typedef unsigned int u_int16_t __attribute__ ((__mode__ (__HI__)));
typedef unsigned int u_int32_t __attribute__ ((__mode__ (__SI__)));
typedef unsigned int u_int64_t __attribute__ ((__mode__ (__DI__)));

typedef int register_t __attribute__ ((__mode__ (__word__)));


typedef int __sig_atomic_t;




typedef struct
  {
    unsigned long int __val[(1024 / (8 * sizeof (unsigned long int)))];
  } __sigset_t;



typedef __sigset_t sigset_t;





struct timespec
  {
    __time_t tv_sec;
    long int tv_nsec;
  };






struct timeval
  {
    __time_t tv_sec;
    __suseconds_t tv_usec;
  };
typedef long int __fd_mask;
typedef struct
  {



    __fd_mask fds_bits[1024 / (8 * (int) sizeof (__fd_mask))];





  } fd_set;






typedef __fd_mask fd_mask;
extern "C" {
extern int select (int __nfds, fd_set *__restrict __readfds,
     fd_set *__restrict __writefds,
     fd_set *__restrict __exceptfds,
     struct timeval *__restrict __timeout);
extern int pselect (int __nfds, fd_set *__restrict __readfds,
      fd_set *__restrict __writefds,
      fd_set *__restrict __exceptfds,
      const struct timespec *__restrict __timeout,
      const __sigset_t *__restrict __sigmask);


}


__extension__
extern unsigned int gnu_dev_major (unsigned long long int __dev)
     throw ();
__extension__
extern unsigned int gnu_dev_minor (unsigned long long int __dev)
     throw ();
__extension__
extern unsigned long long int gnu_dev_makedev (unsigned int __major,
            unsigned int __minor)
     throw ();





typedef __blksize_t blksize_t;
typedef __blkcnt64_t blkcnt_t;



typedef __fsblkcnt64_t fsblkcnt_t;



typedef __fsfilcnt64_t fsfilcnt_t;





typedef __blkcnt64_t blkcnt64_t;
typedef __fsblkcnt64_t fsblkcnt64_t;
typedef __fsfilcnt64_t fsfilcnt64_t;





typedef unsigned long int pthread_t;


typedef union
{
  char __size[56];
  long int __align;
} pthread_attr_t;



typedef struct __pthread_internal_list
{
  struct __pthread_internal_list *__prev;
  struct __pthread_internal_list *__next;
} __pthread_list_t;
typedef union
{
  struct __pthread_mutex_s
  {
    int __lock;
    unsigned int __count;
    int __owner;

    unsigned int __nusers;



    int __kind;

    int __spins;
    __pthread_list_t __list;
  } __data;
  char __size[40];
  long int __align;
} pthread_mutex_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_mutexattr_t;




typedef union
{
  struct
  {
    int __lock;
    unsigned int __futex;
    __extension__ unsigned long long int __total_seq;
    __extension__ unsigned long long int __wakeup_seq;
    __extension__ unsigned long long int __woken_seq;
    void *__mutex;
    unsigned int __nwaiters;
    unsigned int __broadcast_seq;
  } __data;
  char __size[48];
  __extension__ long long int __align;
} pthread_cond_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_condattr_t;



typedef unsigned int pthread_key_t;



typedef int pthread_once_t;





typedef union
{

  struct
  {
    int __lock;
    unsigned int __nr_readers;
    unsigned int __readers_wakeup;
    unsigned int __writer_wakeup;
    unsigned int __nr_readers_queued;
    unsigned int __nr_writers_queued;
    int __writer;
    int __shared;
    unsigned long int __pad1;
    unsigned long int __pad2;


    unsigned int __flags;
  } __data;
  char __size[56];
  long int __align;
} pthread_rwlock_t;

typedef union
{
  char __size[8];
  long int __align;
} pthread_rwlockattr_t;





typedef volatile int pthread_spinlock_t;




typedef union
{
  char __size[32];
  long int __align;
} pthread_barrier_t;

typedef union
{
  char __size[4];
  int __align;
} pthread_barrierattr_t;


}
typedef unsigned char uint8_t;
typedef unsigned short int uint16_t;

typedef unsigned int uint32_t;



typedef unsigned long int uint64_t;
typedef signed char int_least8_t;
typedef short int int_least16_t;
typedef int int_least32_t;

typedef long int int_least64_t;






typedef unsigned char uint_least8_t;
typedef unsigned short int uint_least16_t;
typedef unsigned int uint_least32_t;

typedef unsigned long int uint_least64_t;
typedef signed char int_fast8_t;

typedef long int int_fast16_t;
typedef long int int_fast32_t;
typedef long int int_fast64_t;
typedef unsigned char uint_fast8_t;

typedef unsigned long int uint_fast16_t;
typedef unsigned long int uint_fast32_t;
typedef unsigned long int uint_fast64_t;
typedef long int intptr_t;


typedef unsigned long int uintptr_t;
typedef long int intmax_t;
typedef unsigned long int uintmax_t;
extern "C" {




typedef struct
  {
    long int quot;
    long int rem;
  } imaxdiv_t;
extern intmax_t imaxabs (intmax_t __n) throw () __attribute__ ((__const__));


extern imaxdiv_t imaxdiv (intmax_t __numer, intmax_t __denom)
      throw () __attribute__ ((__const__));


extern intmax_t strtoimax (__const char *__restrict __nptr,
      char **__restrict __endptr, int __base) throw ();


extern uintmax_t strtoumax (__const char *__restrict __nptr,
       char ** __restrict __endptr, int __base) throw ();


extern intmax_t wcstoimax (__const wchar_t *__restrict __nptr,
      wchar_t **__restrict __endptr, int __base)
     throw ();


extern uintmax_t wcstoumax (__const wchar_t *__restrict __nptr,
       wchar_t ** __restrict __endptr, int __base)
     throw ();
}
    typedef int8_t i8;
    typedef int16_t i16;
    typedef int32_t i32;
    typedef int64_t i64;
    typedef uint8_t ui8;
    typedef uint16_t ui16;
    typedef uint32_t ui32;
    typedef uint64_t ui64;
typedef ui16 __attribute__((__may_alias__)) ui16a;
typedef ui32 __attribute__((__may_alias__)) ui32a;
typedef ui64 __attribute__((__may_alias__)) ui64a;
union u_u16 {
  ui16a v;
  struct {
    ui8 lo8, hi8;
  } __attribute__((__may_alias__)) u;
} __attribute__((__may_alias__));
union u_u32 {
  ui32a v;
  float __attribute__((__may_alias__)) f;
  struct {
    u_u16 lo16, hi16;
  } u;
} __attribute__((__may_alias__));
union u_u64 {
  ui64a v;
  double __attribute__((__may_alias__)) f;
  struct {
    u_u32 lo32, hi32;
  } u;
} __attribute__((__may_alias__));
typedef i64 SUPERLONG;
typedef ui16 wchar16;


typedef wchar16 TChar;

typedef ui32 wchar32;



typedef i32 dochandle;
typedef ui32 udochandle;



template <bool>
struct TStaticAssertionFailed;

template <>
struct TStaticAssertionFailed <true> {
};

template <int x>
struct TStaticAssertTest {
};
template<int> struct TCompileTimeError;
template<> struct TCompileTimeError<true> {};




struct TNone {
    enum {
        Length = 0
    };

    template <class V>
    struct THave {
        enum {
            Result = false
        };
    };

    template <template <class> class P>
    struct TSelectBy {
        typedef TNone TResult;
    };
};



typedef long int ptrdiff_t;




namespace std __attribute__ ((__visibility__ ("default"))) {

  using ::ptrdiff_t;
  using ::size_t;

}
extern "C" {













extern void *memcpy (void *__restrict __dest,
       __const void *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));


extern void *memmove (void *__dest, __const void *__src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));






extern void *memccpy (void *__restrict __dest, __const void *__restrict __src,
        int __c, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));





extern void *memset (void *__s, int __c, size_t __n) throw () __attribute__ ((__nonnull__ (1)));


extern int memcmp (__const void *__s1, __const void *__s2, size_t __n)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern void *memchr (__const void *__s, int __c, size_t __n)
      throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));


extern void *rawmemchr (__const void *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern void *memrchr (__const void *__s, int __c, size_t __n)
      throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));






extern char *strcpy (char *__restrict __dest, __const char *__restrict __src)
     throw () __attribute__ ((__nonnull__ (1, 2)));

extern char *strncpy (char *__restrict __dest,
        __const char *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));


extern char *strcat (char *__restrict __dest, __const char *__restrict __src)
     throw () __attribute__ ((__nonnull__ (1, 2)));

extern char *strncat (char *__restrict __dest, __const char *__restrict __src,
        size_t __n) throw () __attribute__ ((__nonnull__ (1, 2)));


extern int strcmp (__const char *__s1, __const char *__s2)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));

extern int strncmp (__const char *__s1, __const char *__s2, size_t __n)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern int strcoll (__const char *__s1, __const char *__s2)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));

extern size_t strxfrm (char *__restrict __dest,
         __const char *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (2)));






typedef struct __locale_struct
{

  struct __locale_data *__locales[13];


  const unsigned short int *__ctype_b;
  const int *__ctype_tolower;
  const int *__ctype_toupper;


  const char *__names[13];
} *__locale_t;


typedef __locale_t locale_t;


extern int strcoll_l (__const char *__s1, __const char *__s2, __locale_t __l)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));

extern size_t strxfrm_l (char *__dest, __const char *__src, size_t __n,
    __locale_t __l) throw () __attribute__ ((__nonnull__ (2, 4)));





extern char *strdup (__const char *__s)
     throw () __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));






extern char *strndup (__const char *__string, size_t __n)
     throw () __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));

extern char *strchr (__const char *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern char *strrchr (__const char *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));


extern char *strchrnul (__const char *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));






extern size_t strcspn (__const char *__s, __const char *__reject)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern size_t strspn (__const char *__s, __const char *__accept)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strpbrk (__const char *__s, __const char *__accept)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strstr (__const char *__haystack, __const char *__needle)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));




extern char *strtok (char *__restrict __s, __const char *__restrict __delim)
     throw () __attribute__ ((__nonnull__ (2)));




extern char *__strtok_r (char *__restrict __s,
    __const char *__restrict __delim,
    char **__restrict __save_ptr)
     throw () __attribute__ ((__nonnull__ (2, 3)));

extern char *strtok_r (char *__restrict __s, __const char *__restrict __delim,
         char **__restrict __save_ptr)
     throw () __attribute__ ((__nonnull__ (2, 3)));
extern char *strcasestr (__const char *__haystack, __const char *__needle)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));







extern void *memmem (__const void *__haystack, size_t __haystacklen,
       __const void *__needle, size_t __needlelen)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 3)));



extern void *__mempcpy (void *__restrict __dest,
   __const void *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));
extern void *mempcpy (void *__restrict __dest,
        __const void *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));





extern size_t strlen (__const char *__s)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));





extern size_t strnlen (__const char *__string, size_t __maxlen)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));





extern char *strerror (int __errnum) throw ();

extern char *strerror_r (int __errnum, char *__buf, size_t __buflen)
     throw () __attribute__ ((__nonnull__ (2)));





extern char *strerror_l (int __errnum, __locale_t __l) throw ();





extern void __bzero (void *__s, size_t __n) throw () __attribute__ ((__nonnull__ (1)));



extern void bcopy (__const void *__src, void *__dest, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));


extern void bzero (void *__s, size_t __n) throw () __attribute__ ((__nonnull__ (1)));


extern int bcmp (__const void *__s1, __const void *__s2, size_t __n)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *index (__const char *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern char *rindex (__const char *__s, int __c)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));




extern int ffs (int __i) throw () __attribute__ ((__const__));




extern int ffsl (long int __l) throw () __attribute__ ((__const__));

__extension__ extern int ffsll (long long int __ll)
     throw () __attribute__ ((__const__));




extern int strcasecmp (__const char *__s1, __const char *__s2)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern int strncasecmp (__const char *__s1, __const char *__s2, size_t __n)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));





extern int strcasecmp_l (__const char *__s1, __const char *__s2,
    __locale_t __loc)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));

extern int strncasecmp_l (__const char *__s1, __const char *__s2,
     size_t __n, __locale_t __loc)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 4)));





extern char *strsep (char **__restrict __stringp,
       __const char *__restrict __delim)
     throw () __attribute__ ((__nonnull__ (1, 2)));




extern char *strsignal (int __sig) throw ();


extern char *__stpcpy (char *__restrict __dest, __const char *__restrict __src)
     throw () __attribute__ ((__nonnull__ (1, 2)));
extern char *stpcpy (char *__restrict __dest, __const char *__restrict __src)
     throw () __attribute__ ((__nonnull__ (1, 2)));



extern char *__stpncpy (char *__restrict __dest,
   __const char *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));
extern char *stpncpy (char *__restrict __dest,
        __const char *__restrict __src, size_t __n)
     throw () __attribute__ ((__nonnull__ (1, 2)));




extern int strverscmp (__const char *__s1, __const char *__s2)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));


extern char *strfry (char *__string) throw () __attribute__ ((__nonnull__ (1)));


extern void *memfrob (void *__s, size_t __n) throw () __attribute__ ((__nonnull__ (1)));
extern char *basename (__const char *__filename) throw () __attribute__ ((__nonnull__ (1)));
}
namespace std __attribute__ ((__visibility__ ("default"))) {

  using ::memchr;
  using ::memcmp;
  using ::memcpy;
  using ::memmove;
  using ::memset;
  using ::strcat;
  using ::strcmp;
  using ::strcoll;
  using ::strcpy;
  using ::strcspn;
  using ::strerror;
  using ::strlen;
  using ::strncat;
  using ::strncmp;
  using ::strncpy;
  using ::strspn;
  using ::strtok;
  using ::strxfrm;
  using ::strchr;
  using ::strpbrk;
  using ::strrchr;
  using ::strstr;


  inline void*
  memchr(void* __p, int __c, size_t __n)
  { return memchr(const_cast<const void*>(__p), __c, __n); }

  inline char*
  strchr(char* __s1, int __n)
  { return __builtin_strchr(const_cast<const char*>(__s1), __n); }

  inline char*
  strpbrk(char* __s1, const char* __s2)
  { return __builtin_strpbrk(const_cast<const char*>(__s1), __s2); }

  inline char*
  strrchr(char* __s1, int __n)
  { return __builtin_strrchr(const_cast<const char*>(__s1), __n); }

  inline char*
  strstr(char* __s1, const char* __s2)
  { return __builtin_strstr(const_cast<const char*>(__s1), __s2); }


}





namespace NStl {
using __std_alias::size_t;
using __std_alias::memmove;
using __std_alias::memcpy;




using __std_alias::strcoll;
using __std_alias::strerror;
using __std_alias::strxfrm;





using __std_alias::memchr;
using __std_alias::strchr;
using __std_alias::strpbrk;
using __std_alias::strrchr;
using __std_alias::strstr;




using __std_alias::memcmp;
using __std_alias::memset;

using __std_alias::strcat;


using __std_alias::strcmp;



using __std_alias::strcpy;

using __std_alias::strcspn;
using __std_alias::strlen;
using __std_alias::strncat;
using __std_alias::strncmp;

using __std_alias::strncpy;
using __std_alias::strspn;

using __std_alias::strtok;
}





namespace NStl {

struct __true_type {};
struct __false_type {};


} namespace NStlPriv {
using ::NStl::__true_type;
using ::NStl::__false_type;
} namespace NStl {



template <int _Is>
struct __bool2type
{ typedef __true_type _Ret; };

template<>
struct __bool2type<1> { typedef __true_type _Ret; };

template<>
struct __bool2type<0> { typedef __false_type _Ret; };


template <class __bool_type>
struct __type2bool { enum {_Ret = 1}; };

template<>
struct __type2bool<__true_type> { enum {_Ret = 1}; };

template<>
struct __type2bool<__false_type> { enum {_Ret = 0}; };


template <class _BoolType>
struct _Not { typedef __false_type _Ret; };

template<>
struct _Not<__false_type> { typedef __true_type _Ret; };


template <class _P1, class _P2>
struct _Land2 { typedef __false_type _Ret; };

template<>
struct _Land2<__true_type, __true_type> { typedef __true_type _Ret; };


template <class _P1, class _P2, class _P3>
struct _Land3 { typedef __false_type _Ret; };

template<>
struct _Land3<__true_type, __true_type, __true_type> { typedef __true_type _Ret; };


template <class _P1, class _P2>
struct _Lor2 { typedef __true_type _Ret; };

template<>
struct _Lor2<__false_type, __false_type> { typedef __false_type _Ret; };


template <class _P1, class _P2, class _P3>
struct _Lor3 { typedef __true_type _Ret; };

template<>
struct _Lor3<__false_type, __false_type, __false_type> { typedef __false_type _Ret; };
template <bool _Cond, class _Tp1, class _Tp2>
struct __select { typedef _Tp1 _Ret; };

template <class _Tp1, class _Tp2>
struct __select<false, _Tp1, _Tp2> { typedef _Tp2 _Ret; };
template <class _Tp1, class _Tp2>
struct _IsSameAux {
  typedef __false_type _RetT;
  enum { _Ret = 0 };
};

template <class _Tp>
struct _UnConstType { typedef _Tp _Type; };

template <class _Tp>
struct _UnVolatileType { typedef _Tp _Type; };

template <class _Tp>
struct _UnCVType {
  typedef typename _UnVolatileType<_Tp>::_Type _UnVType;
  typedef typename _UnConstType<_UnVType>::_Type _Type;
};


template <class _Tp>
struct _IsSameAux<_Tp, _Tp> {
  typedef __true_type _RetT;
  enum { _Ret = 1 };
};


template <class _Tp>
struct _UnConstType<const _Tp> { typedef _Tp _Type; };

template <class _Tp>
struct _UnVolatileType<volatile _Tp> { typedef _Tp _Type; };
template <class _Tp1, class _Tp2>
struct _IsSame {
  typedef typename _UnCVType<_Tp1>::_Type _Type1;
  typedef typename _UnCVType<_Tp2>::_Type _Type2;

  typedef _IsSameAux<_Type1, _Type2> _Aux;
  enum { _Ret = _Aux::_Ret };
  typedef typename _Aux::_RetT _RetT;
};
template <class _Tp1, class _Tp2>
struct _AreSameUnCVTypes {
  enum { _Same = _IsSame<_Tp1, _Tp2>::_Ret };
  typedef typename _IsSame<_Tp1, _Tp2>::_RetT _Ret;
};






template <class _Src, class _Dst>
struct _ConversionHelper {
  static char _Test(bool, _Dst);
  static char* _Test(bool, ...);
  static _Src _MakeSource();
};

template <class _Src, class _Dst>
struct _IsConvertible {
  typedef _ConversionHelper<_Src*, const volatile _Dst*> _H;
  enum { value = (sizeof(char) == sizeof(_H::_Test(false, _H::_MakeSource()))) };
  typedef typename __bool2type<value>::_Ret _Ret;
};







template <class _Src, class _Dst>
struct _IsCVConvertible {

  typedef _ConversionHelper<_Src, _Dst> _H;
  enum { value = (sizeof(char) == sizeof(_H::_Test(false, _H::_MakeSource()))) };





  typedef typename __bool2type<value>::_Ret _Ret;
};
template <class _Tp>
struct _IsConst { typedef __false_type _Ret; };


template <class _Tp>
struct _IsConst <const _Tp> { typedef __true_type _Ret; };
}
namespace NStl {






template <class _Tp> struct _IsIntegral
{ typedef __false_type _Ret; };


template<> struct _IsIntegral<bool>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<char>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<signed char>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<unsigned char>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<wchar_t>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<short>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<unsigned short>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<int>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<unsigned int>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<long>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<unsigned long>
{ typedef __true_type _Ret; };


template<> struct _IsIntegral<long long>
{ typedef __true_type _Ret; };

template<> struct _IsIntegral<unsigned long long>
{ typedef __true_type _Ret; };


template <class _Tp> struct _IsRational
{ typedef __false_type _Ret; };

template<> struct _IsRational<float>
{ typedef __true_type _Ret; };

template<> struct _IsRational<double>
{ typedef __true_type _Ret; };


template<> struct _IsRational<long double>
{ typedef __true_type _Ret; };



template <class _Tp> struct __type_traits;
template <class _IsPOD> struct __type_traits_aux {
   typedef __false_type has_trivial_default_constructor;
   typedef __false_type has_trivial_copy_constructor;
   typedef __false_type has_trivial_assignment_operator;
   typedef __false_type has_trivial_destructor;
   typedef __false_type is_POD_type;
};

template<>
struct __type_traits_aux<__false_type> {
   typedef __false_type has_trivial_default_constructor;
   typedef __false_type has_trivial_copy_constructor;
   typedef __false_type has_trivial_assignment_operator;
   typedef __false_type has_trivial_destructor;
   typedef __false_type is_POD_type;
};

template<>
struct __type_traits_aux<__true_type> {
  typedef __true_type has_trivial_default_constructor;
  typedef __true_type has_trivial_copy_constructor;
  typedef __true_type has_trivial_assignment_operator;
  typedef __true_type has_trivial_destructor;
  typedef __true_type is_POD_type;
};

template <class _Tp>
struct _IsRef {
  typedef __false_type _Ret;
};
template <class _Tp> struct _IsPtr {
  typedef __false_type _Ret;
};

template <class _Tp>
struct __type_traits {
   typedef __true_type this_dummy_member_must_be_first;
   typedef __false_type has_trivial_default_constructor;
   typedef __false_type has_trivial_copy_constructor;
   typedef __false_type has_trivial_assignment_operator;
   typedef __false_type has_trivial_destructor;
   typedef __false_type is_POD_type;







};


template <class _Tp> struct _IsPtr<_Tp*>
{ typedef __true_type _Ret; };
template <class _Tp> struct _IsRef<_Tp&>
{ typedef __true_type _Ret; };

template <class _Tp> struct __type_traits<_Tp*> : __type_traits_aux<__true_type>
{};
template<> struct __type_traits< bool > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const bool > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile bool > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile bool > : __type_traits_aux<__true_type> {};

template<> struct __type_traits< char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile char > : __type_traits_aux<__true_type> {};

template<> struct __type_traits< signed char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const signed char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile signed char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile signed char > : __type_traits_aux<__true_type> {};

template<> struct __type_traits< unsigned char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const unsigned char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile unsigned char > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile unsigned char > : __type_traits_aux<__true_type> {};

template<> struct __type_traits< wchar_t > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const wchar_t > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile wchar_t > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile wchar_t > : __type_traits_aux<__true_type> {};


template<> struct __type_traits< short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile short > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< unsigned short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const unsigned short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile unsigned short > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile unsigned short > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile int > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< unsigned int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const unsigned int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile unsigned int > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile unsigned int > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile long > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< unsigned long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const unsigned long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile unsigned long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile unsigned long > : __type_traits_aux<__true_type> {};


template<> struct __type_traits< long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile long long > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< unsigned long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const unsigned long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile unsigned long long > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile unsigned long long > : __type_traits_aux<__true_type> {};


template<> struct __type_traits< float > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const float > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile float > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile float > : __type_traits_aux<__true_type> {};
template<> struct __type_traits< double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile double > : __type_traits_aux<__true_type> {};


template<> struct __type_traits< long double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const long double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< volatile long double > : __type_traits_aux<__true_type> {}; template<> struct __type_traits< const volatile long double > : __type_traits_aux<__true_type> {};



template <class _ArePtrs, class _Src, class _Dst>
struct _IsCVConvertibleIf
{ typedef typename _IsCVConvertible<_Src, _Dst>::_Ret _Ret; };

template <class _Src, class _Dst>
struct _IsCVConvertibleIf<__false_type, _Src, _Dst>
{ typedef __false_type _Ret; };
template <class _Src, class _Dst>
struct _TrivialNativeTypeCopy {
  typedef typename _IsPtr<_Src>::_Ret _Ptr1;
  typedef typename _IsPtr<_Dst>::_Ret _Ptr2;
  typedef typename _Land2<_Ptr1, _Ptr2>::_Ret _BothPtrs;
  typedef typename _IsCVConvertibleIf<_BothPtrs, _Src, _Dst>::_Ret _Convertible;
  typedef typename _Land2<_BothPtrs, _Convertible>::_Ret _Trivial1;

  typedef typename __bool2type<(sizeof(_Src) == sizeof(_Dst))>::_Ret _SameSize;

  typedef typename _IsIntegral<_Src>::_Ret _Int1;
  typedef typename _IsIntegral<_Dst>::_Ret _Int2;
  typedef typename _Land2<_Int1, _Int2>::_Ret _BothInts;

  typedef typename _IsRational<_Src>::_Ret _Rat1;
  typedef typename _IsRational<_Dst>::_Ret _Rat2;
  typedef typename _Land2<_Rat1, _Rat2>::_Ret _BothRats;

  typedef typename _Lor2<_BothInts, _BothRats>::_Ret _BothNatives;
  typedef typename _Land2<_BothNatives, _SameSize>::_Ret _Trivial2;

  typedef typename _Lor2<_Trivial1, _Trivial2>::_Ret _Ret;
};

template <class _Src, class _Dst>
struct _TrivialCopy {
  typedef typename _TrivialNativeTypeCopy<_Src, _Dst>::_Ret _NativeRet;


  typedef typename __type_traits<_Src>::has_trivial_assignment_operator _Tr1;




  typedef typename _AreSameUnCVTypes<_Src, _Dst>::_Ret _Tr2;
  typedef typename _Land2<_Tr1, _Tr2>::_Ret _UserRet;

  typedef typename _Lor2<_NativeRet, _UserRet>::_Ret _Ret;
  static _Ret _Answer() { return _Ret(); }
};

template <class _Src, class _Dst>
struct _TrivialUCopy {
  typedef typename _TrivialNativeTypeCopy<_Src, _Dst>::_Ret _NativeRet;


  typedef typename __type_traits<_Src>::has_trivial_copy_constructor _Tr1;




  typedef typename _AreSameUnCVTypes<_Src, _Dst>::_Ret _Tr2;
  typedef typename _Land2<_Tr1, _Tr2>::_Ret _UserRet;

  typedef typename _Lor2<_NativeRet, _UserRet>::_Ret _Ret;
  static _Ret _Answer() { return _Ret(); }
};

template <class _Tp>
struct _DefaultZeroValue {
  typedef typename _IsIntegral<_Tp>::_Ret _Tr1;
  typedef typename _IsRational<_Tp>::_Ret _Tr2;
  typedef typename _IsPtr<_Tp>::_Ret _Tr3;
  typedef typename _Lor3<_Tr1, _Tr2, _Tr3>::_Ret _Ret;
};

template <class _Tp>
struct _TrivialInit {

  typedef typename __type_traits<_Tp>::has_trivial_default_constructor _Tr1;




  typedef typename _DefaultZeroValue<_Tp>::_Ret _Tr2;
  typedef typename _Not<_Tr2>::_Ret _Tr3;
  typedef typename _Land2<_Tr1, _Tr3>::_Ret _Ret;
  static _Ret _Answer() { return _Ret(); }
};



template <class _Tp>
struct _IsPtrType {
  typedef typename _IsPtr<_Tp>::_Ret _Type;
  static _Type _Ret() { return _Type(); }
};

template <class _Tp>
struct _IsRefType {
  typedef typename _IsRef<_Tp>::_Ret _Type;
  static _Type _Ret() { return _Type();}
};

template <class _Tp>
struct __call_traits {




  typedef const _Tp& param_type;

};


template <class _Tp>
struct __call_traits<_Tp&>
{ typedef _Tp& param_type; };


template <class _Tp1, class _Tp2>
struct _BothPtrType {
  typedef typename _IsPtr<_Tp1>::_Ret _IsPtr1;
  typedef typename _IsPtr<_Tp2>::_Ret _IsPtr2;

  typedef typename _Land2<_IsPtr1, _IsPtr2>::_Ret _Ret;
  static _Ret _Answer() { return _Ret(); }
};

template <class _Tp1, class _Tp2, class _IsRef1, class _IsRef2>
struct _OKToSwap {
  typedef typename _AreSameUnCVTypes<_Tp1, _Tp2>::_Ret _Same;
  typedef typename _Land3<_Same, _IsRef1, _IsRef2>::_Ret _Type;
  static _Type _Answer() { return _Type(); }
};

template <class _Tp1, class _Tp2, class _IsRef1, class _IsRef2>
inline _OKToSwap<_Tp1, _Tp2, _IsRef1, _IsRef2>
_IsOKToSwap(_Tp1*, _Tp2*, const _IsRef1&, const _IsRef2&)
{ return _OKToSwap<_Tp1, _Tp2, _IsRef1, _IsRef2>(); }

template <class _Src, class _Dst>
inline _TrivialCopy<_Src, _Dst> _UseTrivialCopy(_Src*, _Dst*)
{ return _TrivialCopy<_Src, _Dst>(); }

template <class _Src, class _Dst>
inline _TrivialUCopy<_Src, _Dst> _UseTrivialUCopy(_Src*, _Dst*)
{ return _TrivialUCopy<_Src, _Dst>(); }

template <class _Tp>
inline _TrivialInit<_Tp> _UseTrivialInit(_Tp*)
{ return _TrivialInit<_Tp>(); }

template <class _Tp>
struct _IsPOD {
  typedef typename __type_traits<_Tp>::is_POD_type _Type;
  static _Type _Answer() { return _Type(); }
};

template <class _Tp>
inline _IsPOD<_Tp> _Is_POD(_Tp*)
{ return _IsPOD<_Tp>(); }

template <class _Tp>
struct _DefaultZeroValueQuestion {
  typedef typename _DefaultZeroValue<_Tp>::_Ret _Ret;
  static _Ret _Answer() { return _Ret(); }
};

template <class _Tp>
inline _DefaultZeroValueQuestion<_Tp> _HasDefaultZeroValue(_Tp*)
{ return _DefaultZeroValueQuestion<_Tp>(); }







template <class _Tp>
struct __stlport_class
{ typedef _Tp _Type; };

template <class _Tp>
struct _IsSTLportClass {
  typedef typename _IsConvertible<_Tp, __stlport_class<_Tp> >::_Ret _Ret;



};
template <class _Tp>
class _TpWithState : private _Tp {
  _TpWithState();
  int _state;
};



template <class _Tp>
struct _IsStateless {
  enum { _Is = sizeof(_TpWithState<_Tp>) == sizeof(int) };
  typedef typename __bool2type<_Is>::_Ret _Ret;
};

}







namespace NStl {
template <class _Tp>
class __move_source {
public:
  explicit __move_source (_Tp &_src) : _M_data(_src)
  {}

  _Tp& get() const
  { return _M_data; }
private:
  _Tp &_M_data;


  typedef __move_source<_Tp> _Self;
  _Self& operator = (_Self const&);
};


template <class _Tp>
struct __move_traits {
  typedef __false_type implemented;





  typedef typename __type_traits<_Tp>::has_trivial_destructor complete;
};


typedef __true_type __stlp_movable;




} namespace NStlPriv {







template <class _Tp>
struct _MoveSourceTraits {
  typedef typename __move_traits<_Tp>::implemented _MvImpRet;



  enum {_MvImp = __type2bool<_MvImpRet>::_Ret};
  typedef typename __select<_MvImp,

                            __move_source<_Tp>,
                            _Tp const&>::_Ret _Type;
};


template <class _Tp>
inline typename _MoveSourceTraits<_Tp>::_Type
_AsMoveSource (_Tp &src) {
  typedef typename _MoveSourceTraits<_Tp>::_Type _SrcType;
  return _SrcType(src);
}


template <class _Tp>
struct __move_traits_aux {
  typedef typename __move_traits<_Tp>::implemented implemented;
  typedef typename __move_traits<_Tp>::complete complete;
};

template <class _Tp1, class _Tp2>
struct __move_traits_aux2 {
  typedef __move_traits<_Tp1> _MoveTraits1;
  typedef __move_traits<_Tp2> _MoveTraits2;

  typedef typename _Lor2<typename _MoveTraits1::implemented,
                         typename _MoveTraits2::implemented>::_Ret implemented;
  typedef typename _Land2<typename _MoveTraits1::complete,
                          typename _MoveTraits2::complete>::_Ret complete;
};





template <class _Tp>
struct __move_traits_help {
  typedef __true_type implemented;
  typedef typename __move_traits<_Tp>::complete complete;
};

template <class _Tp1, class _Tp2>
struct __move_traits_help1 {
  typedef __move_traits<_Tp1> _MoveTraits1;
  typedef __move_traits<_Tp2> _MoveTraits2;

  typedef typename _Lor2<typename _MoveTraits1::implemented,
                         typename _MoveTraits2::implemented>::_Ret implemented;
  typedef typename _Land2<typename _MoveTraits1::complete,
                          typename _MoveTraits2::complete>::_Ret complete;
};

template <class _Tp1, class _Tp2>
struct __move_traits_help2 {
  typedef __move_traits<_Tp1> _MoveTraits1;
  typedef __move_traits<_Tp2> _MoveTraits2;

  typedef __stlp_movable implemented;
  typedef typename _Land2<typename _MoveTraits1::complete,
                          typename _MoveTraits2::complete>::_Ret complete;
};

} namespace NStl {

}


namespace NStl {

template <class _T1, class _T2>
struct pair {
  typedef _T1 first_type;
  typedef _T2 second_type;

  _T1 first;
  _T2 second;



  pair() : first(_T1()), second(_T2()) {}

  pair(const _T1& __a, const _T2& __b) : first(__a), second(__b) {}


  template <class _U1, class _U2>
  pair(const pair<_U1, _U2>& __p) : first(__p.first), second(__p.second) {}

  pair(const pair<_T1,_T2>& __o) : first(__o.first), second(__o.second) {}


  pair(__move_source<pair<_T1, _T2> > src) : first(::NStlPriv:: _AsMoveSource(src.get().first)),
                                             second(::NStlPriv:: _AsMoveSource(src.get().second))
  {}


};

template <class _T1, class _T2>
inline bool operator==(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
{ return __x.first == __y.first && __x.second == __y.second; }

template <class _T1, class _T2>
inline bool operator<(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y) {
  return __x.first < __y.first ||
         (!(__y.first < __x.first) && __x.second < __y.second);
}


template <class _T1, class _T2>
inline bool operator!=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
{ return !(__x == __y); }

template <class _T1, class _T2>
inline bool operator>(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
{ return __y < __x; }

template <class _T1, class _T2>
inline bool operator<=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
{ return !(__y < __x); }

template <class _T1, class _T2>
inline bool operator>=(const pair<_T1, _T2>& __x, const pair<_T1, _T2>& __y)
{ return !(__x < __y); }



template <class _T1, class _T2, int _Sz>
inline pair<_T1, _T2 const*> make_pair(_T1 const& __x,
                                       _T2 const (&__y)[_Sz])
{ return pair<_T1, _T2 const*>(__x, static_cast<_T2 const*>(__y)); }

template <class _T1, class _T2, int _Sz>
inline pair<_T1 const*, _T2> make_pair(_T1 const (&__x)[_Sz],
                                       _T2 const& __y)
{ return pair<_T1 const*, _T2>(static_cast<_T1 const*>(__x), __y); }

template <class _T1, class _T2, int _Sz1, int _Sz2>
inline pair<_T1 const*, _T2 const*> make_pair(_T1 const (&__x)[_Sz1],
                                              _T2 const (&__y)[_Sz2]) {
  return pair<_T1 const*, _T2 const*>(static_cast<_T1 const*>(__x),
                                      static_cast<_T2 const*>(__y));
}


template <class _T1, class _T2>
inline pair<_T1, _T2> make_pair(_T1 __x, _T2 __y)
{ return pair<_T1, _T2>(__x, __y); }

}


namespace NStl { namespace rel_ops {

template <class _Tp>
inline bool operator!=(const _Tp& __x, const _Tp& __y)
{ return !(__x == __y); }

template <class _Tp>
inline bool operator>(const _Tp& __x, const _Tp& __y)
{ return __y < __x; }

template <class _Tp>
inline bool operator<=(const _Tp& __x, const _Tp& __y)
{ return !(__y < __x); }

template <class _Tp>
inline bool operator>=(const _Tp& __x, const _Tp& __y)
{ return !(__x < __y); }

} }



namespace NStl {

template <class _T1, class _T2>
struct __type_traits<pair<_T1, _T2> > {
  typedef __type_traits<_T1> _T1Traits;
  typedef __type_traits<_T2> _T2Traits;
  typedef typename _Land2<typename _T1Traits::has_trivial_default_constructor,
                          typename _T2Traits::has_trivial_default_constructor>::_Ret has_trivial_default_constructor;
  typedef typename _Land2<typename _T1Traits::has_trivial_copy_constructor,
                          typename _T2Traits::has_trivial_copy_constructor>::_Ret has_trivial_copy_constructor;
  typedef typename _Land2<typename _T1Traits::has_trivial_assignment_operator,
                          typename _T2Traits::has_trivial_assignment_operator>::_Ret has_trivial_assignment_operator;
  typedef typename _Land2<typename _T1Traits::has_trivial_destructor,
                          typename _T2Traits::has_trivial_destructor>::_Ret has_trivial_destructor;
  typedef __false_type is_POD_type;





};

template <class _T1, class _T2>
struct __move_traits<pair<_T1, _T2> >
  : ::NStlPriv:: __move_traits_help1<_T1, _T2> {};

}


template <class T1, class T2 = T1>
struct TPair : NStl::pair<T1, T2> {
    typedef T1 TFirst;
    typedef T2 TSecond;

    TPair() {
    }

    TPair(const T1& x, const T2& y)
        : NStl::pair<T1, T2> (x, y)
    {
    }

    TPair(NStl::__move_source<TPair<T1, T2> > src)
        : NStl::pair<T1, T2> (src)
    {
    }

    TPair(NStl::__move_source<NStl::pair<T1, T2> > src)
        : NStl::pair<T1, T2> (src)
    {
    }

    template <class TU, class TV>
    TPair(const NStl::pair<TU, TV>& p)
        : NStl::pair<T1, T2>(p)
    {
    }

    template <class TU, class TV>
    TPair(const TPair<TU, TV>& p)
        : NStl::pair<T1, T2>(p)
    {
    }

    TFirst& First() {
        return this->first;
    }

    TSecond& Second() {
        return this->second;
    }

    const TFirst& First() const {
        return this->first;
    }

    const TSecond& Second() const {
        return this->second;
    }
};

template<class T1, class T2>
inline TPair<T1, T2> MakePair(T1 v1, T2 v2) {
    return (TPair<T1, T2>(v1, v2));
}

template<class T>
inline TPair<T, T> MakePair(T v) {
    return (TPair<T, T>(v, v));
}

typedef TPair<ui64, ui64> uint128;

inline ui64 Uint128Low64(const uint128& x) {
    return x.first;
}

inline ui64 Uint128High64(const uint128& x) {
    return x.second;
}


ui64 CityHash64(const char* buf, size_t len);



ui64 CityHash64WithSeed(const char* buf, size_t len, ui64 seed);



ui64 CityHash64WithSeeds(const char* buf, size_t len, ui64 seed0, ui64 seed1);


uint128 CityHash128(const char* s, size_t len);



uint128 CityHash128WithSeed(const char* s, size_t len, uint128 seed);



inline ui64 Hash128to64(const uint128& x) {

    const ui64 kMul = 0x9ddfea08eb382d69ULL;
    ui64 a = (Uint128Low64(x) ^ Uint128High64(x)) * kMul;
    a ^= (a >> 47);
    ui64 b = (Uint128High64(x) ^ a) * kMul;
    b ^= (b >> 47);
    b *= kMul;
    return b;
}

typedef ui8 uint8;
typedef ui32 uint32;
typedef ui64 uint64;











extern "C" {



struct _IO_FILE;



typedef struct _IO_FILE FILE;





typedef struct _IO_FILE __FILE;




typedef struct
{
  int __count;
  union
  {

    unsigned int __wch;



    char __wchb[4];
  } __value;
} __mbstate_t;





typedef struct
{
  __off_t __pos;
  __mbstate_t __state;
} _G_fpos_t;
typedef struct
{
  __off64_t __pos;
  __mbstate_t __state;
} _G_fpos64_t;
typedef int _G_int16_t __attribute__ ((__mode__ (__HI__)));
typedef int _G_int32_t __attribute__ ((__mode__ (__SI__)));
typedef unsigned int _G_uint16_t __attribute__ ((__mode__ (__HI__)));
typedef unsigned int _G_uint32_t __attribute__ ((__mode__ (__SI__)));
typedef __builtin_va_list __gnuc_va_list;
struct _IO_jump_t; struct _IO_FILE;
typedef void _IO_lock_t;





struct _IO_marker {
  struct _IO_marker *_next;
  struct _IO_FILE *_sbuf;



  int _pos;
};


enum __codecvt_result
{
  __codecvt_ok,
  __codecvt_partial,
  __codecvt_error,
  __codecvt_noconv
};
struct _IO_FILE {
  int _flags;




  char* _IO_read_ptr;
  char* _IO_read_end;
  char* _IO_read_base;
  char* _IO_write_base;
  char* _IO_write_ptr;
  char* _IO_write_end;
  char* _IO_buf_base;
  char* _IO_buf_end;

  char *_IO_save_base;
  char *_IO_backup_base;
  char *_IO_save_end;

  struct _IO_marker *_markers;

  struct _IO_FILE *_chain;

  int _fileno;



  int _flags2;

  __off_t _old_offset;



  unsigned short _cur_column;
  signed char _vtable_offset;
  char _shortbuf[1];



  _IO_lock_t *_lock;
  __off64_t _offset;
  void *__pad1;
  void *__pad2;
  void *__pad3;
  void *__pad4;
  size_t __pad5;

  int _mode;

  char _unused2[15 * sizeof (int) - 4 * sizeof (void *) - sizeof (size_t)];

};





struct _IO_FILE_plus;

extern struct _IO_FILE_plus _IO_2_1_stdin_;
extern struct _IO_FILE_plus _IO_2_1_stdout_;
extern struct _IO_FILE_plus _IO_2_1_stderr_;
typedef __ssize_t __io_read_fn (void *__cookie, char *__buf, size_t __nbytes);







typedef __ssize_t __io_write_fn (void *__cookie, __const char *__buf,
     size_t __n);







typedef int __io_seek_fn (void *__cookie, __off64_t *__pos, int __w);


typedef int __io_close_fn (void *__cookie);




typedef __io_read_fn cookie_read_function_t;
typedef __io_write_fn cookie_write_function_t;
typedef __io_seek_fn cookie_seek_function_t;
typedef __io_close_fn cookie_close_function_t;


typedef struct
{
  __io_read_fn *read;
  __io_write_fn *write;
  __io_seek_fn *seek;
  __io_close_fn *close;
} _IO_cookie_io_functions_t;
typedef _IO_cookie_io_functions_t cookie_io_functions_t;

struct _IO_cookie_file;


extern void _IO_cookie_init (struct _IO_cookie_file *__cfile, int __read_write,
        void *__cookie, _IO_cookie_io_functions_t __fns);




extern "C" {


extern int __underflow (_IO_FILE *);
extern int __uflow (_IO_FILE *);
extern int __overflow (_IO_FILE *, int);
extern int _IO_getc (_IO_FILE *__fp);
extern int _IO_putc (int __c, _IO_FILE *__fp);
extern int _IO_feof (_IO_FILE *__fp) throw ();
extern int _IO_ferror (_IO_FILE *__fp) throw ();

extern int _IO_peekc_locked (_IO_FILE *__fp);





extern void _IO_flockfile (_IO_FILE *) throw ();
extern void _IO_funlockfile (_IO_FILE *) throw ();
extern int _IO_ftrylockfile (_IO_FILE *) throw ();
extern int _IO_vfscanf (_IO_FILE * __restrict, const char * __restrict,
   __gnuc_va_list, int *__restrict);
extern int _IO_vfprintf (_IO_FILE *__restrict, const char *__restrict,
    __gnuc_va_list);
extern __ssize_t _IO_padn (_IO_FILE *, int, __ssize_t);
extern size_t _IO_sgetn (_IO_FILE *, void *, size_t);

extern __off64_t _IO_seekoff (_IO_FILE *, __off64_t, int, int);
extern __off64_t _IO_seekpos (_IO_FILE *, __off64_t, int);

extern void _IO_free_backup_area (_IO_FILE *) throw ();
}




typedef __gnuc_va_list va_list;




typedef _G_fpos64_t fpos_t;



typedef _G_fpos64_t fpos64_t;



extern struct _IO_FILE *stdin;
extern struct _IO_FILE *stdout;
extern struct _IO_FILE *stderr;







extern int remove (__const char *__filename) throw ();

extern int rename (__const char *__old, __const char *__new) throw ();




extern int renameat (int __oldfd, __const char *__old, int __newfd,
       __const char *__new) throw ();



extern FILE *tmpfile (void) __asm__ ("" "tmpfile64") ;






extern FILE *tmpfile64 (void) ;



extern char *tmpnam (char *__s) throw () ;





extern char *tmpnam_r (char *__s) throw () ;
extern char *tempnam (__const char *__dir, __const char *__pfx)
     throw () __attribute__ ((__malloc__)) ;








extern int fclose (FILE *__stream);




extern int fflush (FILE *__stream);

extern int fflush_unlocked (FILE *__stream);
extern int fcloseall (void);




extern FILE *fopen (__const char *__restrict __filename, __const char *__restrict __modes) __asm__ ("" "fopen64")

  ;
extern FILE *freopen (__const char *__restrict __filename, __const char *__restrict __modes, FILE *__restrict __stream) __asm__ ("" "freopen64")


  ;







extern FILE *fopen64 (__const char *__restrict __filename,
        __const char *__restrict __modes) ;
extern FILE *freopen64 (__const char *__restrict __filename,
   __const char *__restrict __modes,
   FILE *__restrict __stream) ;




extern FILE *fdopen (int __fd, __const char *__modes) throw () ;





extern FILE *fopencookie (void *__restrict __magic_cookie,
     __const char *__restrict __modes,
     _IO_cookie_io_functions_t __io_funcs) throw () ;




extern FILE *fmemopen (void *__s, size_t __len, __const char *__modes)
  throw () ;




extern FILE *open_memstream (char **__bufloc, size_t *__sizeloc) throw () ;






extern void setbuf (FILE *__restrict __stream, char *__restrict __buf) throw ();



extern int setvbuf (FILE *__restrict __stream, char *__restrict __buf,
      int __modes, size_t __n) throw ();





extern void setbuffer (FILE *__restrict __stream, char *__restrict __buf,
         size_t __size) throw ();


extern void setlinebuf (FILE *__stream) throw ();








extern int fprintf (FILE *__restrict __stream,
      __const char *__restrict __format, ...);




extern int printf (__const char *__restrict __format, ...);

extern int sprintf (char *__restrict __s,
      __const char *__restrict __format, ...) throw ();





extern int vfprintf (FILE *__restrict __s, __const char *__restrict __format,
       __gnuc_va_list __arg);




extern int vprintf (__const char *__restrict __format, __gnuc_va_list __arg);

extern int vsprintf (char *__restrict __s, __const char *__restrict __format,
       __gnuc_va_list __arg) throw ();





extern int snprintf (char *__restrict __s, size_t __maxlen,
       __const char *__restrict __format, ...)
     throw () __attribute__ ((__format__ (__printf__, 3, 4)));

extern int vsnprintf (char *__restrict __s, size_t __maxlen,
        __const char *__restrict __format, __gnuc_va_list __arg)
     throw () __attribute__ ((__format__ (__printf__, 3, 0)));






extern int vasprintf (char **__restrict __ptr, __const char *__restrict __f,
        __gnuc_va_list __arg)
     throw () __attribute__ ((__format__ (__printf__, 2, 0))) ;
extern int __asprintf (char **__restrict __ptr,
         __const char *__restrict __fmt, ...)
     throw () __attribute__ ((__format__ (__printf__, 2, 3))) ;
extern int asprintf (char **__restrict __ptr,
       __const char *__restrict __fmt, ...)
     throw () __attribute__ ((__format__ (__printf__, 2, 3))) ;
extern int vdprintf (int __fd, __const char *__restrict __fmt,
       __gnuc_va_list __arg)
     __attribute__ ((__format__ (__printf__, 2, 0)));
extern int dprintf (int __fd, __const char *__restrict __fmt, ...)
     __attribute__ ((__format__ (__printf__, 2, 3)));








extern int fscanf (FILE *__restrict __stream,
     __const char *__restrict __format, ...) ;




extern int scanf (__const char *__restrict __format, ...) ;

extern int sscanf (__const char *__restrict __s,
     __const char *__restrict __format, ...) throw ();








extern int vfscanf (FILE *__restrict __s, __const char *__restrict __format,
      __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 2, 0))) ;





extern int vscanf (__const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__format__ (__scanf__, 1, 0))) ;


extern int vsscanf (__const char *__restrict __s,
      __const char *__restrict __format, __gnuc_va_list __arg)
     throw () __attribute__ ((__format__ (__scanf__, 2, 0)));









extern int fgetc (FILE *__stream);
extern int getc (FILE *__stream);





extern int getchar (void);

extern int getc_unlocked (FILE *__stream);
extern int getchar_unlocked (void);
extern int fgetc_unlocked (FILE *__stream);











extern int fputc (int __c, FILE *__stream);
extern int putc (int __c, FILE *__stream);





extern int putchar (int __c);

extern int fputc_unlocked (int __c, FILE *__stream);







extern int putc_unlocked (int __c, FILE *__stream);
extern int putchar_unlocked (int __c);






extern int getw (FILE *__stream);


extern int putw (int __w, FILE *__stream);








extern char *fgets (char *__restrict __s, int __n, FILE *__restrict __stream)
     ;






extern char *gets (char *__s) ;

extern char *fgets_unlocked (char *__restrict __s, int __n,
        FILE *__restrict __stream) ;
extern __ssize_t __getdelim (char **__restrict __lineptr,
          size_t *__restrict __n, int __delimiter,
          FILE *__restrict __stream) ;
extern __ssize_t getdelim (char **__restrict __lineptr,
        size_t *__restrict __n, int __delimiter,
        FILE *__restrict __stream) ;







extern __ssize_t getline (char **__restrict __lineptr,
       size_t *__restrict __n,
       FILE *__restrict __stream) ;








extern int fputs (__const char *__restrict __s, FILE *__restrict __stream);





extern int puts (__const char *__s);






extern int ungetc (int __c, FILE *__stream);






extern size_t fread (void *__restrict __ptr, size_t __size,
       size_t __n, FILE *__restrict __stream) ;




extern size_t fwrite (__const void *__restrict __ptr, size_t __size,
        size_t __n, FILE *__restrict __s);

extern int fputs_unlocked (__const char *__restrict __s,
      FILE *__restrict __stream);
extern size_t fread_unlocked (void *__restrict __ptr, size_t __size,
         size_t __n, FILE *__restrict __stream) ;
extern size_t fwrite_unlocked (__const void *__restrict __ptr, size_t __size,
          size_t __n, FILE *__restrict __stream);








extern int fseek (FILE *__stream, long int __off, int __whence);




extern long int ftell (FILE *__stream) ;




extern void rewind (FILE *__stream);

extern int fseeko (FILE *__stream, __off64_t __off, int __whence) __asm__ ("" "fseeko64");


extern __off64_t ftello (FILE *__stream) __asm__ ("" "ftello64");








extern int fgetpos (FILE *__restrict __stream, fpos_t *__restrict __pos) __asm__ ("" "fgetpos64");

extern int fsetpos (FILE *__stream, __const fpos_t *__pos) __asm__ ("" "fsetpos64");









extern int fseeko64 (FILE *__stream, __off64_t __off, int __whence);
extern __off64_t ftello64 (FILE *__stream) ;
extern int fgetpos64 (FILE *__restrict __stream, fpos64_t *__restrict __pos);
extern int fsetpos64 (FILE *__stream, __const fpos64_t *__pos);




extern void clearerr (FILE *__stream) throw ();

extern int feof (FILE *__stream) throw () ;

extern int ferror (FILE *__stream) throw () ;




extern void clearerr_unlocked (FILE *__stream) throw ();
extern int feof_unlocked (FILE *__stream) throw () ;
extern int ferror_unlocked (FILE *__stream) throw () ;








extern void perror (__const char *__s);






extern int sys_nerr;
extern __const char *__const sys_errlist[];


extern int _sys_nerr;
extern __const char *__const _sys_errlist[];




extern int fileno (FILE *__stream) throw () ;




extern int fileno_unlocked (FILE *__stream) throw () ;
extern FILE *popen (__const char *__command, __const char *__modes) ;





extern int pclose (FILE *__stream);





extern char *ctermid (char *__s) throw ();





extern char *cuserid (char *__s);




struct obstack;


extern int obstack_printf (struct obstack *__restrict __obstack,
      __const char *__restrict __format, ...)
     throw () __attribute__ ((__format__ (__printf__, 2, 3)));
extern int obstack_vprintf (struct obstack *__restrict __obstack,
       __const char *__restrict __format,
       __gnuc_va_list __args)
     throw () __attribute__ ((__format__ (__printf__, 2, 0)));







extern void flockfile (FILE *__stream) throw ();



extern int ftrylockfile (FILE *__stream) throw () ;


extern void funlockfile (FILE *__stream) throw ();
}
namespace std __attribute__ ((__visibility__ ("default"))) {

  using ::FILE;
  using ::fpos_t;

  using ::clearerr;
  using ::fclose;
  using ::feof;
  using ::ferror;
  using ::fflush;
  using ::fgetc;
  using ::fgetpos;
  using ::fgets;
  using ::fopen;
  using ::fprintf;
  using ::fputc;
  using ::fputs;
  using ::fread;
  using ::freopen;
  using ::fscanf;
  using ::fseek;
  using ::fsetpos;
  using ::ftell;
  using ::fwrite;
  using ::getc;
  using ::getchar;
  using ::gets;
  using ::perror;
  using ::printf;
  using ::putc;
  using ::putchar;
  using ::puts;
  using ::remove;
  using ::rename;
  using ::rewind;
  using ::scanf;
  using ::setbuf;
  using ::setvbuf;
  using ::sprintf;
  using ::sscanf;
  using ::tmpfile;
  using ::tmpnam;
  using ::ungetc;
  using ::vfprintf;
  using ::vprintf;
  using ::vsprintf;

}
namespace __gnu_cxx __attribute__ ((__visibility__ ("default"))) {
  using ::snprintf;
  using ::vfscanf;
  using ::vscanf;
  using ::vsnprintf;
  using ::vsscanf;


}

namespace std __attribute__ ((__visibility__ ("default"))) {

  using ::__gnu_cxx::snprintf;
  using ::__gnu_cxx::vfscanf;
  using ::__gnu_cxx::vscanf;
  using ::__gnu_cxx::vsnprintf;
  using ::__gnu_cxx::vsscanf;

}
namespace NStl {
using __std_alias::FILE;
using __std_alias::fpos_t;
using __std_alias::size_t;
using __std_alias::clearerr;
using __std_alias::fclose;
using __std_alias::feof;
using __std_alias::ferror;
using __std_alias::fflush;
using __std_alias::fgetc;
using __std_alias::fgetpos;
using __std_alias::fgets;
using __std_alias::fopen;
using __std_alias::fprintf;
using __std_alias::fputc;
using __std_alias::fputs;
using __std_alias::fread;

using __std_alias::freopen;

using __std_alias::fscanf;
using __std_alias::fseek;
using __std_alias::fsetpos;
using __std_alias::ftell;
using __std_alias::fwrite;



 using __std_alias::getc;
 using __std_alias::putc;

 using __std_alias::getchar;
 using __std_alias::putchar;


using __std_alias::gets;

using __std_alias::perror;

using __std_alias::printf;
using __std_alias::puts;

using __std_alias::remove;
using __std_alias::rename;
using __std_alias::rewind;
using __std_alias::setbuf;
using __std_alias::tmpfile;
using __std_alias::tmpnam;

using __std_alias::scanf;
using __std_alias::setvbuf;
using __std_alias::sprintf;
using __std_alias::sscanf;
using __std_alias::ungetc;
using __std_alias::vfprintf;
using __std_alias::vprintf;
using __std_alias::vsprintf;





}











namespace NStl {
using __std_alias::ptrdiff_t;
using __std_alias::size_t;
}



















extern "C" {






union wait
  {
    int w_status;
    struct
      {

 unsigned int __w_termsig:7;
 unsigned int __w_coredump:1;
 unsigned int __w_retcode:8;
 unsigned int:16;







      } __wait_terminated;
    struct
      {

 unsigned int __w_stopval:8;
 unsigned int __w_stopsig:8;
 unsigned int:16;






      } __wait_stopped;
  };


typedef struct
  {
    int quot;
    int rem;
  } div_t;



typedef struct
  {
    long int quot;
    long int rem;
  } ldiv_t;







__extension__ typedef struct
  {
    long long int quot;
    long long int rem;
  } lldiv_t;


extern size_t __ctype_get_mb_cur_max (void) throw () ;




extern double atof (__const char *__nptr)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern int atoi (__const char *__nptr)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

extern long int atol (__const char *__nptr)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;





__extension__ extern long long int atoll (__const char *__nptr)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;





extern double strtod (__const char *__restrict __nptr,
        char **__restrict __endptr)
     throw () __attribute__ ((__nonnull__ (1))) ;





extern float strtof (__const char *__restrict __nptr,
       char **__restrict __endptr) throw () __attribute__ ((__nonnull__ (1))) ;

extern long double strtold (__const char *__restrict __nptr,
       char **__restrict __endptr)
     throw () __attribute__ ((__nonnull__ (1))) ;





extern long int strtol (__const char *__restrict __nptr,
   char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;

extern unsigned long int strtoul (__const char *__restrict __nptr,
      char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;




__extension__
extern long long int strtoq (__const char *__restrict __nptr,
        char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;

__extension__
extern unsigned long long int strtouq (__const char *__restrict __nptr,
           char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;





__extension__
extern long long int strtoll (__const char *__restrict __nptr,
         char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;

__extension__
extern unsigned long long int strtoull (__const char *__restrict __nptr,
     char **__restrict __endptr, int __base)
     throw () __attribute__ ((__nonnull__ (1))) ;

extern long int strtol_l (__const char *__restrict __nptr,
     char **__restrict __endptr, int __base,
     __locale_t __loc) throw () __attribute__ ((__nonnull__ (1, 4))) ;

extern unsigned long int strtoul_l (__const char *__restrict __nptr,
        char **__restrict __endptr,
        int __base, __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 4))) ;

__extension__
extern long long int strtoll_l (__const char *__restrict __nptr,
    char **__restrict __endptr, int __base,
    __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 4))) ;

__extension__
extern unsigned long long int strtoull_l (__const char *__restrict __nptr,
       char **__restrict __endptr,
       int __base, __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 4))) ;

extern double strtod_l (__const char *__restrict __nptr,
   char **__restrict __endptr, __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 3))) ;

extern float strtof_l (__const char *__restrict __nptr,
         char **__restrict __endptr, __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 3))) ;

extern long double strtold_l (__const char *__restrict __nptr,
         char **__restrict __endptr,
         __locale_t __loc)
     throw () __attribute__ ((__nonnull__ (1, 3))) ;
extern char *l64a (long int __n) throw () ;


extern long int a64l (__const char *__s)
     throw () __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
extern long int random (void) throw ();


extern void srandom (unsigned int __seed) throw ();





extern char *initstate (unsigned int __seed, char *__statebuf,
   size_t __statelen) throw () __attribute__ ((__nonnull__ (2)));



extern char *setstate (char *__statebuf) throw () __attribute__ ((__nonnull__ (1)));







struct random_data
  {
    int32_t *fptr;
    int32_t *rptr;
    int32_t *state;
    int rand_type;
    int rand_deg;
    int rand_sep;
    int32_t *end_ptr;
  };

extern int random_r (struct random_data *__restrict __buf,
       int32_t *__restrict __result) throw () __attribute__ ((__nonnull__ (1, 2)));

extern int srandom_r (unsigned int __seed, struct random_data *__buf)
     throw () __attribute__ ((__nonnull__ (2)));

extern int initstate_r (unsigned int __seed, char *__restrict __statebuf,
   size_t __statelen,
   struct random_data *__restrict __buf)
     throw () __attribute__ ((__nonnull__ (2, 4)));

extern int setstate_r (char *__restrict __statebuf,
         struct random_data *__restrict __buf)
     throw () __attribute__ ((__nonnull__ (1, 2)));






extern int rand (void) throw ();

extern void srand (unsigned int __seed) throw ();




extern int rand_r (unsigned int *__seed) throw ();







extern double drand48 (void) throw ();
extern double erand48 (unsigned short int __xsubi[3]) throw () __attribute__ ((__nonnull__ (1)));


extern long int lrand48 (void) throw ();
extern long int nrand48 (unsigned short int __xsubi[3])
     throw () __attribute__ ((__nonnull__ (1)));


extern long int mrand48 (void) throw ();
extern long int jrand48 (unsigned short int __xsubi[3])
     throw () __attribute__ ((__nonnull__ (1)));


extern void srand48 (long int __seedval) throw ();
extern unsigned short int *seed48 (unsigned short int __seed16v[3])
     throw () __attribute__ ((__nonnull__ (1)));
extern void lcong48 (unsigned short int __param[7]) throw () __attribute__ ((__nonnull__ (1)));





struct drand48_data
  {
    unsigned short int __x[3];
    unsigned short int __old_x[3];
    unsigned short int __c;
    unsigned short int __init;
    unsigned long long int __a;
  };


extern int drand48_r (struct drand48_data *__restrict __buffer,
        double *__restrict __result) throw () __attribute__ ((__nonnull__ (1, 2)));
extern int erand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        double *__restrict __result) throw () __attribute__ ((__nonnull__ (1, 2)));


extern int lrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     throw () __attribute__ ((__nonnull__ (1, 2)));
extern int nrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     throw () __attribute__ ((__nonnull__ (1, 2)));


extern int mrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     throw () __attribute__ ((__nonnull__ (1, 2)));
extern int jrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     throw () __attribute__ ((__nonnull__ (1, 2)));


extern int srand48_r (long int __seedval, struct drand48_data *__buffer)
     throw () __attribute__ ((__nonnull__ (2)));

extern int seed48_r (unsigned short int __seed16v[3],
       struct drand48_data *__buffer) throw () __attribute__ ((__nonnull__ (1, 2)));

extern int lcong48_r (unsigned short int __param[7],
        struct drand48_data *__buffer)
     throw () __attribute__ ((__nonnull__ (1, 2)));









extern void *malloc (size_t __size) throw () __attribute__ ((__malloc__)) ;

extern void *calloc (size_t __nmemb, size_t __size)
     throw () __attribute__ ((__malloc__)) ;










extern void *realloc (void *__ptr, size_t __size)
     throw () __attribute__ ((__warn_unused_result__));

extern void free (void *__ptr) throw ();




extern void cfree (void *__ptr) throw ();




extern "C" {





extern void *alloca (size_t __size) throw ();





}





extern void *valloc (size_t __size) throw () __attribute__ ((__malloc__)) ;




extern int posix_memalign (void **__memptr, size_t __alignment, size_t __size)
     throw () __attribute__ ((__nonnull__ (1))) ;




extern void abort (void) throw () __attribute__ ((__noreturn__));



extern int atexit (void (*__func) (void)) throw () __attribute__ ((__nonnull__ (1)));






extern "C++" int at_quick_exit (void (*__func) (void))
     throw () __asm ("at_quick_exit") __attribute__ ((__nonnull__ (1)));









extern int on_exit (void (*__func) (int __status, void *__arg), void *__arg)
     throw () __attribute__ ((__nonnull__ (1)));






extern void exit (int __status) throw () __attribute__ ((__noreturn__));







extern void quick_exit (int __status) throw () __attribute__ ((__noreturn__));







extern void _Exit (int __status) throw () __attribute__ ((__noreturn__));






extern char *getenv (__const char *__name) throw () __attribute__ ((__nonnull__ (1))) ;




extern char *__secure_getenv (__const char *__name)
     throw () __attribute__ ((__nonnull__ (1))) ;





extern int putenv (char *__string) throw () __attribute__ ((__nonnull__ (1)));





extern int setenv (__const char *__name, __const char *__value, int __replace)
     throw () __attribute__ ((__nonnull__ (2)));


extern int unsetenv (__const char *__name) throw () __attribute__ ((__nonnull__ (1)));






extern int clearenv (void) throw ();
extern char *mktemp (char *__template) throw () __attribute__ ((__nonnull__ (1))) ;
extern int mkstemp (char *__template) __asm__ ("" "mkstemp64")
     __attribute__ ((__nonnull__ (1))) ;





extern int mkstemp64 (char *__template) __attribute__ ((__nonnull__ (1))) ;
extern int mkstemps (char *__template, int __suffixlen) __asm__ ("" "mkstemps64") __attribute__ ((__nonnull__ (1))) ;






extern int mkstemps64 (char *__template, int __suffixlen)
     __attribute__ ((__nonnull__ (1))) ;
extern char *mkdtemp (char *__template) throw () __attribute__ ((__nonnull__ (1))) ;
extern int mkostemp (char *__template, int __flags) __asm__ ("" "mkostemp64")
     __attribute__ ((__nonnull__ (1))) ;





extern int mkostemp64 (char *__template, int __flags) __attribute__ ((__nonnull__ (1))) ;
extern int mkostemps (char *__template, int __suffixlen, int __flags) __asm__ ("" "mkostemps64")

     __attribute__ ((__nonnull__ (1))) ;





extern int mkostemps64 (char *__template, int __suffixlen, int __flags)
     __attribute__ ((__nonnull__ (1))) ;









extern int system (__const char *__command) ;






extern char *canonicalize_file_name (__const char *__name)
     throw () __attribute__ ((__nonnull__ (1))) ;
extern char *realpath (__const char *__restrict __name,
         char *__restrict __resolved) throw () ;






typedef int (*__compar_fn_t) (__const void *, __const void *);


typedef __compar_fn_t comparison_fn_t;



typedef int (*__compar_d_fn_t) (__const void *, __const void *, void *);





extern void *bsearch (__const void *__key, __const void *__base,
        size_t __nmemb, size_t __size, __compar_fn_t __compar)
     __attribute__ ((__nonnull__ (1, 2, 5))) ;



extern void qsort (void *__base, size_t __nmemb, size_t __size,
     __compar_fn_t __compar) __attribute__ ((__nonnull__ (1, 4)));

extern void qsort_r (void *__base, size_t __nmemb, size_t __size,
       __compar_d_fn_t __compar, void *__arg)
  __attribute__ ((__nonnull__ (1, 4)));




extern int abs (int __x) throw () __attribute__ ((__const__)) ;
extern long int labs (long int __x) throw () __attribute__ ((__const__)) ;



__extension__ extern long long int llabs (long long int __x)
     throw () __attribute__ ((__const__)) ;







extern div_t div (int __numer, int __denom)
     throw () __attribute__ ((__const__)) ;
extern ldiv_t ldiv (long int __numer, long int __denom)
     throw () __attribute__ ((__const__)) ;




__extension__ extern lldiv_t lldiv (long long int __numer,
        long long int __denom)
     throw () __attribute__ ((__const__)) ;

extern char *ecvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) throw () __attribute__ ((__nonnull__ (3, 4))) ;




extern char *fcvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) throw () __attribute__ ((__nonnull__ (3, 4))) ;




extern char *gcvt (double __value, int __ndigit, char *__buf)
     throw () __attribute__ ((__nonnull__ (3))) ;




extern char *qecvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     throw () __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qfcvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     throw () __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qgcvt (long double __value, int __ndigit, char *__buf)
     throw () __attribute__ ((__nonnull__ (3))) ;




extern int ecvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) throw () __attribute__ ((__nonnull__ (3, 4, 5)));
extern int fcvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) throw () __attribute__ ((__nonnull__ (3, 4, 5)));

extern int qecvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     throw () __attribute__ ((__nonnull__ (3, 4, 5)));
extern int qfcvt_r (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign,
      char *__restrict __buf, size_t __len)
     throw () __attribute__ ((__nonnull__ (3, 4, 5)));







extern int mblen (__const char *__s, size_t __n) throw () ;


extern int mbtowc (wchar_t *__restrict __pwc,
     __const char *__restrict __s, size_t __n) throw () ;


extern int wctomb (char *__s, wchar_t __wchar) throw () ;



extern size_t mbstowcs (wchar_t *__restrict __pwcs,
   __const char *__restrict __s, size_t __n) throw ();

extern size_t wcstombs (char *__restrict __s,
   __const wchar_t *__restrict __pwcs, size_t __n)
     throw ();








extern int rpmatch (__const char *__response) throw () __attribute__ ((__nonnull__ (1))) ;
extern int getsubopt (char **__restrict __optionp,
        char *__const *__restrict __tokens,
        char **__restrict __valuep)
     throw () __attribute__ ((__nonnull__ (1, 2, 3))) ;





extern void setkey (__const char *__key) throw () __attribute__ ((__nonnull__ (1)));







extern int posix_openpt (int __oflag) ;







extern int grantpt (int __fd) throw ();



extern int unlockpt (int __fd) throw ();




extern char *ptsname (int __fd) throw () ;






extern int ptsname_r (int __fd, char *__buf, size_t __buflen)
     throw () __attribute__ ((__nonnull__ (2)));


extern int getpt (void);






extern int getloadavg (double __loadavg[], int __nelem)
     throw () __attribute__ ((__nonnull__ (1)));
}
namespace std __attribute__ ((__visibility__ ("default"))) {

  using ::div_t;
  using ::ldiv_t;

  using ::abort;
  using ::abs;
  using ::atexit;
  using ::atof;
  using ::atoi;
  using ::atol;
  using ::bsearch;
  using ::calloc;
  using ::div;
  using ::exit;
  using ::free;
  using ::getenv;
  using ::labs;
  using ::ldiv;
  using ::malloc;

  using ::mblen;
  using ::mbstowcs;
  using ::mbtowc;

  using ::qsort;
  using ::rand;
  using ::realloc;
  using ::srand;
  using ::strtod;
  using ::strtol;
  using ::strtoul;
  using ::system;

  using ::wcstombs;
  using ::wctomb;


  inline long
  abs(long __i) { return labs(__i); }

  inline ldiv_t
  div(long __i, long __j) { return ldiv(__i, __j); }

}
namespace __gnu_cxx __attribute__ ((__visibility__ ("default"))) {


  using ::lldiv_t;





  using ::_Exit;


  inline long long
  abs(long long __x) { return __x >= 0 ? __x : -__x; }


  using ::llabs;

  inline lldiv_t
  div(long long __n, long long __d)
  { lldiv_t __q; __q.quot = __n / __d; __q.rem = __n % __d; return __q; }

  using ::lldiv;
  using ::atoll;
  using ::strtoll;
  using ::strtoull;

  using ::strtof;
  using ::strtold;

}

namespace std __attribute__ ((__visibility__ ("default"))) {


  using ::__gnu_cxx::lldiv_t;

  using ::__gnu_cxx::_Exit;
  using ::__gnu_cxx::abs;

  using ::__gnu_cxx::llabs;
  using ::__gnu_cxx::div;
  using ::__gnu_cxx::lldiv;

  using ::__gnu_cxx::atoll;
  using ::__gnu_cxx::strtof;
  using ::__gnu_cxx::strtoll;
  using ::__gnu_cxx::strtoull;
  using ::__gnu_cxx::strtold;

}
namespace NStl {
using __std_alias::div_t;
using __std_alias::ldiv_t;
using __std_alias::size_t;




using __std_alias::abort;
using __std_alias::getenv;
using __std_alias::mblen;
using __std_alias::mbtowc;
using __std_alias::system;
using __std_alias::bsearch;

using __std_alias::atexit;
using __std_alias::exit;
using __std_alias::calloc;
using __std_alias::free;
using __std_alias::malloc;
using __std_alias::realloc;
using __std_alias::atof;
using __std_alias::atoi;
using __std_alias::atol;
using __std_alias::mbstowcs;
using __std_alias::strtod;
using __std_alias::strtol;
using __std_alias::strtoul;


using __std_alias::wcstombs;

using __std_alias::wctomb;


using __std_alias::qsort;
using __std_alias::labs;
using __std_alias::ldiv;


using __std_alias::llabs;
using __std_alias::lldiv_t;
using __std_alias::lldiv;






using __std_alias::rand;
using __std_alias::srand;

}
inline long abs(long __x) { return __std_alias::labs(__x); }




inline __std_alias::ldiv_t div(long __x, long __y) { return __std_alias::ldiv(__x, __y); }
inline long long abs(long long __x) { return __std_alias::llabs(__x); }
inline lldiv_t div(long long __x, long long __y) { return __std_alias::lldiv(__x, __y); }
















namespace __gnu_cxx __attribute__ ((__visibility__ ("default"))) {

  template<typename _Iterator, typename _Container>
    class __normal_iterator;

}

namespace std __attribute__ ((__visibility__ ("default"))) {

  struct __true_type { };
  struct __false_type { };

  template<bool>
    struct __truth_type
    { typedef __false_type __type; };

  template<>
    struct __truth_type<true>
    { typedef __true_type __type; };



  template<class _Sp, class _Tp>
    struct __traitor
    {
      enum { __value = bool(_Sp::__value) || bool(_Tp::__value) };
      typedef typename __truth_type<__value>::__type __type;
    };


  template<typename, typename>
    struct __are_same
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<typename _Tp>
    struct __are_same<_Tp, _Tp>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<typename _Tp>
    struct __is_void
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_void<void>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_integer
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };




  template<>
    struct __is_integer<bool>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<signed char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<>
    struct __is_integer<wchar_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };
  template<>
    struct __is_integer<short>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned short>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<int>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned int>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<long long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_integer<unsigned long long>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_floating
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };


  template<>
    struct __is_floating<float>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_floating<double>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_floating<long double>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_pointer
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<typename _Tp>
    struct __is_pointer<_Tp*>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_normal_iterator
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<typename _Iterator, typename _Container>
    struct __is_normal_iterator< __gnu_cxx::__normal_iterator<_Iterator,
             _Container> >
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_arithmetic
    : public __traitor<__is_integer<_Tp>, __is_floating<_Tp> >
    { };




  template<typename _Tp>
    struct __is_fundamental
    : public __traitor<__is_void<_Tp>, __is_arithmetic<_Tp> >
    { };




  template<typename _Tp>
    struct __is_scalar
    : public __traitor<__is_arithmetic<_Tp>, __is_pointer<_Tp> >
    { };




  template<typename _Tp>
    struct __is_char
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_char<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<>
    struct __is_char<wchar_t>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };


  template<typename _Tp>
    struct __is_byte
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };

  template<>
    struct __is_byte<char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_byte<signed char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };

  template<>
    struct __is_byte<unsigned char>
    {
      enum { __value = 1 };
      typedef __true_type __type;
    };




  template<typename _Tp>
    struct __is_move_iterator
    {
      enum { __value = 0 };
      typedef __false_type __type;
    };
}





namespace __gnu_cxx __attribute__ ((__visibility__ ("default"))) {


  template<bool, typename>
    struct __enable_if
    { };

  template<typename _Tp>
    struct __enable_if<true, _Tp>
    { typedef _Tp __type; };



  template<bool _Cond, typename _Iftrue, typename _Iffalse>
    struct __conditional_type
    { typedef _Iftrue __type; };

  template<typename _Iftrue, typename _Iffalse>
    struct __conditional_type<false, _Iftrue, _Iffalse>
    { typedef _Iffalse __type; };



  template<typename _Tp>
    struct __add_unsigned
    {
    private:
      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;

    public:
      typedef typename __if_type::__type __type;
    };

  template<>
    struct __add_unsigned<char>
    { typedef unsigned char __type; };

  template<>
    struct __add_unsigned<signed char>
    { typedef unsigned char __type; };

  template<>
    struct __add_unsigned<short>
    { typedef unsigned short __type; };

  template<>
    struct __add_unsigned<int>
    { typedef unsigned int __type; };

  template<>
    struct __add_unsigned<long>
    { typedef unsigned long __type; };

  template<>
    struct __add_unsigned<long long>
    { typedef unsigned long long __type; };


  template<>
    struct __add_unsigned<bool>;

  template<>
    struct __add_unsigned<wchar_t>;



  template<typename _Tp>
    struct __remove_unsigned
    {
    private:
      typedef __enable_if<std::__is_integer<_Tp>::__value, _Tp> __if_type;

    public:
      typedef typename __if_type::__type __type;
    };

  template<>
    struct __remove_unsigned<char>
    { typedef signed char __type; };

  template<>
    struct __remove_unsigned<unsigned char>
    { typedef signed char __type; };

  template<>
    struct __remove_unsigned<unsigned short>
    { typedef short __type; };

  template<>
    struct __remove_unsigned<unsigned int>
    { typedef int __type; };

  template<>
    struct __remove_unsigned<unsigned long>
    { typedef long __type; };

  template<>
    struct __remove_unsigned<unsigned long long>
    { typedef long long __type; };


  template<>
    struct __remove_unsigned<bool>;

  template<>
    struct __remove_unsigned<wchar_t>;



  template<typename _Type>
    inline bool
    __is_null_pointer(_Type* __ptr)
    { return __ptr == 0; }

  template<typename _Type>
    inline bool
    __is_null_pointer(_Type)
    { return false; }



  template<typename _Tp, bool = std::__is_integer<_Tp>::__value>
    struct __promote
    { typedef double __type; };

  template<typename _Tp>
    struct __promote<_Tp, false>
    { typedef _Tp __type; };

  template<typename _Tp, typename _Up>
    struct __promote_2
    {
    private:
      typedef typename __promote<_Tp>::__type __type1;
      typedef typename __promote<_Up>::__type __type2;

    public:
      typedef __typeof__(__type1() + __type2()) __type;
    };

  template<typename _Tp, typename _Up, typename _Vp>
    struct __promote_3
    {
    private:
      typedef typename __promote<_Tp>::__type __type1;
      typedef typename __promote<_Up>::__type __type2;
      typedef typename __promote<_Vp>::__type __type3;

    public:
      typedef __typeof__(__type1() + __type2() + __type3()) __type;
    };

  template<typename _Tp, typename _Up, typename _Vp, typename _Wp>
    struct __promote_4
    {
    private:
      typedef typename __promote<_Tp>::__type __type1;
      typedef typename __promote<_Up>::__type __type2;
      typedef typename __promote<_Vp>::__type __type3;
      typedef typename __promote<_Wp>::__type __type4;

    public:
      typedef __typeof__(__type1() + __type2() + __type3() + __type4()) __type;
    };

}
extern "C" {















typedef float float_t;
typedef double double_t;


extern double acos (double __x) throw (); extern double __acos (double __x) throw ();

extern double asin (double __x) throw (); extern double __asin (double __x) throw ();

extern double atan (double __x) throw (); extern double __atan (double __x) throw ();

extern double atan2 (double __y, double __x) throw (); extern double __atan2 (double __y, double __x) throw ();


extern double cos (double __x) throw (); extern double __cos (double __x) throw ();

extern double sin (double __x) throw (); extern double __sin (double __x) throw ();

extern double tan (double __x) throw (); extern double __tan (double __x) throw ();




extern double cosh (double __x) throw (); extern double __cosh (double __x) throw ();

extern double sinh (double __x) throw (); extern double __sinh (double __x) throw ();

extern double tanh (double __x) throw (); extern double __tanh (double __x) throw ();




extern void sincos (double __x, double *__sinx, double *__cosx) throw (); extern void __sincos (double __x, double *__sinx, double *__cosx) throw ();






extern double acosh (double __x) throw (); extern double __acosh (double __x) throw ();

extern double asinh (double __x) throw (); extern double __asinh (double __x) throw ();

extern double atanh (double __x) throw (); extern double __atanh (double __x) throw ();







extern double exp (double __x) throw (); extern double __exp (double __x) throw ();


extern double frexp (double __x, int *__exponent) throw (); extern double __frexp (double __x, int *__exponent) throw ();


extern double ldexp (double __x, int __exponent) throw (); extern double __ldexp (double __x, int __exponent) throw ();


extern double log (double __x) throw (); extern double __log (double __x) throw ();


extern double log10 (double __x) throw (); extern double __log10 (double __x) throw ();


extern double modf (double __x, double *__iptr) throw (); extern double __modf (double __x, double *__iptr) throw ();




extern double exp10 (double __x) throw (); extern double __exp10 (double __x) throw ();

extern double pow10 (double __x) throw (); extern double __pow10 (double __x) throw ();





extern double expm1 (double __x) throw (); extern double __expm1 (double __x) throw ();


extern double log1p (double __x) throw (); extern double __log1p (double __x) throw ();


extern double logb (double __x) throw (); extern double __logb (double __x) throw ();






extern double exp2 (double __x) throw (); extern double __exp2 (double __x) throw ();


extern double log2 (double __x) throw (); extern double __log2 (double __x) throw ();








extern double pow (double __x, double __y) throw (); extern double __pow (double __x, double __y) throw ();


extern double sqrt (double __x) throw (); extern double __sqrt (double __x) throw ();





extern double hypot (double __x, double __y) throw (); extern double __hypot (double __x, double __y) throw ();






extern double cbrt (double __x) throw (); extern double __cbrt (double __x) throw ();








extern double ceil (double __x) throw () __attribute__ ((__const__)); extern double __ceil (double __x) throw () __attribute__ ((__const__));


extern double fabs (double __x) throw () __attribute__ ((__const__)); extern double __fabs (double __x) throw () __attribute__ ((__const__));


extern double floor (double __x) throw () __attribute__ ((__const__)); extern double __floor (double __x) throw () __attribute__ ((__const__));


extern double fmod (double __x, double __y) throw (); extern double __fmod (double __x, double __y) throw ();




extern int __isinf (double __value) throw () __attribute__ ((__const__));


extern int __finite (double __value) throw () __attribute__ ((__const__));





extern int isinf (double __value) throw () __attribute__ ((__const__));


extern int finite (double __value) throw () __attribute__ ((__const__));


extern double drem (double __x, double __y) throw (); extern double __drem (double __x, double __y) throw ();



extern double significand (double __x) throw (); extern double __significand (double __x) throw ();





extern double copysign (double __x, double __y) throw () __attribute__ ((__const__)); extern double __copysign (double __x, double __y) throw () __attribute__ ((__const__));






extern double nan (__const char *__tagb) throw () __attribute__ ((__const__)); extern double __nan (__const char *__tagb) throw () __attribute__ ((__const__));





extern int __isnan (double __value) throw () __attribute__ ((__const__));



extern int isnan (double __value) throw () __attribute__ ((__const__));


extern double j0 (double) throw (); extern double __j0 (double) throw ();
extern double j1 (double) throw (); extern double __j1 (double) throw ();
extern double jn (int, double) throw (); extern double __jn (int, double) throw ();
extern double y0 (double) throw (); extern double __y0 (double) throw ();
extern double y1 (double) throw (); extern double __y1 (double) throw ();
extern double yn (int, double) throw (); extern double __yn (int, double) throw ();






extern double erf (double) throw (); extern double __erf (double) throw ();
extern double erfc (double) throw (); extern double __erfc (double) throw ();
extern double lgamma (double) throw (); extern double __lgamma (double) throw ();






extern double tgamma (double) throw (); extern double __tgamma (double) throw ();





extern double gamma (double) throw (); extern double __gamma (double) throw ();






extern double lgamma_r (double, int *__signgamp) throw (); extern double __lgamma_r (double, int *__signgamp) throw ();







extern double rint (double __x) throw (); extern double __rint (double __x) throw ();


extern double nextafter (double __x, double __y) throw () __attribute__ ((__const__)); extern double __nextafter (double __x, double __y) throw () __attribute__ ((__const__));

extern double nexttoward (double __x, long double __y) throw () __attribute__ ((__const__)); extern double __nexttoward (double __x, long double __y) throw () __attribute__ ((__const__));



extern double remainder (double __x, double __y) throw (); extern double __remainder (double __x, double __y) throw ();



extern double scalbn (double __x, int __n) throw (); extern double __scalbn (double __x, int __n) throw ();



extern int ilogb (double __x) throw (); extern int __ilogb (double __x) throw ();




extern double scalbln (double __x, long int __n) throw (); extern double __scalbln (double __x, long int __n) throw ();



extern double nearbyint (double __x) throw (); extern double __nearbyint (double __x) throw ();



extern double round (double __x) throw () __attribute__ ((__const__)); extern double __round (double __x) throw () __attribute__ ((__const__));



extern double trunc (double __x) throw () __attribute__ ((__const__)); extern double __trunc (double __x) throw () __attribute__ ((__const__));




extern double remquo (double __x, double __y, int *__quo) throw (); extern double __remquo (double __x, double __y, int *__quo) throw ();






extern long int lrint (double __x) throw (); extern long int __lrint (double __x) throw ();
extern long long int llrint (double __x) throw (); extern long long int __llrint (double __x) throw ();



extern long int lround (double __x) throw (); extern long int __lround (double __x) throw ();
extern long long int llround (double __x) throw (); extern long long int __llround (double __x) throw ();



extern double fdim (double __x, double __y) throw (); extern double __fdim (double __x, double __y) throw ();


extern double fmax (double __x, double __y) throw (); extern double __fmax (double __x, double __y) throw ();


extern double fmin (double __x, double __y) throw (); extern double __fmin (double __x, double __y) throw ();



extern int __fpclassify (double __value) throw ()
     __attribute__ ((__const__));


extern int __signbit (double __value) throw ()
     __attribute__ ((__const__));



extern double fma (double __x, double __y, double __z) throw (); extern double __fma (double __x, double __y, double __z) throw ();








extern double scalb (double __x, double __n) throw (); extern double __scalb (double __x, double __n) throw ();


extern float acosf (float __x) throw (); extern float __acosf (float __x) throw ();

extern float asinf (float __x) throw (); extern float __asinf (float __x) throw ();

extern float atanf (float __x) throw (); extern float __atanf (float __x) throw ();

extern float atan2f (float __y, float __x) throw (); extern float __atan2f (float __y, float __x) throw ();


extern float cosf (float __x) throw (); extern float __cosf (float __x) throw ();

extern float sinf (float __x) throw (); extern float __sinf (float __x) throw ();

extern float tanf (float __x) throw (); extern float __tanf (float __x) throw ();




extern float coshf (float __x) throw (); extern float __coshf (float __x) throw ();

extern float sinhf (float __x) throw (); extern float __sinhf (float __x) throw ();

extern float tanhf (float __x) throw (); extern float __tanhf (float __x) throw ();




extern void sincosf (float __x, float *__sinx, float *__cosx) throw (); extern void __sincosf (float __x, float *__sinx, float *__cosx) throw ();






extern float acoshf (float __x) throw (); extern float __acoshf (float __x) throw ();

extern float asinhf (float __x) throw (); extern float __asinhf (float __x) throw ();

extern float atanhf (float __x) throw (); extern float __atanhf (float __x) throw ();







extern float expf (float __x) throw (); extern float __expf (float __x) throw ();


extern float frexpf (float __x, int *__exponent) throw (); extern float __frexpf (float __x, int *__exponent) throw ();


extern float ldexpf (float __x, int __exponent) throw (); extern float __ldexpf (float __x, int __exponent) throw ();


extern float logf (float __x) throw (); extern float __logf (float __x) throw ();


extern float log10f (float __x) throw (); extern float __log10f (float __x) throw ();


extern float modff (float __x, float *__iptr) throw (); extern float __modff (float __x, float *__iptr) throw ();




extern float exp10f (float __x) throw (); extern float __exp10f (float __x) throw ();

extern float pow10f (float __x) throw (); extern float __pow10f (float __x) throw ();





extern float expm1f (float __x) throw (); extern float __expm1f (float __x) throw ();


extern float log1pf (float __x) throw (); extern float __log1pf (float __x) throw ();


extern float logbf (float __x) throw (); extern float __logbf (float __x) throw ();






extern float exp2f (float __x) throw (); extern float __exp2f (float __x) throw ();


extern float log2f (float __x) throw (); extern float __log2f (float __x) throw ();








extern float powf (float __x, float __y) throw (); extern float __powf (float __x, float __y) throw ();


extern float sqrtf (float __x) throw (); extern float __sqrtf (float __x) throw ();





extern float hypotf (float __x, float __y) throw (); extern float __hypotf (float __x, float __y) throw ();






extern float cbrtf (float __x) throw (); extern float __cbrtf (float __x) throw ();








extern float ceilf (float __x) throw () __attribute__ ((__const__)); extern float __ceilf (float __x) throw () __attribute__ ((__const__));


extern float fabsf (float __x) throw () __attribute__ ((__const__)); extern float __fabsf (float __x) throw () __attribute__ ((__const__));


extern float floorf (float __x) throw () __attribute__ ((__const__)); extern float __floorf (float __x) throw () __attribute__ ((__const__));


extern float fmodf (float __x, float __y) throw (); extern float __fmodf (float __x, float __y) throw ();




extern int __isinff (float __value) throw () __attribute__ ((__const__));


extern int __finitef (float __value) throw () __attribute__ ((__const__));





extern int isinff (float __value) throw () __attribute__ ((__const__));


extern int finitef (float __value) throw () __attribute__ ((__const__));


extern float dremf (float __x, float __y) throw (); extern float __dremf (float __x, float __y) throw ();



extern float significandf (float __x) throw (); extern float __significandf (float __x) throw ();





extern float copysignf (float __x, float __y) throw () __attribute__ ((__const__)); extern float __copysignf (float __x, float __y) throw () __attribute__ ((__const__));






extern float nanf (__const char *__tagb) throw () __attribute__ ((__const__)); extern float __nanf (__const char *__tagb) throw () __attribute__ ((__const__));





extern int __isnanf (float __value) throw () __attribute__ ((__const__));



extern int isnanf (float __value) throw () __attribute__ ((__const__));


extern float j0f (float) throw (); extern float __j0f (float) throw ();
extern float j1f (float) throw (); extern float __j1f (float) throw ();
extern float jnf (int, float) throw (); extern float __jnf (int, float) throw ();
extern float y0f (float) throw (); extern float __y0f (float) throw ();
extern float y1f (float) throw (); extern float __y1f (float) throw ();
extern float ynf (int, float) throw (); extern float __ynf (int, float) throw ();






extern float erff (float) throw (); extern float __erff (float) throw ();
extern float erfcf (float) throw (); extern float __erfcf (float) throw ();
extern float lgammaf (float) throw (); extern float __lgammaf (float) throw ();






extern float tgammaf (float) throw (); extern float __tgammaf (float) throw ();





extern float gammaf (float) throw (); extern float __gammaf (float) throw ();






extern float lgammaf_r (float, int *__signgamp) throw (); extern float __lgammaf_r (float, int *__signgamp) throw ();







extern float rintf (float __x) throw (); extern float __rintf (float __x) throw ();


extern float nextafterf (float __x, float __y) throw () __attribute__ ((__const__)); extern float __nextafterf (float __x, float __y) throw () __attribute__ ((__const__));

extern float nexttowardf (float __x, long double __y) throw () __attribute__ ((__const__)); extern float __nexttowardf (float __x, long double __y) throw () __attribute__ ((__const__));



extern float remainderf (float __x, float __y) throw (); extern float __remainderf (float __x, float __y) throw ();



extern float scalbnf (float __x, int __n) throw (); extern float __scalbnf (float __x, int __n) throw ();



extern int ilogbf (float __x) throw (); extern int __ilogbf (float __x) throw ();




extern float scalblnf (float __x, long int __n) throw (); extern float __scalblnf (float __x, long int __n) throw ();



extern float nearbyintf (float __x) throw (); extern float __nearbyintf (float __x) throw ();



extern float roundf (float __x) throw () __attribute__ ((__const__)); extern float __roundf (float __x) throw () __attribute__ ((__const__));



extern float truncf (float __x) throw () __attribute__ ((__const__)); extern float __truncf (float __x) throw () __attribute__ ((__const__));




extern float remquof (float __x, float __y, int *__quo) throw (); extern float __remquof (float __x, float __y, int *__quo) throw ();






extern long int lrintf (float __x) throw (); extern long int __lrintf (float __x) throw ();
extern long long int llrintf (float __x) throw (); extern long long int __llrintf (float __x) throw ();



extern long int lroundf (float __x) throw (); extern long int __lroundf (float __x) throw ();
extern long long int llroundf (float __x) throw (); extern long long int __llroundf (float __x) throw ();



extern float fdimf (float __x, float __y) throw (); extern float __fdimf (float __x, float __y) throw ();


extern float fmaxf (float __x, float __y) throw (); extern float __fmaxf (float __x, float __y) throw ();


extern float fminf (float __x, float __y) throw (); extern float __fminf (float __x, float __y) throw ();



extern int __fpclassifyf (float __value) throw ()
     __attribute__ ((__const__));


extern int __signbitf (float __value) throw ()
     __attribute__ ((__const__));



extern float fmaf (float __x, float __y, float __z) throw (); extern float __fmaf (float __x, float __y, float __z) throw ();








extern float scalbf (float __x, float __n) throw (); extern float __scalbf (float __x, float __n) throw ();


extern long double acosl (long double __x) throw (); extern long double __acosl (long double __x) throw ();

extern long double asinl (long double __x) throw (); extern long double __asinl (long double __x) throw ();

extern long double atanl (long double __x) throw (); extern long double __atanl (long double __x) throw ();

extern long double atan2l (long double __y, long double __x) throw (); extern long double __atan2l (long double __y, long double __x) throw ();


extern long double cosl (long double __x) throw (); extern long double __cosl (long double __x) throw ();

extern long double sinl (long double __x) throw (); extern long double __sinl (long double __x) throw ();

extern long double tanl (long double __x) throw (); extern long double __tanl (long double __x) throw ();




extern long double coshl (long double __x) throw (); extern long double __coshl (long double __x) throw ();

extern long double sinhl (long double __x) throw (); extern long double __sinhl (long double __x) throw ();

extern long double tanhl (long double __x) throw (); extern long double __tanhl (long double __x) throw ();




extern void sincosl (long double __x, long double *__sinx, long double *__cosx) throw (); extern void __sincosl (long double __x, long double *__sinx, long double *__cosx) throw ();






extern long double acoshl (long double __x) throw (); extern long double __acoshl (long double __x) throw ();

extern long double asinhl (long double __x) throw (); extern long double __asinhl (long double __x) throw ();

extern long double atanhl (long double __x) throw (); extern long double __atanhl (long double __x) throw ();







extern long double expl (long double __x) throw (); extern long double __expl (long double __x) throw ();


extern long double frexpl (long double __x, int *__exponent) throw (); extern long double __frexpl (long double __x, int *__exponent) throw ();


extern long double ldexpl (long double __x, int __exponent) throw (); extern long double __ldexpl (long double __x, int __exponent) throw ();


extern long double logl (long double __x) throw (); extern long double __logl (long double __x) throw ();


extern long double log10l (long double __x) throw (); extern long double __log10l (long double __x) throw ();


extern long double modfl (long double __x, long double *__iptr) throw (); extern long double __modfl (long double __x, long double *__iptr) throw ();




extern long double exp10l (long double __x) throw (); extern long double __exp10l (long double __x) throw ();

extern long double pow10l (long double __x) throw (); extern long double __pow10l (long double __x) throw ();





extern long double expm1l (long double __x) throw (); extern long double __expm1l (long double __x) throw ();


extern long double log1pl (long double __x) throw (); extern long double __log1pl (long double __x) throw ();


extern long double logbl (long double __x) throw (); extern long double __logbl (long double __x) throw ();






extern long double exp2l (long double __x) throw (); extern long double __exp2l (long double __x) throw ();


extern long double log2l (long double __x) throw (); extern long double __log2l (long double __x) throw ();








extern long double powl (long double __x, long double __y) throw (); extern long double __powl (long double __x, long double __y) throw ();


extern long double sqrtl (long double __x) throw (); extern long double __sqrtl (long double __x) throw ();





extern long double hypotl (long double __x, long double __y) throw (); extern long double __hypotl (long double __x, long double __y) throw ();






extern long double cbrtl (long double __x) throw (); extern long double __cbrtl (long double __x) throw ();








extern long double ceill (long double __x) throw () __attribute__ ((__const__)); extern long double __ceill (long double __x) throw () __attribute__ ((__const__));


extern long double fabsl (long double __x) throw () __attribute__ ((__const__)); extern long double __fabsl (long double __x) throw () __attribute__ ((__const__));


extern long double floorl (long double __x) throw () __attribute__ ((__const__)); extern long double __floorl (long double __x) throw () __attribute__ ((__const__));


extern long double fmodl (long double __x, long double __y) throw (); extern long double __fmodl (long double __x, long double __y) throw ();




extern int __isinfl (long double __value) throw () __attribute__ ((__const__));


extern int __finitel (long double __value) throw () __attribute__ ((__const__));





extern int isinfl (long double __value) throw () __attribute__ ((__const__));


extern int finitel (long double __value) throw () __attribute__ ((__const__));


extern long double dreml (long double __x, long double __y) throw (); extern long double __dreml (long double __x, long double __y) throw ();



extern long double significandl (long double __x) throw (); extern long double __significandl (long double __x) throw ();





extern long double copysignl (long double __x, long double __y) throw () __attribute__ ((__const__)); extern long double __copysignl (long double __x, long double __y) throw () __attribute__ ((__const__));






extern long double nanl (__const char *__tagb) throw () __attribute__ ((__const__)); extern long double __nanl (__const char *__tagb) throw () __attribute__ ((__const__));





extern int __isnanl (long double __value) throw () __attribute__ ((__const__));



extern int isnanl (long double __value) throw () __attribute__ ((__const__));


extern long double j0l (long double) throw (); extern long double __j0l (long double) throw ();
extern long double j1l (long double) throw (); extern long double __j1l (long double) throw ();
extern long double jnl (int, long double) throw (); extern long double __jnl (int, long double) throw ();
extern long double y0l (long double) throw (); extern long double __y0l (long double) throw ();
extern long double y1l (long double) throw (); extern long double __y1l (long double) throw ();
extern long double ynl (int, long double) throw (); extern long double __ynl (int, long double) throw ();






extern long double erfl (long double) throw (); extern long double __erfl (long double) throw ();
extern long double erfcl (long double) throw (); extern long double __erfcl (long double) throw ();
extern long double lgammal (long double) throw (); extern long double __lgammal (long double) throw ();






extern long double tgammal (long double) throw (); extern long double __tgammal (long double) throw ();





extern long double gammal (long double) throw (); extern long double __gammal (long double) throw ();






extern long double lgammal_r (long double, int *__signgamp) throw (); extern long double __lgammal_r (long double, int *__signgamp) throw ();







extern long double rintl (long double __x) throw (); extern long double __rintl (long double __x) throw ();


extern long double nextafterl (long double __x, long double __y) throw () __attribute__ ((__const__)); extern long double __nextafterl (long double __x, long double __y) throw () __attribute__ ((__const__));

extern long double nexttowardl (long double __x, long double __y) throw () __attribute__ ((__const__)); extern long double __nexttowardl (long double __x, long double __y) throw () __attribute__ ((__const__));



extern long double remainderl (long double __x, long double __y) throw (); extern long double __remainderl (long double __x, long double __y) throw ();



extern long double scalbnl (long double __x, int __n) throw (); extern long double __scalbnl (long double __x, int __n) throw ();



extern int ilogbl (long double __x) throw (); extern int __ilogbl (long double __x) throw ();




extern long double scalblnl (long double __x, long int __n) throw (); extern long double __scalblnl (long double __x, long int __n) throw ();



extern long double nearbyintl (long double __x) throw (); extern long double __nearbyintl (long double __x) throw ();



extern long double roundl (long double __x) throw () __attribute__ ((__const__)); extern long double __roundl (long double __x) throw () __attribute__ ((__const__));



extern long double truncl (long double __x) throw () __attribute__ ((__const__)); extern long double __truncl (long double __x) throw () __attribute__ ((__const__));




extern long double remquol (long double __x, long double __y, int *__quo) throw (); extern long double __remquol (long double __x, long double __y, int *__quo) throw ();






extern long int lrintl (long double __x) throw (); extern long int __lrintl (long double __x) throw ();
extern long long int llrintl (long double __x) throw (); extern long long int __llrintl (long double __x) throw ();



extern long int lroundl (long double __x) throw (); extern long int __lroundl (long double __x) throw ();
extern long long int llroundl (long double __x) throw (); extern long long int __llroundl (long double __x) throw ();



extern long double fdiml (long double __x, long double __y) throw (); extern long double __fdiml (long double __x, long double __y) throw ();


extern long double fmaxl (long double __x, long double __y) throw (); extern long double __fmaxl (long double __x, long double __y) throw ();


extern long double fminl (long double __x, long double __y) throw (); extern long double __fminl (long double __x, long double __y) throw ();



extern int __fpclassifyl (long double __value) throw ()
     __attribute__ ((__const__));


extern int __signbitl (long double __value) throw ()
     __attribute__ ((__const__));



extern long double fmal (long double __x, long double __y, long double __z) throw (); extern long double __fmal (long double __x, long double __y, long double __z) throw ();








extern long double scalbl (long double __x, long double __n) throw (); extern long double __scalbl (long double __x, long double __n) throw ();
extern int signgam;
enum
  {
    FP_NAN,

    FP_INFINITE,

    FP_ZERO,

    FP_SUBNORMAL,

    FP_NORMAL

  };
typedef enum
{
  _IEEE_ = -1,
  _SVID_,
  _XOPEN_,
  _POSIX_,
  _ISOC_
} _LIB_VERSION_TYPE;




extern _LIB_VERSION_TYPE _LIB_VERSION;
struct __exception



  {
    int type;
    char *name;
    double arg1;
    double arg2;
    double retval;
  };


extern int matherr (struct __exception *__exc) throw ();
}
namespace std __attribute__ ((__visibility__ ("default"))) {



  template<typename _Tp>
    _Tp __cmath_power(_Tp, unsigned int);

  template<typename _Tp>
    inline _Tp
    __pow_helper(_Tp __x, int __n)
    {
      return __n < 0
        ? _Tp(1)/__cmath_power(__x, -__n)
        : __cmath_power(__x, __n);
    }

  inline double
  abs(double __x)
  { return __builtin_fabs(__x); }

  inline float
  abs(float __x)
  { return __builtin_fabsf(__x); }

  inline long double
  abs(long double __x)
  { return __builtin_fabsl(__x); }

  using ::acos;

  inline float
  acos(float __x)
  { return __builtin_acosf(__x); }

  inline long double
  acos(long double __x)
  { return __builtin_acosl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    acos(_Tp __x)
    { return __builtin_acos(__x); }

  using ::asin;

  inline float
  asin(float __x)
  { return __builtin_asinf(__x); }

  inline long double
  asin(long double __x)
  { return __builtin_asinl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    asin(_Tp __x)
    { return __builtin_asin(__x); }

  using ::atan;

  inline float
  atan(float __x)
  { return __builtin_atanf(__x); }

  inline long double
  atan(long double __x)
  { return __builtin_atanl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    atan(_Tp __x)
    { return __builtin_atan(__x); }

  using ::atan2;

  inline float
  atan2(float __y, float __x)
  { return __builtin_atan2f(__y, __x); }

  inline long double
  atan2(long double __y, long double __x)
  { return __builtin_atan2l(__y, __x); }

  template<typename _Tp, typename _Up>
    inline
    typename __gnu_cxx::__promote_2<
    typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value
        && __is_arithmetic<_Up>::__value,
        _Tp>::__type, _Up>::__type
    atan2(_Tp __y, _Up __x)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return atan2(__type(__y), __type(__x));
    }

  using ::ceil;

  inline float
  ceil(float __x)
  { return __builtin_ceilf(__x); }

  inline long double
  ceil(long double __x)
  { return __builtin_ceill(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    ceil(_Tp __x)
    { return __builtin_ceil(__x); }

  using ::cos;

  inline float
  cos(float __x)
  { return __builtin_cosf(__x); }

  inline long double
  cos(long double __x)
  { return __builtin_cosl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    cos(_Tp __x)
    { return __builtin_cos(__x); }

  using ::cosh;

  inline float
  cosh(float __x)
  { return __builtin_coshf(__x); }

  inline long double
  cosh(long double __x)
  { return __builtin_coshl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    cosh(_Tp __x)
    { return __builtin_cosh(__x); }

  using ::exp;

  inline float
  exp(float __x)
  { return __builtin_expf(__x); }

  inline long double
  exp(long double __x)
  { return __builtin_expl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    exp(_Tp __x)
    { return __builtin_exp(__x); }

  using ::fabs;

  inline float
  fabs(float __x)
  { return __builtin_fabsf(__x); }

  inline long double
  fabs(long double __x)
  { return __builtin_fabsl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    fabs(_Tp __x)
    { return __builtin_fabs(__x); }

  using ::floor;

  inline float
  floor(float __x)
  { return __builtin_floorf(__x); }

  inline long double
  floor(long double __x)
  { return __builtin_floorl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    floor(_Tp __x)
    { return __builtin_floor(__x); }

  using ::fmod;

  inline float
  fmod(float __x, float __y)
  { return __builtin_fmodf(__x, __y); }

  inline long double
  fmod(long double __x, long double __y)
  { return __builtin_fmodl(__x, __y); }

  using ::frexp;

  inline float
  frexp(float __x, int* __exp)
  { return __builtin_frexpf(__x, __exp); }

  inline long double
  frexp(long double __x, int* __exp)
  { return __builtin_frexpl(__x, __exp); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    frexp(_Tp __x, int* __exp)
    { return __builtin_frexp(__x, __exp); }

  using ::ldexp;

  inline float
  ldexp(float __x, int __exp)
  { return __builtin_ldexpf(__x, __exp); }

  inline long double
  ldexp(long double __x, int __exp)
  { return __builtin_ldexpl(__x, __exp); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
  ldexp(_Tp __x, int __exp)
  { return __builtin_ldexp(__x, __exp); }

  using ::log;

  inline float
  log(float __x)
  { return __builtin_logf(__x); }

  inline long double
  log(long double __x)
  { return __builtin_logl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    log(_Tp __x)
    { return __builtin_log(__x); }

  using ::log10;

  inline float
  log10(float __x)
  { return __builtin_log10f(__x); }

  inline long double
  log10(long double __x)
  { return __builtin_log10l(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    log10(_Tp __x)
    { return __builtin_log10(__x); }

  using ::modf;

  inline float
  modf(float __x, float* __iptr)
  { return __builtin_modff(__x, __iptr); }

  inline long double
  modf(long double __x, long double* __iptr)
  { return __builtin_modfl(__x, __iptr); }

  using ::pow;

  inline float
  pow(float __x, float __y)
  { return __builtin_powf(__x, __y); }

  inline long double
  pow(long double __x, long double __y)
  { return __builtin_powl(__x, __y); }




  inline double
  pow(double __x, int __i)
  { return __builtin_powi(__x, __i); }

  inline float
  pow(float __x, int __n)
  { return __builtin_powif(__x, __n); }

  inline long double
  pow(long double __x, int __n)
  { return __builtin_powil(__x, __n); }


  template<typename _Tp, typename _Up>
    inline
    typename __gnu_cxx::__promote_2<
    typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value
        && __is_arithmetic<_Up>::__value,
        _Tp>::__type, _Up>::__type
    pow(_Tp __x, _Up __y)
    {
      typedef typename __gnu_cxx::__promote_2<_Tp, _Up>::__type __type;
      return pow(__type(__x), __type(__y));
    }

  using ::sin;

  inline float
  sin(float __x)
  { return __builtin_sinf(__x); }

  inline long double
  sin(long double __x)
  { return __builtin_sinl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    sin(_Tp __x)
    { return __builtin_sin(__x); }

  using ::sinh;

  inline float
  sinh(float __x)
  { return __builtin_sinhf(__x); }

  inline long double
  sinh(long double __x)
  { return __builtin_sinhl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    sinh(_Tp __x)
    { return __builtin_sinh(__x); }

  using ::sqrt;

  inline float
  sqrt(float __x)
  { return __builtin_sqrtf(__x); }

  inline long double
  sqrt(long double __x)
  { return __builtin_sqrtl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    sqrt(_Tp __x)
    { return __builtin_sqrt(__x); }

  using ::tan;

  inline float
  tan(float __x)
  { return __builtin_tanf(__x); }

  inline long double
  tan(long double __x)
  { return __builtin_tanl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    tan(_Tp __x)
    { return __builtin_tan(__x); }

  using ::tanh;

  inline float
  tanh(float __x)
  { return __builtin_tanhf(__x); }

  inline long double
  tanh(long double __x)
  { return __builtin_tanhl(__x); }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_integer<_Tp>::__value,
        double>::__type
    tanh(_Tp __x)
    { return __builtin_tanh(__x); }

}
namespace std __attribute__ ((__visibility__ ("default"))) {

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    fpclassify(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_fpclassify(FP_NAN, FP_INFINITE, FP_NORMAL,
      FP_SUBNORMAL, FP_ZERO, __type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isfinite(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isfinite(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isinf(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isinf(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isnan(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnan(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isnormal(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isnormal(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    signbit(_Tp __f)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_signbit(__type(__f));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreater(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isgreaterequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isgreaterequal(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isless(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isless(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    islessequal(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessequal(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    islessgreater(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_islessgreater(__type(__f1), __type(__f2));
    }

  template<typename _Tp>
    inline typename __gnu_cxx::__enable_if<__is_arithmetic<_Tp>::__value,
        int>::__type
    isunordered(_Tp __f1, _Tp __f2)
    {
      typedef typename __gnu_cxx::__promote<_Tp>::__type __type;
      return __builtin_isunordered(__type(__f1), __type(__f2));
    }

}





namespace std __attribute__ ((__visibility__ ("default"))) {

  template<typename _Tp>
    inline _Tp
    __cmath_power(_Tp __x, unsigned int __n)
    {
      _Tp __y = __n % 2 ? __x : _Tp(1);

      while (__n >>= 1)
        {
          __x = __x * __x;
          if (__n % 2)
            __y = __y * __x;
        }

      return __y;
    }

}
inline double abs(double __x)
{ return ::fabs(__x); }

inline float abs (float x) { return ::fabsf(x); } inline long double abs (long double x) { return ::fabsl(x); }




inline float acos (float x) { return ::acosf(x); } inline long double acos (long double x) { return ::acosl(x); }
inline float asin (float x) { return ::asinf(x); } inline long double asin (long double x) { return ::asinl(x); }
inline float atan (float x) { return ::atanf(x); } inline long double atan (long double x) { return ::atanl(x); }
inline float atan2 (float x, float y) { return ::atan2f(x, y); } inline long double atan2 (long double x, long double y) { return ::atan2l(x, y); }
inline float ceil (float x) { return ::ceilf(x); } inline long double ceil (long double x) { return ::ceill(x); }
inline float cos (float x) { return ::cosf(x); } inline long double cos (long double x) { return ::cosl(x); }
inline float cosh (float x) { return ::coshf(x); } inline long double cosh (long double x) { return ::coshl(x); }
inline float exp (float x) { return ::expf(x); } inline long double exp (long double x) { return ::expl(x); }
inline float fabs (float x) { return ::fabsf(x); } inline long double fabs (long double x) { return ::fabsl(x); }
inline float floor (float x) { return ::floorf(x); } inline long double floor (long double x) { return ::floorl(x); }
inline float fmod (float x, float y) { return ::fmodf(x, y); } inline long double fmod (long double x, long double y) { return ::fmodl(x, y); }
inline float frexp (float x, int * y) { return ::frexpf(x, y); } inline long double frexp (long double x, int * y) { return ::frexpl(x, y); }
inline float ldexp (float x, int y) { return ::ldexpf(x, y); } inline long double ldexp (long double x, int y) { return ::ldexpl(x, y); }
inline float log (float x) { return ::logf(x); } inline long double log (long double x) { return ::logl(x); }
inline float log10 (float x) { return ::log10f(x); } inline long double log10 (long double x) { return ::log10l(x); }
inline float modf (float x, float * y) { return ::modff(x, y); } inline long double modf (long double x, long double * y) { return ::modfl(x, y); }
inline float sin (float x) { return ::sinf(x); } inline long double sin (long double x) { return ::sinl(x); }
inline float sinh (float x) { return ::sinhf(x); } inline long double sinh (long double x) { return ::sinhl(x); }
inline float sqrt (float x) { return ::sqrtf(x); } inline long double sqrt (long double x) { return ::sqrtl(x); }
inline float tan (float x) { return ::tanf(x); } inline long double tan (long double x) { return ::tanl(x); }
inline float tanh (float x) { return ::tanhf(x); } inline long double tanh (long double x) { return ::tanhl(x); }
inline float pow (float x, float y) { return ::powf(x, y); } inline long double pow (long double x, long double y) { return ::powl(x, y); }




inline float pow(float __x, int __y) { return ::powf(__x, static_cast<float>(__y)); }






inline double pow(double __x, int __y) { return ::pow(__x, static_cast<double>(__y)); }



inline long double pow(long double __x, int __y) { return ::powl(__x, static_cast<long double>(__y)); }
namespace NStl {
using ::abs;
using ::acos;
using ::asin;
using ::atan;
using ::atan2;
using ::ceil;
using ::cos;
using ::cosh;
using ::exp;
using ::fabs;
using ::floor;
using ::fmod;
using ::frexp;
using ::hypot;
using ::ldexp;
using ::log;
using ::log10;
using ::modf;
using ::pow;
using ::sin;
using ::sinh;
using ::sqrt;
using ::tan;
using ::tanh;
}




namespace NStl {
using ::abs;

using ::div;





}







namespace NStl {

struct input_iterator_tag {};
struct output_iterator_tag {};
struct forward_iterator_tag : public input_iterator_tag {};
struct bidirectional_iterator_tag : public forward_iterator_tag {};
struct random_access_iterator_tag : public bidirectional_iterator_tag {};


template <class _Category, class _Tp, class _Distance = ptrdiff_t,
          class _Pointer = _Tp*, class _Reference = _Tp& >
struct iterator {
  typedef _Category iterator_category;
  typedef _Tp value_type;
  typedef _Distance difference_type;
  typedef _Pointer pointer;
  typedef _Reference reference;
};
template<>
struct iterator<output_iterator_tag, void, void, void, void> {
  typedef output_iterator_tag iterator_category;

  typedef void value_type;
  typedef void difference_type;
  typedef void pointer;
  typedef void reference;

};
template <class _Iterator>
struct iterator_traits {
  typedef typename _Iterator::iterator_category iterator_category;
  typedef typename _Iterator::value_type value_type;
  typedef typename _Iterator::difference_type difference_type;
  typedef typename _Iterator::pointer pointer;
  typedef typename _Iterator::reference reference;
};
template <class _Tp>
struct iterator_traits<const _Tp*> {
  typedef random_access_iterator_tag iterator_category;
  typedef _Tp value_type;
  typedef ptrdiff_t difference_type;
  typedef const _Tp* pointer;
  typedef const _Tp& reference;
};

template <class _Tp>
struct iterator_traits<_Tp*> {
  typedef random_access_iterator_tag iterator_category;
  typedef _Tp value_type;
  typedef ptrdiff_t difference_type;
  typedef _Tp* pointer;
  typedef _Tp& reference;
};
template <class _Iter>
inline typename iterator_traits<_Iter>::iterator_category __iterator_category(const _Iter&) {
  typedef typename iterator_traits<_Iter>::iterator_category _Category;
  return _Category();
}

template <class _Iter>
inline typename iterator_traits<_Iter>::difference_type* __distance_type(const _Iter&) {
  typedef typename iterator_traits<_Iter>::difference_type _diff_type;
  return static_cast<_diff_type*>(0);
}

template <class _Iter>
inline typename iterator_traits<_Iter>::value_type* __value_type(const _Iter&) {
  typedef typename iterator_traits<_Iter>::value_type _value_type;
  return static_cast<_value_type*>(0);
}
template <class _Tp, class _Distance> struct input_iterator :
  public iterator <input_iterator_tag, _Tp, _Distance, _Tp*, _Tp&> {};
struct output_iterator : public iterator <output_iterator_tag, void, void, void, void> {};
template <class _Tp, class _Distance> struct forward_iterator :
  public iterator<forward_iterator_tag, _Tp, _Distance, _Tp*, _Tp&> {};
template <class _Tp, class _Distance> struct bidirectional_iterator :
  public iterator<bidirectional_iterator_tag, _Tp, _Distance, _Tp*, _Tp&> {};
template <class _Tp, class _Distance> struct random_access_iterator :
  public iterator<random_access_iterator_tag, _Tp, _Distance, _Tp*, _Tp&> {};
template <class _InputIterator, class _Distance>
inline void __distance(const _InputIterator& __first, const _InputIterator& __last,
                                  _Distance& __n, const input_iterator_tag &) {
  _InputIterator __it(__first);
  while (__it != __last) { ++__it; ++__n; }
}
template <class _RandomAccessIterator, class _Distance>
inline void __distance(const _RandomAccessIterator& __first,
                                  const _RandomAccessIterator& __last,
                                  _Distance& __n, const random_access_iterator_tag &) {
  __n += __last - __first;
}


template <class _InputIterator, class _Distance>
inline void distance(const _InputIterator& __first,
        const _InputIterator& __last, _Distance& __n) {
  __distance(__first, __last, __n, typename iterator_traits< _InputIterator >::iterator_category());
}


template <class _InputIterator>
inline typename iterator_traits<_InputIterator>::difference_type
__distance(const _InputIterator& __first, const _InputIterator& __last, const input_iterator_tag &) {
  typename iterator_traits<_InputIterator>::difference_type __n = 0;
  _InputIterator __it(__first);
  while (__it != __last) {
    ++__it; ++__n;
  }
  return __n;
}
template <class _RandomAccessIterator>
inline typename iterator_traits<_RandomAccessIterator>::difference_type
__distance(const _RandomAccessIterator& __first, const _RandomAccessIterator& __last,
           const random_access_iterator_tag &) {
  return __last - __first;
}

template <class _InputIterator>
inline typename iterator_traits<_InputIterator>::difference_type
distance(_InputIterator __first, _InputIterator __last) {
  return __distance(__first, __last, typename iterator_traits< _InputIterator >::iterator_category());
}


template <class _Tp>
struct _Nonconst_traits;

template <class _Tp>
struct _Const_traits {
  typedef _Tp value_type;
  typedef const _Tp& reference;
  typedef const _Tp* pointer;
  typedef _Const_traits<_Tp> _ConstTraits;
  typedef _Nonconst_traits<_Tp> _NonConstTraits;
};

template <class _Tp>
struct _Nonconst_traits {
  typedef _Tp value_type;
  typedef _Tp& reference;
  typedef _Tp* pointer;
  typedef _Const_traits<_Tp> _ConstTraits;
  typedef _Nonconst_traits<_Tp> _NonConstTraits;
};





template <class _Tp>
struct _Nonconst_Const_traits;

template <class _Tp>
struct _Const_Const_traits {
  typedef _Tp value_type;
  typedef const _Tp& reference;
  typedef const _Tp* pointer;
  typedef _Const_Const_traits<_Tp> _ConstTraits;
  typedef _Nonconst_Const_traits<_Tp> _NonConstTraits;
};

template <class _Tp>
struct _Nonconst_Const_traits {
  typedef _Tp value_type;
  typedef const _Tp& reference;
  typedef const _Tp* pointer;
  typedef _Const_Const_traits<_Tp> _ConstTraits;
  typedef _Nonconst_Const_traits<_Tp> _NonConstTraits;
};
template <class _InputIter, class _Distance>
inline void
__advance(_InputIter& __i, _Distance __n, const input_iterator_tag &) {
  while (__n--) ++__i;
}


template <class _InputIter, class _Distance>
inline void
__advance(_InputIter& __i, _Distance __n, const output_iterator_tag &) {
  while (__n--) ++__i;
}
template <class _BidirectionalIterator, class _Distance>
inline void
__advance(_BidirectionalIterator& __i, _Distance __n,
          const bidirectional_iterator_tag &) {
  if (__n > 0)
    while (__n--) ++__i;
  else
    while (__n++) --__i;
}

template <class _RandomAccessIterator, class _Distance>
inline void
__advance(_RandomAccessIterator& __i, _Distance __n,
          const random_access_iterator_tag &) {
  __i += __n;
}

template <class _InputIterator, class _Distance>
inline void advance(_InputIterator& __i, _Distance __n) {
  __advance(__i, __n, typename iterator_traits< _InputIterator >::iterator_category());
}

}






namespace NStl {
template <class _Tp>
inline void swap(_Tp& __a, _Tp& __b) {
  _Tp __tmp = __a;
  __a = __b;
  __b = __tmp;

}

} namespace NStlPriv {

template <class _ForwardIter1, class _ForwardIter2, class _Value>
inline void __iter_swap_aux_aux(_ForwardIter1& __i1, _ForwardIter2& __i2, _Value *) {
  _Value tmp = *__i1;
  *__i1 = *__i2;
  *__i2 = tmp;
}

template <class _ForwardIter1, class _ForwardIter2>
inline void __iter_swap_aux(_ForwardIter1& __i1, _ForwardIter2& __i2, const __true_type& ) {
  ::NStl::swap(*__i1, *__i2);
}

template <class _ForwardIter1, class _ForwardIter2>
inline void __iter_swap_aux(_ForwardIter1& __i1, _ForwardIter2& __i2, const __false_type& ) {
  ::NStlPriv:: __iter_swap_aux_aux( __i1, __i2, (typename iterator_traits< _ForwardIter1 >::value_type*)0 );
}

} namespace NStl {

template <class _ForwardIter1, class _ForwardIter2>
inline void iter_swap(_ForwardIter1 __i1, _ForwardIter2 __i2) {

  ::NStlPriv:: __iter_swap_aux( __i1, __i2, _IsOKToSwap((typename iterator_traits< _ForwardIter1 >::value_type*)0, (typename iterator_traits< _ForwardIter2 >::value_type*)0,
                                                      _IsRefType< typename iterator_traits< _ForwardIter1 >::reference >::_Ret(),
                                                      _IsRefType< typename iterator_traits< _ForwardIter2 >::reference >::_Ret())._Answer());
}
template <class _Tp>
inline const _Tp& (min)(const _Tp& __a, const _Tp& __b) { return __b < __a ? __b : __a; }
template <class _Tp>
inline const _Tp& (max)(const _Tp& __a, const _Tp& __b) { return __a < __b ? __b : __a; }
template <class _Tp, class _Compare>
inline const _Tp& (min)(const _Tp& __a, const _Tp& __b, _Compare __comp) {
  return __comp(__b, __a) ? __b : __a;
}

template <class _Tp, class _Compare>
inline const _Tp& (max)(const _Tp& __a, const _Tp& __b, _Compare __comp) {
  return __comp(__a, __b) ? __b : __a;
}
} namespace NStlPriv {

template <class _InputIter, class _OutputIter, class _Distance>
inline _OutputIter __copy(_InputIter __first, _InputIter __last,
                          _OutputIter __result, const input_iterator_tag &, _Distance*) {
  for ( ; __first != __last; ++__result, ++__first)
    *__result = *__first;
  return __result;
}
template <class _RandomAccessIter, class _OutputIter, class _Distance>
inline _OutputIter
__copy(_RandomAccessIter __first, _RandomAccessIter __last,
       _OutputIter __result, const random_access_iterator_tag &, _Distance*) {
  for (_Distance __n = __last - __first; __n > 0; --__n) {
    *__result = *__first;
    ++__first;
    ++__result;
  }
  return __result;
}

inline void*
__copy_trivial(const void* __first, const void* __last, void* __result) {
  size_t __n = (const char*)__last - (const char*)__first;
  return __n ? (void *)((char*)memmove(__result, __first, __n) + __n) : __result;
}




template <class _BidirectionalIter1, class _BidirectionalIter2,
          class _Distance>
inline _BidirectionalIter2 __copy_backward(_BidirectionalIter1 __first,
                                           _BidirectionalIter1 __last,
                                           _BidirectionalIter2 __result,
                                           const bidirectional_iterator_tag &,
                                           _Distance*) {
  while (__first != __last)
    *--__result = *--__last;
  return __result;
}

template <class _RandomAccessIter, class _BidirectionalIter, class _Distance>
inline _BidirectionalIter __copy_backward(_RandomAccessIter __first,
                                          _RandomAccessIter __last,
                                          _BidirectionalIter __result,
                                          const random_access_iterator_tag &,
                                          _Distance*) {
  for (_Distance __n = __last - __first; __n > 0; --__n)
    *--__result = *--__last;
  return __result;
}

inline void*
__copy_trivial_backward(const void* __first, const void* __last, void* __result) {
  const ptrdiff_t _Num = (const char*)__last - (const char*)__first;
  return (_Num > 0) ? memmove((char*)__result - _Num, __first, _Num) : __result ;
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_ptrs(_InputIter __first, _InputIter __last, _OutputIter __result,
                               const __false_type& ) {
  return ::NStlPriv:: __copy(__first, __last, __result, random_access_iterator_tag(), (ptrdiff_t*)0);
}
template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_ptrs(_InputIter __first, _InputIter __last, _OutputIter __result,
                               const __true_type& ) {


  return (_OutputIter)::NStlPriv:: __copy_trivial(__first, __last, __result);
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_aux(_InputIter __first, _InputIter __last, _OutputIter __result,
                              const __true_type& ) {
  return ::NStlPriv:: __copy_ptrs(__first, __last, __result,
                     _UseTrivialCopy((typename iterator_traits< _InputIter >::value_type*)0,
                                     (typename iterator_traits< _OutputIter >::value_type*)0)._Answer());
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_aux(_InputIter __first, _InputIter __last, _OutputIter __result,
                              const __false_type& ) {
  return ::NStlPriv:: __copy(__first, __last, __result,
                typename iterator_traits< _InputIter >::iterator_category(),
                (typename iterator_traits< _InputIter >::difference_type*)0);
}

} namespace NStl {

template <class _InputIter, class _OutputIter>
inline _OutputIter copy(_InputIter __first, _InputIter __last, _OutputIter __result) {

  return ::NStlPriv:: __copy_aux(__first, __last, __result, _BothPtrType< _InputIter, _OutputIter>::_Answer());
}

} namespace NStlPriv {

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_backward_ptrs(_InputIter __first, _InputIter __last,
                                        _OutputIter __result, const __false_type& ) {
  return ::NStlPriv:: __copy_backward(__first, __last, __result, typename iterator_traits< _InputIter >::iterator_category(), (typename iterator_traits< _InputIter >::difference_type*)0);
}
template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_backward_ptrs(_InputIter __first, _InputIter __last,
                                        _OutputIter __result, const __true_type& ) {
  return (_OutputIter)::NStlPriv:: __copy_trivial_backward(__first, __last, __result);
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_backward_aux(_InputIter __first, _InputIter __last, _OutputIter __result, const __false_type&) {
  return ::NStlPriv:: __copy_backward(__first, __last, __result, typename iterator_traits< _InputIter >::iterator_category(), (typename iterator_traits< _InputIter >::difference_type*)0);
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __copy_backward_aux(_InputIter __first, _InputIter __last, _OutputIter __result, const __true_type&) {
  return ::NStlPriv:: __copy_backward_ptrs(__first, __last, __result,
                              _UseTrivialCopy((typename iterator_traits< _InputIter >::value_type*)0,
                                              (typename iterator_traits< _OutputIter >::value_type*)0)._Answer());
}

} namespace NStl {

template <class _InputIter, class _OutputIter>
inline _OutputIter copy_backward(_InputIter __first, _InputIter __last, _OutputIter __result) {

  return ::NStlPriv:: __copy_backward_aux(__first, __last, __result, _BothPtrType< _InputIter, _OutputIter>::_Answer() );
}
} namespace NStlPriv {

template <class _InputIter, class _Size, class _OutputIter>
inline pair<_InputIter, _OutputIter>
__copy_n(_InputIter __first, _Size __count,
         _OutputIter __result,
         const input_iterator_tag &) {
  for ( ; __count > 0; --__count) {
    *__result = *__first;
    ++__first;
    ++__result;
  }
  return pair<_InputIter, _OutputIter>(__first, __result);
}

template <class _RAIter, class _Size, class _OutputIter>
inline pair<_RAIter, _OutputIter>
__copy_n(_RAIter __first, _Size __count,
         _OutputIter __result,
         const random_access_iterator_tag &) {
  _RAIter __last = __first + __count;
  return pair<_RAIter, _OutputIter>(__last, copy(__first, __last, __result));
}

} namespace NStl {

template <class _InputIter, class _Size, class _OutputIter>
inline pair<_InputIter, _OutputIter>
copy_n(_InputIter __first, _Size __count, _OutputIter __result) {

  return ::NStlPriv:: __copy_n(__first, __count, __result, typename iterator_traits< _InputIter >::iterator_category());
}




template <class _ForwardIter, class _Tp>
inline
void fill(_ForwardIter __first, _ForwardIter __last, const _Tp& __val) {

  for ( ; __first != __last; ++__first)
    *__first = __val;
}

} namespace NStlPriv {

template <class _OutputIter, class _Size, class _Tp>
inline
_OutputIter __fill_n(_OutputIter __first, _Size __n, const _Tp& __val) {

  for ( ; __n > 0; --__n, ++__first)
    *__first = __val;
  return __first;
}

} namespace NStl {

template <class _OutputIter, class _Size, class _Tp>
inline
void fill_n(_OutputIter __first, _Size __n, const _Tp& __val) {

  ::NStlPriv:: __fill_n(__first, __n, __val);
}


inline void fill(unsigned char* __first, unsigned char* __last,
                 const unsigned char& __val) {
  unsigned char __tmp = __val;
  memset(__first, __tmp, __last - __first);
}

inline void fill(signed char* __first, signed char* __last,
                 const signed char& __val) {
  signed char __tmp = __val;
  memset(__first, static_cast<unsigned char>(__tmp), __last - __first);
}

inline void fill(char* __first, char* __last, const char& __val) {
  char __tmp = __val;
  memset(__first, static_cast<unsigned char>(__tmp), __last - __first);
}


} namespace NStlPriv {

template <class _Size>
inline unsigned char* __fill_n(unsigned char* __first, _Size __n,
                             const unsigned char& __val) {
  fill(__first, __first + __n, __val);
  return __first + __n;
}

template <class _Size>
inline signed char* __fill_n(char* __first, _Size __n,
                           const signed char& __val) {
  fill(__first, __first + __n, __val);
  return __first + __n;
}

template <class _Size>
inline char* __fill_n(char* __first, _Size __n, const char& __val) {
  fill(__first, __first + __n, __val);
  return __first + __n;
}

} namespace NStl {






template <class _InputIter1, class _InputIter2>
inline
pair<_InputIter1, _InputIter2> mismatch(_InputIter1 __first1,
                                        _InputIter1 __last1,
                                        _InputIter2 __first2) {


  while (__first1 != __last1 && *__first1 == *__first2) {
    ++__first1;
    ++__first2;
  }
  return pair<_InputIter1, _InputIter2>(__first1, __first2);
}

template <class _InputIter1, class _InputIter2, class _BinaryPredicate>
inline
pair<_InputIter1, _InputIter2> mismatch(_InputIter1 __first1,
                                        _InputIter1 __last1,
                                        _InputIter2 __first2,
                                        _BinaryPredicate __binary_pred) {


  while (__first1 != __last1 && __binary_pred(*__first1, *__first2)) {
    ++__first1;
    ++__first2;
  }
  return pair<_InputIter1, _InputIter2>(__first1, __first2);
}

template <class _InputIter1, class _InputIter2>
inline
bool equal(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2) {


  for ( ; __first1 != __last1; ++__first1, ++__first2)
    if (!(*__first1 == *__first2))
      return false;
  return true;
}

template <class _InputIter1, class _InputIter2, class _BinaryPredicate>
inline
bool equal(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _BinaryPredicate __binary_pred) {


  for ( ; __first1 != __last1; ++__first1, ++__first2)
    if (!__binary_pred(*__first1, *__first2))
      return false;
  return true;
}





template <class _InputIter1, class _InputIter2>
bool lexicographical_compare(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2);

template <class _InputIter1, class _InputIter2, class _Compare>
bool lexicographical_compare(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _Compare __comp);

inline bool
lexicographical_compare(const unsigned char* __first1,
                        const unsigned char* __last1,
                        const unsigned char* __first2,
                        const unsigned char* __last2) {
  const size_t __len1 = __last1 - __first1;
  const size_t __len2 = __last2 - __first2;



  const int __result = memcmp(__first1, __first2, (min) (__len1, __len2));
  return __result != 0 ? (__result < 0) : (__len1 < __len2);
}
} namespace NStlPriv {

template <class _InputIter1, class _InputIter2>
int __lexicographical_compare_3way(_InputIter1 __first1, _InputIter1 __last1,
                                   _InputIter2 __first2, _InputIter2 __last2);

inline int
__lexicographical_compare_3way(const unsigned char* __first1,
                               const unsigned char* __last1,
                               const unsigned char* __first2,
                               const unsigned char* __last2) {
  const ptrdiff_t __len1 = __last1 - __first1;
  const ptrdiff_t __len2 = __last2 - __first2;
  const int __result = memcmp(__first1, __first2, (min) (__len1, __len2));
  return __result != 0 ? __result
                       : (__len1 == __len2 ? 0 : (__len1 < __len2 ? -1 : 1));
}
} namespace NStl {


template <class _InputIter1, class _InputIter2>
int lexicographical_compare_3way(_InputIter1 __first1, _InputIter1 __last1,
                                 _InputIter2 __first2, _InputIter2 __last2);




template <class _InputIter, class _Tp>
inline typename iterator_traits<_InputIter>::difference_type
count(_InputIter __first, _InputIter __last, const _Tp& __val) {

  typename iterator_traits<_InputIter>::difference_type __n = 0;
  for ( ; __first != __last; ++__first)
    if (*__first == __val)
      ++__n;
  return __n;
}


template <class _InputIter, class _Tp>
_InputIter find(_InputIter __first, _InputIter __last, const _Tp& __val);

template <class _InputIter, class _Predicate>
_InputIter find_if(_InputIter __first, _InputIter __last, _Predicate __pred);


template <class _ForwardIter1, class _ForwardIter2, class _BinaryPred>
_ForwardIter1 search(_ForwardIter1 __first1, _ForwardIter1 __last1,
                     _ForwardIter2 __first2, _ForwardIter2 __last2, _BinaryPred __predicate);

} namespace NStlPriv {


template <class _InputIter, class _ForwardIter, class _BinaryPredicate>
_InputIter __find_first_of(_InputIter __first1, _InputIter __last1,
                           _ForwardIter __first2, _ForwardIter __last2,
                           _BinaryPredicate __comp);

} namespace NStl {

template <class _ForwardIter1, class _ForwardIter2,
          class _BinaryPredicate>
_ForwardIter1
find_end(_ForwardIter1 __first1, _ForwardIter1 __last1,
         _ForwardIter2 __first2, _ForwardIter2 __last2,
         _BinaryPredicate __comp);


template <class _ForwardIter, class _Tp>
inline void
replace(_ForwardIter __first, _ForwardIter __last,
        const _Tp& __old_value, const _Tp& __new_value) {

  for ( ; __first != __last; ++__first)
    if (*__first == __old_value)
      *__first = __new_value;
}

} namespace NStlPriv {

template <class _ForwardIter, class _Tp, class _Compare1, class _Compare2, class _Distance>
_ForwardIter __lower_bound(_ForwardIter __first, _ForwardIter __last,
                           const _Tp& __val, _Compare1 __comp1, _Compare2 __comp2, _Distance*);

} namespace NStl {

}


namespace NStl {

template <class _InputIter1, class _InputIter2>
bool lexicographical_compare(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2) {


  for ( ; __first1 != __last1 && __first2 != __last2
        ; ++__first1, ++__first2) {
    if (*__first1 < *__first2) {
      return true;
    }
    if (*__first2 < *__first1)
      return false;
  }
  return __first1 == __last1 && __first2 != __last2;
}

template <class _InputIter1, class _InputIter2, class _Compare>
bool lexicographical_compare(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _Compare __comp) {


  for ( ; __first1 != __last1 && __first2 != __last2
        ; ++__first1, ++__first2) {
    if (__comp(*__first1, *__first2)) {
      return true;
    }
    if (__comp(*__first2, *__first1))
      return false;
  }
  return __first1 == __last1 && __first2 != __last2;
}


} namespace NStlPriv {

template <class _InputIter1, class _InputIter2>
int __lexicographical_compare_3way(_InputIter1 __first1, _InputIter1 __last1,
                                   _InputIter2 __first2, _InputIter2 __last2) {
  while (__first1 != __last1 && __first2 != __last2) {
    if (*__first1 < *__first2) {

      return -1;
    }
    if (*__first2 < *__first1)
      return 1;
    ++__first1;
    ++__first2;
  }
  if (__first2 == __last2) {
    return !(__first1 == __last1);
  }
  else {
    return -1;
  }
}

} namespace NStl {

template <class _InputIter1, class _InputIter2>
int lexicographical_compare_3way(_InputIter1 __first1, _InputIter1 __last1,
                                 _InputIter2 __first2, _InputIter2 __last2) {


  return ::NStlPriv:: __lexicographical_compare_3way(__first1, __last1, __first2, __last2);
}


} namespace NStlPriv {

template <class _RandomAccessIter, class _Tp>
inline _RandomAccessIter __find(_RandomAccessIter __first, _RandomAccessIter __last,
                                           const _Tp& __val,
                                           const random_access_iterator_tag &) {
  typename iterator_traits<_RandomAccessIter>::difference_type __trip_count = (__last - __first) >> 2;

  for ( ; __trip_count > 0 ; --__trip_count) {
    if (*__first == __val) return __first;
    ++__first;

    if (*__first == __val) return __first;
    ++__first;

    if (*__first == __val) return __first;
    ++__first;

    if (*__first == __val) return __first;
    ++__first;
  }

  switch (__last - __first) {
  case 3:
    if (*__first == __val) return __first;
    ++__first;
  case 2:
    if (*__first == __val) return __first;
    ++__first;
  case 1:
    if (*__first == __val) return __first;

  case 0:
  default:
    return __last;
  }
}

inline char*
__find(char* __first, char* __last, char __val, const random_access_iterator_tag &) {
  void *res = memchr(__first, __val, __last - __first);
  return res != 0 ? static_cast<char*>(res) : __last;
}
inline const char*
__find(const char* __first, const char* __last, char __val, const random_access_iterator_tag &) {
  const void *res = memchr(__first, __val, __last - __first);
  return res != 0 ? static_cast<const char*>(res) : __last;
}

template <class _RandomAccessIter, class _Predicate>
inline _RandomAccessIter __find_if(_RandomAccessIter __first, _RandomAccessIter __last,
                                              _Predicate __pred,
                                              const random_access_iterator_tag &) {
  typename iterator_traits<_RandomAccessIter>::difference_type __trip_count = (__last - __first) >> 2;

  for ( ; __trip_count > 0 ; --__trip_count) {
    if (__pred(*__first)) return __first;
    ++__first;

    if (__pred(*__first)) return __first;
    ++__first;

    if (__pred(*__first)) return __first;
    ++__first;

    if (__pred(*__first)) return __first;
    ++__first;
  }

  switch(__last - __first) {
  case 3:
    if (__pred(*__first)) return __first;
    ++__first;
  case 2:
    if (__pred(*__first)) return __first;
    ++__first;
  case 1:
    if (__pred(*__first)) return __first;

  case 0:
  default:
    return __last;
  }
}

template <class _InputIter, class _Tp>
inline _InputIter __find(_InputIter __first, _InputIter __last,
                                    const _Tp& __val,
                                    const input_iterator_tag &) {
  while (__first != __last && !(*__first == __val)) ++__first;
  return __first;
}

template <class _InputIter, class _Predicate>
inline _InputIter __find_if(_InputIter __first, _InputIter __last,
                                       _Predicate __pred,
                                       const input_iterator_tag &) {
  while (__first != __last && !__pred(*__first))
    ++__first;
  return __first;
}

} namespace NStl {

template <class _InputIter, class _Predicate>
_InputIter find_if(_InputIter __first, _InputIter __last,
                   _Predicate __pred) {

  return ::NStlPriv:: __find_if(__first, __last, __pred, typename iterator_traits< _InputIter >::iterator_category());
}

template <class _InputIter, class _Tp>
_InputIter find(_InputIter __first, _InputIter __last, const _Tp& __val) {

  return ::NStlPriv:: __find(__first, __last, __val, typename iterator_traits< _InputIter >::iterator_category());
}

template <class _ForwardIter1, class _ForwardIter2, class _BinaryPred>
_ForwardIter1 search(_ForwardIter1 __first1, _ForwardIter1 __last1,
                     _ForwardIter2 __first2, _ForwardIter2 __last2,
                     _BinaryPred __pred) {



  if (__first1 == __last1 || __first2 == __last2)
    return __first1;


  _ForwardIter2 __p1(__first2);

  if ( ++__p1 == __last2 ) {
    while (__first1 != __last1 && !__pred(*__first1, *__first2)) {
      ++__first1;
    }
    return __first1;
  }



  for ( ; ; ) {
    while (__first1 != __last1 && !__pred(*__first1, *__first2)) {
      ++__first1;
    }
    if (__first1 == __last1) {
      return __last1;
    }
    _ForwardIter2 __p = __p1;
    _ForwardIter1 __current = __first1;
    if (++__current == __last1) return __last1;

    while (__pred(*__current, *__p)) {
      if (++__p == __last2)
        return __first1;
      if (++__current == __last1)
        return __last1;
    }

    ++__first1;
  }
  return __first1;
}

} namespace NStlPriv {


template <class _InputIter, class _ForwardIter, class _BinaryPredicate>
_InputIter __find_first_of(_InputIter __first1, _InputIter __last1,
                           _ForwardIter __first2, _ForwardIter __last2,
                           _BinaryPredicate __comp) {
  for ( ; __first1 != __last1; ++__first1) {
    for (_ForwardIter __iter = __first2; __iter != __last2; ++__iter) {
      if (__comp(*__first1, *__iter)) {
        return __first1;
      }
    }
  }
  return __last1;
}







template <class _ForwardIter1, class _ForwardIter2,
  class _BinaryPredicate>
_ForwardIter1 __find_end(_ForwardIter1 __first1, _ForwardIter1 __last1,
                         _ForwardIter2 __first2, _ForwardIter2 __last2,
                         const forward_iterator_tag &, const forward_iterator_tag &,
                         _BinaryPredicate __comp) {
  if (__first2 == __last2)
    return __last1;
  else {
    _ForwardIter1 __result = __last1;
    for (;;) {
      _ForwardIter1 __new_result = search(__first1, __last1, __first2, __last2, __comp);
      if (__new_result == __last1)
        return __result;
      else {
        __result = __new_result;
        __first1 = __new_result;
        ++__first1;
      }
    }
  }
}

} namespace NStl {





}
namespace NStl {
template <class _Iterator>
class reverse_iterator :
  public iterator<typename iterator_traits<_Iterator>::iterator_category,
                  typename iterator_traits<_Iterator>::value_type,
                  typename iterator_traits<_Iterator>::difference_type,
                  typename iterator_traits<_Iterator>::pointer,
                  typename iterator_traits<_Iterator>::reference> {
protected:
  _Iterator current;
  typedef reverse_iterator<_Iterator> _Self;
public:
  typedef typename iterator_traits<_Iterator>::iterator_category iterator_category;
  typedef typename iterator_traits<_Iterator>::value_type value_type;
  typedef typename iterator_traits<_Iterator>::difference_type difference_type;
  typedef typename iterator_traits<_Iterator>::pointer pointer;
  typedef typename iterator_traits<_Iterator>::reference reference;
  typedef _Iterator iterator_type;
public:
  reverse_iterator() {}
  explicit reverse_iterator(iterator_type __x) : current(__x) {}
  reverse_iterator(const _Self& __x) : current(__x.current) {}
  _Self& operator = (const _Self& __x) { current = __x.base(); return *this; }

  template <class _Iter>
  reverse_iterator(const reverse_iterator<_Iter>& __x) : current(__x.base()) {}
  template <class _Iter>
  _Self& operator = (const reverse_iterator<_Iter>& __x) { current = __x.base(); return *this; }


  iterator_type base() const { return current; }
  reference operator*() const {
    _Iterator __tmp = current;
    return *--__tmp;
  }
  pointer operator->() const { return &(operator*()); }
  _Self& operator++() {
    --current;
    return *this;
  }
  _Self operator++(int) {
    _Self __tmp = *this;
    --current;
    return __tmp;
  }
  _Self& operator--() {
    ++current;
    return *this;
  }
  _Self operator--(int) {
    _Self __tmp = *this;
    ++current;
    return __tmp;
  }

  _Self operator+(difference_type __n) const { return _Self(current - __n); }
  _Self& operator+=(difference_type __n) {
    current -= __n;
    return *this;
  }
  _Self operator-(difference_type __n) const { return _Self(current + __n); }
  _Self& operator-=(difference_type __n) {
    current += __n;
    return *this;
  }
  reference operator[](difference_type __n) const { return *(*this + __n); }
};

template <class _Iterator>
inline bool operator==(const reverse_iterator<_Iterator>& __x,
                                   const reverse_iterator<_Iterator>& __y)
{ return __x.base() == __y.base(); }

template <class _Iterator>
inline bool operator<(const reverse_iterator<_Iterator>& __x,
                                 const reverse_iterator<_Iterator>& __y)
{ return __y.base() < __x.base(); }


template <class _Iterator>
inline bool operator!=(const reverse_iterator<_Iterator>& __x,
                                  const reverse_iterator<_Iterator>& __y)
{ return !(__x == __y); }

template <class _Iterator>
inline bool operator>(const reverse_iterator<_Iterator>& __x,
                                 const reverse_iterator<_Iterator>& __y)
{ return __y < __x; }

template <class _Iterator>
inline bool operator<=(const reverse_iterator<_Iterator>& __x,
                                  const reverse_iterator<_Iterator>& __y)
{ return !(__y < __x); }

template <class _Iterator>
inline bool operator>=(const reverse_iterator<_Iterator>& __x,
                                  const reverse_iterator<_Iterator>& __y)
{ return !(__x < __y); }


template <class _Iterator>



inline typename reverse_iterator<_Iterator>::difference_type

operator-(const reverse_iterator<_Iterator>& __x,
          const reverse_iterator<_Iterator>& __y)
{ return __y.base() - __x.base(); }

template <class _Iterator, class _DifferenceType>
inline reverse_iterator<_Iterator>
operator+(_DifferenceType n,const reverse_iterator<_Iterator>& x)
{ return x.operator+(n); }


template <class _Container>
class back_insert_iterator
  : public iterator<output_iterator_tag, void, void, void, void> {
  typedef back_insert_iterator<_Container> _Self;
protected:

  _Container *container;
public:
  typedef _Container container_type;
  typedef output_iterator_tag iterator_category;

  explicit back_insert_iterator(_Container& __x) : container(&__x) {}

  _Self& operator=(const _Self& __other) {
    container = __other.container;
    return *this;
  }
  _Self& operator=(const typename _Container::value_type& __val) {
    container->push_back(__val);
    return *this;
  }
  _Self& operator*() { return *this; }
  _Self& operator++() { return *this; }
  _Self operator++(int) { return *this; }
};

template <class _Container>
inline back_insert_iterator<_Container> back_inserter(_Container& __x)
{ return back_insert_iterator<_Container>(__x); }

template <class _Container>
class front_insert_iterator
  : public iterator<output_iterator_tag, void, void, void, void> {
  typedef front_insert_iterator<_Container> _Self;
protected:

  _Container *container;
public:
  typedef _Container container_type;
  typedef output_iterator_tag iterator_category;
  explicit front_insert_iterator(_Container& __x) : container(&__x) {}

  _Self& operator=(const _Self& __other) {
    container = __other.container;
    return *this;
  }
  _Self& operator=(const typename _Container::value_type& __val) {
    container->push_front(__val);
    return *this;
  }
  _Self& operator*() { return *this; }
  _Self& operator++() { return *this; }
  _Self operator++(int) { return *this; }
};

template <class _Container>
inline front_insert_iterator<_Container> front_inserter(_Container& __x)
{ return front_insert_iterator<_Container>(__x); }

template <class _Container>
class insert_iterator
  : public iterator<output_iterator_tag, void, void, void, void> {
  typedef insert_iterator<_Container> _Self;
protected:

  _Container *container;
  typename _Container::iterator _M_iter;
public:
  typedef _Container container_type;
  typedef output_iterator_tag iterator_category;
  insert_iterator(_Container& __x, typename _Container::iterator __i)
    : container(&__x), _M_iter(__i) {}

  _Self& operator=(_Self const& __other) {
    container = __other.container;
    _M_iter = __other._M_iter;
    return *this;
  }
  _Self& operator=(const typename _Container::value_type& __val) {
    _M_iter = container->insert(_M_iter, __val);
    ++_M_iter;
    return *this;
  }
  _Self& operator*() { return *this; }
  _Self& operator++() { return *this; }
  _Self& operator++(int) { return *this; }
};

template <class _Container, class _Iterator>
inline insert_iterator<_Container>
inserter(_Container& __x, _Iterator __i) {
  typedef typename _Container::iterator __iter;
  return insert_iterator<_Container>(__x, __iter(__i));
}

}
namespace NStl {


} namespace NStlPriv {

template <class _BidirectionalIter1, class _BidirectionalIter2,
          class _BinaryPredicate>
_BidirectionalIter1
__find_end(_BidirectionalIter1 __first1, _BidirectionalIter1 __last1,
           _BidirectionalIter2 __first2, _BidirectionalIter2 __last2,
           const bidirectional_iterator_tag &, const bidirectional_iterator_tag &,
           _BinaryPredicate __comp) {
  typedef reverse_iterator<_BidirectionalIter1> _RevIter1;
  typedef reverse_iterator<_BidirectionalIter2> _RevIter2;

  _RevIter1 __rlast1(__first1);
  _RevIter2 __rlast2(__first2);
  _RevIter1 __rresult = search(_RevIter1(__last1), __rlast1,
                               _RevIter2(__last2), __rlast2,
                               __comp);

  if (__rresult == __rlast1)
    return __last1;
  else {
    _BidirectionalIter1 __result = __rresult.base();
    advance(__result, -distance(__first2, __last2));
    return __result;
  }
}

} namespace NStl {


template <class _ForwardIter1, class _ForwardIter2,
          class _BinaryPredicate>
_ForwardIter1
find_end(_ForwardIter1 __first1, _ForwardIter1 __last1,
         _ForwardIter2 __first2, _ForwardIter2 __last2,
         _BinaryPredicate __comp) {


  return ::NStlPriv:: __find_end(__first1, __last1, __first2, __last2,

                               typename iterator_traits< _ForwardIter1 >::iterator_category(),
                               typename iterator_traits< _ForwardIter2 >::iterator_category(),




                               __comp);
}

} namespace NStlPriv {

template <class _ForwardIter, class _Tp, class _Compare1, class _Compare2, class _Distance>
_ForwardIter __lower_bound(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
                           _Compare1 __comp1, _Compare2 __comp2, _Distance*) {
  (void)__comp2;
  _Distance __len = distance(__first, __last);
  _Distance __half;
  _ForwardIter __middle;

  while (__len > 0) {
    __half = __len >> 1;
    __middle = __first;
    advance(__middle, __half);
    if (__comp1(*__middle, __val)) {

      __first = __middle;
      ++__first;
      __len = __len - __half - 1;
    }
    else
      __len = __half;
  }
  return __first;
}

} namespace NStl {

}



namespace NStl {



template <class _RandomAccessIterator>
void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last);


template <class _RandomAccessIterator, class _Compare>
void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
          _Compare __comp);

template <class _RandomAccessIterator, class _Distance, class _Tp>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __val);

template <class _RandomAccessIterator, class _Tp, class _Distance>
inline void
__pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
           _RandomAccessIterator __result, _Tp __val, _Distance*)
{
  *__result = *__first;
  __adjust_heap(__first, _Distance(0), _Distance(__last - __first), __val);
}

template <class _RandomAccessIterator>
void pop_heap(_RandomAccessIterator __first,
        _RandomAccessIterator __last);

template <class _RandomAccessIterator, class _Distance,
          class _Tp, class _Compare>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __val, _Compare __comp);

template <class _RandomAccessIterator, class _Tp, class _Compare,
          class _Distance>
inline void
__pop_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
           _RandomAccessIterator __result, _Tp __val, _Compare __comp,
           _Distance*)
{
  *__result = *__first;
  __adjust_heap(__first, _Distance(0), _Distance(__last - __first),
                __val, __comp);
}

template <class _RandomAccessIterator, class _Compare>
void
pop_heap(_RandomAccessIterator __first,
         _RandomAccessIterator __last, _Compare __comp);

template <class _RandomAccessIterator>
void
make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last);

template <class _RandomAccessIterator, class _Compare>
void
make_heap(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp);

template <class _RandomAccessIterator>
inline
void sort_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  while (__last - __first > 1)
    pop_heap(__first, __last--);
}

template <class _RandomAccessIterator, class _Compare>
inline
void
sort_heap(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp)
{
  while (__last - __first > 1)
    pop_heap(__first, __last--, __comp);
}

}


namespace NStl {

template <class _RandomAccessIterator, class _Distance, class _Tp>
inline
void
__push_heap(_RandomAccessIterator __first,
            _Distance __holeIndex, _Distance __topIndex, _Tp __val)
{
  _Distance __parent = (__holeIndex - 1) / 2;
  while (__holeIndex > __topIndex && *(__first + __parent) < __val) {
    *(__first + __holeIndex) = *(__first + __parent);
    __holeIndex = __parent;
    __parent = (__holeIndex - 1) / 2;
  }
  *(__first + __holeIndex) = __val;
}

template <class _RandomAccessIterator, class _Distance, class _Tp>
inline void
__push_heap_aux(_RandomAccessIterator __first,
                _RandomAccessIterator __last, _Distance*, _Tp*)
{
  __push_heap(__first, _Distance((__last - __first) - 1), _Distance(0),
              _Tp(*(__last - 1)));
}

template <class _RandomAccessIterator>
void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __push_heap_aux(__first, __last,
                  (typename iterator_traits< _RandomAccessIterator >::difference_type*)0, (typename iterator_traits< _RandomAccessIterator >::value_type*)0);
}


template <class _RandomAccessIterator, class _Distance, class _Tp,
          class _Compare>
inline
void
__push_heap(_RandomAccessIterator __first, _Distance __holeIndex,
            _Distance __topIndex, _Tp __val, _Compare __comp)
{
  _Distance __parent = (__holeIndex - 1) / 2;
  while (__holeIndex > __topIndex && __comp(*(__first + __parent), __val)) {

    *(__first + __holeIndex) = *(__first + __parent);
    __holeIndex = __parent;
    __parent = (__holeIndex - 1) / 2;
  }
  *(__first + __holeIndex) = __val;
}

template <class _RandomAccessIterator, class _Compare,
          class _Distance, class _Tp>
inline void
__push_heap_aux(_RandomAccessIterator __first,
                _RandomAccessIterator __last, _Compare __comp,
                _Distance*, _Tp*)
{
  __push_heap(__first, _Distance((__last - __first) - 1), _Distance(0),
              _Tp(*(__last - 1)), __comp);
}

template <class _RandomAccessIterator, class _Compare>
void
push_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
          _Compare __comp)
{
  __push_heap_aux(__first, __last, __comp,
                  (typename iterator_traits< _RandomAccessIterator >::difference_type*)0, (typename iterator_traits< _RandomAccessIterator >::value_type*)0);
}

template <class _RandomAccessIterator, class _Distance, class _Tp>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __val) {
  _Distance __topIndex = __holeIndex;
  _Distance __secondChild = 2 * __holeIndex + 2;
  while (__secondChild < __len) {
    if (*(__first + __secondChild) < *(__first + (__secondChild - 1)))
      __secondChild--;
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;
    __secondChild = 2 * (__secondChild + 1);
  }
  if (__secondChild == __len) {
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }
  __push_heap(__first, __holeIndex, __topIndex, __val);
}


template <class _RandomAccessIterator, class _Tp>
inline void
__pop_heap_aux(_RandomAccessIterator __first, _RandomAccessIterator __last, _Tp*) {
  __pop_heap(__first, __last - 1, __last - 1,
             _Tp(*(__last - 1)), (typename iterator_traits< _RandomAccessIterator >::difference_type*)0);
}

template <class _RandomAccessIterator>
void pop_heap(_RandomAccessIterator __first,
        _RandomAccessIterator __last) {
  __pop_heap_aux(__first, __last, (typename iterator_traits< _RandomAccessIterator >::value_type*)0);
}

template <class _RandomAccessIterator, class _Distance,
          class _Tp, class _Compare>
void
__adjust_heap(_RandomAccessIterator __first, _Distance __holeIndex,
              _Distance __len, _Tp __val, _Compare __comp)
{
  _Distance __topIndex = __holeIndex;
  _Distance __secondChild = 2 * __holeIndex + 2;
  while (__secondChild < __len) {
    if (__comp(*(__first + __secondChild), *(__first + (__secondChild - 1)))) {


      __secondChild--;
    }
    *(__first + __holeIndex) = *(__first + __secondChild);
    __holeIndex = __secondChild;
    __secondChild = 2 * (__secondChild + 1);
  }
  if (__secondChild == __len) {
    *(__first + __holeIndex) = *(__first + (__secondChild - 1));
    __holeIndex = __secondChild - 1;
  }
  __push_heap(__first, __holeIndex, __topIndex, __val, __comp);
}


template <class _RandomAccessIterator, class _Tp, class _Compare>
inline void
__pop_heap_aux(_RandomAccessIterator __first,
               _RandomAccessIterator __last, _Tp*, _Compare __comp)
{
  __pop_heap(__first, __last - 1, __last - 1, _Tp(*(__last - 1)), __comp,
             (typename iterator_traits< _RandomAccessIterator >::difference_type*)0);
}


template <class _RandomAccessIterator, class _Compare>
void
pop_heap(_RandomAccessIterator __first,
         _RandomAccessIterator __last, _Compare __comp)
{
    __pop_heap_aux(__first, __last, (typename iterator_traits< _RandomAccessIterator >::value_type*)0, __comp);
}

template <class _RandomAccessIterator, class _Tp, class _Distance>
inline
void
__make_heap(_RandomAccessIterator __first,
            _RandomAccessIterator __last, _Tp*, _Distance*)
{
  if (__last - __first < 2) return;
  _Distance __len = __last - __first;
  _Distance __parent = (__len - 2)/2;

  for (;;) {
    __adjust_heap(__first, __parent, __len, _Tp(*(__first + __parent)));
    if (__parent == 0) return;
    __parent--;
  }
}

template <class _RandomAccessIterator>
void
make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last)
{
  __make_heap(__first, __last,
              (typename iterator_traits< _RandomAccessIterator >::value_type*)0, (typename iterator_traits< _RandomAccessIterator >::difference_type*)0);
}

template <class _RandomAccessIterator, class _Compare,
          class _Tp, class _Distance>
inline
void
__make_heap(_RandomAccessIterator __first, _RandomAccessIterator __last,
            _Compare __comp, _Tp*, _Distance*)
{
  if (__last - __first < 2) return;
  _Distance __len = __last - __first;
  _Distance __parent = (__len - 2)/2;

  for (;;) {
    __adjust_heap(__first, __parent, __len, _Tp(*(__first + __parent)),
                  __comp);
    if (__parent == 0) return;
    __parent--;
  }
}

template <class _RandomAccessIterator, class _Compare>
void
make_heap(_RandomAccessIterator __first,
          _RandomAccessIterator __last, _Compare __comp)
{
  __make_heap(__first, __last, __comp,
              (typename iterator_traits< _RandomAccessIterator >::value_type*)0, (typename iterator_traits< _RandomAccessIterator >::difference_type*)0);
}

}







namespace NStl {

template <class _Arg, class _Result>
struct unary_function {
  typedef _Arg argument_type;
  typedef _Result result_type;
};

template <class _Arg1, class _Arg2, class _Result>
struct binary_function {
  typedef _Arg1 first_argument_type;
  typedef _Arg2 second_argument_type;
  typedef _Result result_type;
};

template <class _Tp>
struct equal_to : public binary_function<_Tp, _Tp, bool> {
  bool operator()(const _Tp& __x, const _Tp& __y) const { return __x == __y; }
};

template <class _Tp>
struct less : public binary_function<_Tp,_Tp,bool>





              , public __stlport_class<less<_Tp> >

{
  bool operator()(const _Tp& __x, const _Tp& __y) const { return __x < __y; }






};


template <class _Tp>
struct __type_traits<less<_Tp> > {

  typedef typename _IsSTLportClass<less<_Tp> >::_Ret _STLportLess;




  typedef _STLportLess has_trivial_default_constructor;
  typedef _STLportLess has_trivial_copy_constructor;
  typedef _STLportLess has_trivial_assignment_operator;
  typedef _STLportLess has_trivial_destructor;
  typedef _STLportLess is_POD_type;
};


} namespace NStlPriv {

template <class _Tp>
less<_Tp> __less(_Tp* ) { return less<_Tp>(); }

template <class _Tp>
equal_to<_Tp> __equal_to(_Tp* ) { return equal_to<_Tp>(); }

} namespace NStl {

template <class _Tp>
struct plus : public binary_function<_Tp, _Tp, _Tp> {
  _Tp operator()(const _Tp& __x, const _Tp& __y) const { return __x + __y; }
};

template <class _Tp>
struct minus : public binary_function<_Tp, _Tp, _Tp> {
  _Tp operator()(const _Tp& __x, const _Tp& __y) const { return __x - __y; }
};

} namespace NStlPriv {

template <class _Tp>
plus<_Tp> __plus(_Tp* ) { return plus<_Tp>(); }

template <class _Tp>
minus<_Tp> __minus(_Tp* ) { return minus<_Tp>(); }

} namespace NStl {

template <class _Tp>
struct multiplies : public binary_function<_Tp, _Tp, _Tp> {
  _Tp operator()(const _Tp& __x, const _Tp& __y) const { return __x * __y; }
};

} namespace NStlPriv {

template <class _Pair>
struct _Select1st : public unary_function<_Pair, typename _Pair::first_type> {
  const typename _Pair::first_type& operator()(const _Pair& __x) const {
    return __x.first;
  }
};

template <class _Pair>
struct _Select2nd : public unary_function<_Pair, typename _Pair::second_type> {
  const typename _Pair::second_type& operator()(const _Pair& __x) const {
    return __x.second;
  }
};


template <class _Arg1, class _Arg2>
struct _Project1st : public binary_function<_Arg1, _Arg2, _Arg1> {
  _Arg1 operator()(const _Arg1& __x, const _Arg2&) const { return __x; }
};

template <class _Arg1, class _Arg2>
struct _Project2nd : public binary_function<_Arg1, _Arg2, _Arg2> {
  _Arg2 operator()(const _Arg1&, const _Arg2& __y) const { return __y; }
};
template <class _Tp>
struct _Identity : public unary_function<_Tp,_Tp> {
  const _Tp& operator()(const _Tp& __x) const { return __x; }
};

template <class _Result, class _Argument>
struct _Constant_unary_fun {
  typedef _Argument argument_type;
  typedef _Result result_type;
  result_type _M_val;

  _Constant_unary_fun(const result_type& __v) : _M_val(__v) {}
  const result_type& operator()(const _Argument&) const { return _M_val; }
};

template <class _Result, class _Arg1, class _Arg2>
struct _Constant_binary_fun {
  typedef _Arg1 first_argument_type;
  typedef _Arg2 second_argument_type;
  typedef _Result result_type;
  _Result _M_val;

  _Constant_binary_fun(const _Result& __v) : _M_val(__v) {}
  const result_type& operator()(const _Arg1&, const _Arg2&) const {
    return _M_val;
  }
};


template <class _Tp> inline _Tp __identity_element(plus<_Tp>) { return _Tp(0); }
template <class _Tp> inline _Tp __identity_element(multiplies<_Tp>) { return _Tp(1); }

} namespace NStl {

}







namespace NStl {


template <class _InputIter, class _Function>
inline _Function
for_each(_InputIter __first, _InputIter __last, _Function __f) {
  for ( ; __first != __last; ++__first)
    __f(*__first);
  return __f;
}


template <class _InputIter, class _Predicate>
inline typename iterator_traits<_InputIter>::difference_type
count_if(_InputIter __first, _InputIter __last, _Predicate __pred) {

  typename iterator_traits<_InputIter>::difference_type __n = 0;
  for ( ; __first != __last; ++__first) {
    if (__pred(*__first))
      ++__n;
  }
  return __n;
}



template <class _ForwardIter, class _BinaryPredicate>
inline _ForwardIter
adjacent_find(_ForwardIter __first, _ForwardIter __last,
              _BinaryPredicate __binary_pred) {

  if (__first == __last)
    return __last;
  _ForwardIter __next = __first;
  while(++__next != __last) {
    if (__binary_pred(*__first, *__next))
      return __first;
    __first = __next;
  }
  return __last;
}

template <class _ForwardIter>
inline _ForwardIter
adjacent_find(_ForwardIter __first, _ForwardIter __last) {
  return adjacent_find(__first, __last,
                       ::NStlPriv:: __equal_to((typename iterator_traits< _ForwardIter >::value_type*)0));
}


template <class _InputIter, class _Tp, class _Size>
inline void
count(_InputIter __first, _InputIter __last, const _Tp& __val, _Size& __n) {

    for ( ; __first != __last; ++__first)
      if (*__first == __val)
        ++__n;
}

template <class _InputIter, class _Predicate, class _Size>
inline void
count_if(_InputIter __first, _InputIter __last, _Predicate __pred, _Size& __n) {

  for ( ; __first != __last; ++__first)
    if (__pred(*__first))
      ++__n;
}


template <class _ForwardIter1, class _ForwardIter2>
_ForwardIter1 search(_ForwardIter1 __first1, _ForwardIter1 __last1,
                     _ForwardIter2 __first2, _ForwardIter2 __last2);


template <class _ForwardIter, class _Integer, class _Tp>
_ForwardIter search_n(_ForwardIter __first, _ForwardIter __last,
                      _Integer __count, const _Tp& __val);
template <class _ForwardIter, class _Integer, class _Tp, class _BinaryPred>
_ForwardIter search_n(_ForwardIter __first, _ForwardIter __last,
                      _Integer __count, const _Tp& __val, _BinaryPred __binary_pred);

template <class _InputIter, class _ForwardIter>
inline _InputIter find_first_of(_InputIter __first1, _InputIter __last1,
                                _ForwardIter __first2, _ForwardIter __last2) {


  return ::NStlPriv:: __find_first_of(__first1, __last1, __first2, __last2,
                                    ::NStlPriv:: __equal_to((typename iterator_traits< _InputIter >::value_type*)0));
}

template <class _InputIter, class _ForwardIter, class _BinaryPredicate>
inline _InputIter
find_first_of(_InputIter __first1, _InputIter __last1,
              _ForwardIter __first2, _ForwardIter __last2, _BinaryPredicate __comp) {


  return ::NStlPriv:: __find_first_of(__first1, __last1, __first2, __last2, __comp);
}

template <class _ForwardIter1, class _ForwardIter2>
_ForwardIter1
find_end(_ForwardIter1 __first1, _ForwardIter1 __last1,
         _ForwardIter2 __first2, _ForwardIter2 __last2);


template <class _ForwardIter1, class _ForwardIter2>
inline _ForwardIter2
swap_ranges(_ForwardIter1 __first1, _ForwardIter1 __last1, _ForwardIter2 __first2) {

  for ( ; __first1 != __last1; ++__first1, ++__first2)
    iter_swap(__first1, __first2);
  return __first2;
}


template <class _InputIter, class _OutputIter, class _UnaryOperation>
inline _OutputIter
transform(_InputIter __first, _InputIter __last, _OutputIter __result, _UnaryOperation __opr) {

  for ( ; __first != __last; ++__first, ++__result)
    *__result = __opr(*__first);
  return __result;
}
template <class _InputIter1, class _InputIter2, class _OutputIter, class _BinaryOperation>
inline _OutputIter
transform(_InputIter1 __first1, _InputIter1 __last1,
          _InputIter2 __first2, _OutputIter __result,_BinaryOperation __binary_op) {

  for ( ; __first1 != __last1; ++__first1, ++__first2, ++__result)
    *__result = __binary_op(*__first1, *__first2);
  return __result;
}



template <class _ForwardIter, class _Predicate, class _Tp>
inline void
replace_if(_ForwardIter __first, _ForwardIter __last, _Predicate __pred, const _Tp& __new_value) {

  for ( ; __first != __last; ++__first)
    if (__pred(*__first))
      *__first = __new_value;
}

template <class _InputIter, class _OutputIter, class _Tp>
inline _OutputIter
replace_copy(_InputIter __first, _InputIter __last,_OutputIter __result,
             const _Tp& __old_value, const _Tp& __new_value) {

  for ( ; __first != __last; ++__first, ++__result)
    *__result = *__first == __old_value ? __new_value : *__first;
  return __result;
}

template <class _Iterator, class _OutputIter, class _Predicate, class _Tp>
inline _OutputIter
replace_copy_if(_Iterator __first, _Iterator __last,
                _OutputIter __result,
                _Predicate __pred, const _Tp& __new_value) {

  for ( ; __first != __last; ++__first, ++__result)
    *__result = __pred(*__first) ? __new_value : *__first;
  return __result;
}



template <class _ForwardIter, class _Generator>
inline void
generate(_ForwardIter __first, _ForwardIter __last, _Generator __gen) {

  for ( ; __first != __last; ++__first)
    *__first = __gen();
}

template <class _OutputIter, class _Size, class _Generator>
inline void
generate_n(_OutputIter __first, _Size __n, _Generator __gen) {
  for ( ; __n > 0; --__n, ++__first)
    *__first = __gen();
}



template <class _InputIter, class _OutputIter, class _Tp>
inline _OutputIter
remove_copy(_InputIter __first, _InputIter __last,_OutputIter __result, const _Tp& __val) {

  for ( ; __first != __last; ++__first) {
    if (!(*__first == __val)) {
      *__result = *__first;
      ++__result;
    }
  }
  return __result;
}

template <class _InputIter, class _OutputIter, class _Predicate>
inline _OutputIter
remove_copy_if(_InputIter __first, _InputIter __last, _OutputIter __result, _Predicate __pred) {

  for ( ; __first != __last; ++__first) {
    if (!__pred(*__first)) {
      *__result = *__first;
      ++__result;
    }
  }
  return __result;
}

template <class _ForwardIter, class _Tp>
inline _ForwardIter
remove(_ForwardIter __first, _ForwardIter __last, const _Tp& __val) {

  __first = find(__first, __last, __val);
  if (__first == __last)
    return __first;
  else {
    _ForwardIter __next = __first;
    return remove_copy(++__next, __last, __first, __val);
  }
}

template <class _ForwardIter, class _Predicate>
inline _ForwardIter
remove_if(_ForwardIter __first, _ForwardIter __last, _Predicate __pred) {

  __first = find_if(__first, __last, __pred);
  if ( __first == __last )
    return __first;
  else {
    _ForwardIter __next = __first;
    return remove_copy_if(++__next, __last, __first, __pred);
  }
}


template <class _InputIter, class _OutputIter>
_OutputIter unique_copy(_InputIter __first, _InputIter __last, _OutputIter __result);

template <class _InputIter, class _OutputIter, class _BinaryPredicate>
_OutputIter unique_copy(_InputIter __first, _InputIter __last,_OutputIter __result,
                        _BinaryPredicate __binary_pred);

template <class _ForwardIter>
inline _ForwardIter unique(_ForwardIter __first, _ForwardIter __last) {
  __first = adjacent_find(__first, __last);
  return unique_copy(__first, __last, __first);
}

template <class _ForwardIter, class _BinaryPredicate>
inline _ForwardIter unique(_ForwardIter __first, _ForwardIter __last,
                           _BinaryPredicate __binary_pred) {
  __first = adjacent_find(__first, __last, __binary_pred);
  return unique_copy(__first, __last, __first, __binary_pred);
}



template <class _BidirectionalIter>
inline void
__reverse(_BidirectionalIter __first, _BidirectionalIter __last, const bidirectional_iterator_tag &) {
  for (; __first != __last && __first != --__last; ++__first)
    iter_swap(__first,__last);
}


template <class _RandomAccessIter>
inline void
__reverse(_RandomAccessIter __first, _RandomAccessIter __last, const random_access_iterator_tag &) {
  for (; __first < __last; ++__first)
    iter_swap(__first, --__last);
}

template <class _BidirectionalIter>
inline void
reverse(_BidirectionalIter __first, _BidirectionalIter __last) {

  __reverse(__first, __last, typename iterator_traits< _BidirectionalIter >::iterator_category());
}

template <class _BidirectionalIter, class _OutputIter>
inline
_OutputIter reverse_copy(_BidirectionalIter __first,
                         _BidirectionalIter __last,
                         _OutputIter __result) {

  while (__first != __last) {
    --__last;
    *__result = *__last;
    ++__result;
  }
  return __result;
}

} namespace NStlPriv {


template <class _EuclideanRingElement>
inline
_EuclideanRingElement __gcd(_EuclideanRingElement __m,
                            _EuclideanRingElement __n) {
  while (__n != 0) {
    _EuclideanRingElement __t = __m % __n;
    __m = __n;
    __n = __t;
  }
  return __m;
}

} namespace NStl {

template <class _ForwardIter>
void rotate(_ForwardIter __first, _ForwardIter __middle, _ForwardIter __last);

template <class _ForwardIter, class _OutputIter>
inline _OutputIter rotate_copy(_ForwardIter __first, _ForwardIter __middle,
                               _ForwardIter __last, _OutputIter __result) {
  return copy(__first, __middle, copy(__middle, __last, __result));
}



template <class _RandomAccessIter>
void random_shuffle(_RandomAccessIter __first, _RandomAccessIter __last);

template <class _RandomAccessIter, class _RandomNumberGenerator>
void random_shuffle(_RandomAccessIter __first, _RandomAccessIter __last,
                    _RandomNumberGenerator& __rand);




template <class _ForwardIter, class _OutputIter, class _Distance>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out_ite, const _Distance __n);

template <class _ForwardIter, class _OutputIter, class _Distance,
          class _RandomNumberGenerator>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out_ite, const _Distance __n,
                            _RandomNumberGenerator& __rand);

template <class _InputIter, class _RandomAccessIter>
_RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last);

template <class _InputIter, class _RandomAccessIter,
          class _RandomNumberGenerator>
_RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last,
              _RandomNumberGenerator& __rand);





template <class _ForwardIter, class _Predicate>
_ForwardIter partition(_ForwardIter __first, _ForwardIter __last, _Predicate __pred);

template <class _ForwardIter, class _Predicate>
_ForwardIter
stable_partition(_ForwardIter __first, _ForwardIter __last, _Predicate __pred);


} namespace NStlPriv {

template <class _Size>
inline _Size __lg(_Size __n) {
  _Size __k;
  for (__k = 0; __n != 1; __n >>= 1) ++__k;
  return __k;
}

} namespace NStl {

template <class _RandomAccessIter>
void sort(_RandomAccessIter __first, _RandomAccessIter __last);
template <class _RandomAccessIter, class _Compare>
void sort(_RandomAccessIter __first, _RandomAccessIter __last, _Compare __comp);


template <class _RandomAccessIter>
void stable_sort(_RandomAccessIter __first,
                 _RandomAccessIter __last);

template <class _RandomAccessIter, class _Compare>
void stable_sort(_RandomAccessIter __first,
                 _RandomAccessIter __last, _Compare __comp);



template <class _RandomAccessIter>
void partial_sort(_RandomAccessIter __first, _RandomAccessIter __middle,
                  _RandomAccessIter __last);

template <class _RandomAccessIter, class _Compare>
void partial_sort(_RandomAccessIter __first,_RandomAccessIter __middle,
                  _RandomAccessIter __last, _Compare __comp);

template <class _InputIter, class _RandomAccessIter>
_RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first, _RandomAccessIter __result_last);

template <class _InputIter, class _RandomAccessIter, class _Compare>
_RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last, _Compare __comp);


template <class _RandomAccessIter>
void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                 _RandomAccessIter __last);

template <class _RandomAccessIter, class _Compare>
void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                 _RandomAccessIter __last, _Compare __comp);


} namespace NStlPriv {

template <class _T1, class _T2>
struct __less_2 {
  bool operator() (const _T1& __x, const _T2& __y) const { return __x < __y ; }
};

template <class _T1, class _T2>
__less_2<_T1,_T2> __less2(_T1*, _T2* ) { return __less_2<_T1, _T2>(); }






} namespace NStl {


template <class _ForwardIter, class _Tp>
inline _ForwardIter lower_bound(_ForwardIter __first, _ForwardIter __last,
                                   const _Tp& __val) {

  return ::NStlPriv:: __lower_bound(__first, __last, __val,
                                  ::NStlPriv:: __less2((typename iterator_traits< _ForwardIter >::value_type*)0, (_Tp*)0),
                                  ::NStlPriv:: __less2((_Tp*)0, (typename iterator_traits< _ForwardIter >::value_type*)0),
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

template <class _ForwardIter, class _Tp, class _Compare>
inline _ForwardIter lower_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val, _Compare __comp) {

  return ::NStlPriv:: __lower_bound(__first, __last, __val, __comp, __comp,
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

} namespace NStlPriv {

template <class _ForwardIter, class _Tp, class _Compare1, class _Compare2, class _Distance>
_ForwardIter __upper_bound(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
                           _Compare1 __comp1, _Compare2 __comp2, _Distance*);

} namespace NStl {

template <class _ForwardIter, class _Tp>
inline _ForwardIter upper_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val) {

  return ::NStlPriv:: __upper_bound(__first, __last, __val,
                                  ::NStlPriv:: __less2((typename iterator_traits< _ForwardIter >::value_type*)0, (_Tp*)0),
                                  ::NStlPriv:: __less2((_Tp*)0, (typename iterator_traits< _ForwardIter >::value_type*)0),
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

template <class _ForwardIter, class _Tp, class _Compare>
inline _ForwardIter upper_bound(_ForwardIter __first, _ForwardIter __last,
                                const _Tp& __val, _Compare __comp) {

  return ::NStlPriv:: __upper_bound(__first, __last, __val, __comp, __comp,
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

} namespace NStlPriv {

template <class _ForwardIter, class _Tp, class _Compare1, class _Compare2, class _Distance>
pair<_ForwardIter, _ForwardIter>
__equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
              _Compare1 __comp1, _Compare2 __comp2, _Distance*);

} namespace NStl {

template <class _ForwardIter, class _Tp>
inline pair<_ForwardIter, _ForwardIter>
equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val) {

  return ::NStlPriv:: __equal_range(__first, __last, __val,
                                  ::NStlPriv:: __less2((typename iterator_traits< _ForwardIter >::value_type*)0, (_Tp*)0),
                                  ::NStlPriv:: __less2((_Tp*)0, (typename iterator_traits< _ForwardIter >::value_type*)0),
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

template <class _ForwardIter, class _Tp, class _Compare>
inline pair<_ForwardIter, _ForwardIter>
equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
            _Compare __comp) {

  return ::NStlPriv:: __equal_range(__first, __last, __val, __comp, __comp,
                                  (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

template <class _ForwardIter, class _Tp>
inline bool binary_search(_ForwardIter __first, _ForwardIter __last,
                   const _Tp& __val) {

  _ForwardIter __i = ::NStlPriv:: __lower_bound(__first, __last, __val,
                                              ::NStlPriv:: __less2((typename iterator_traits< _ForwardIter >::value_type*)0, (_Tp*)0),
                                              ::NStlPriv:: __less2((_Tp*)0, (typename iterator_traits< _ForwardIter >::value_type*)0),
                                              (typename iterator_traits< _ForwardIter >::difference_type*)0);
  return __i != __last && !(__val < *__i);
}

template <class _ForwardIter, class _Tp, class _Compare>
inline bool binary_search(_ForwardIter __first, _ForwardIter __last,
                          const _Tp& __val,
                          _Compare __comp) {

  _ForwardIter __i = ::NStlPriv:: __lower_bound(__first, __last, __val, __comp, __comp,
                                              (typename iterator_traits< _ForwardIter >::difference_type*)0);
  return __i != __last && !__comp(__val, *__i);
}



template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result);

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result, _Compare __comp);





template <class _BidirectionalIter>
void inplace_merge(_BidirectionalIter __first,
                   _BidirectionalIter __middle,
                   _BidirectionalIter __last) ;

template <class _BidirectionalIter, class _Compare>
void inplace_merge(_BidirectionalIter __first,
                   _BidirectionalIter __middle,
                   _BidirectionalIter __last, _Compare __comp);






template <class _InputIter1, class _InputIter2>
bool includes(_InputIter1 __first1, _InputIter1 __last1,
              _InputIter2 __first2, _InputIter2 __last2);

template <class _InputIter1, class _InputIter2, class _Compare>
bool includes(_InputIter1 __first1, _InputIter1 __last1,
              _InputIter2 __first2, _InputIter2 __last2, _Compare __comp);

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_union(_InputIter1 __first1, _InputIter1 __last1,
                      _InputIter2 __first2, _InputIter2 __last2,
                      _OutputIter __result);

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_union(_InputIter1 __first1, _InputIter1 __last1,
                      _InputIter2 __first2, _InputIter2 __last2,
                      _OutputIter __result, _Compare __comp);

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_intersection(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _OutputIter __result);

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_intersection(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _OutputIter __result, _Compare __comp);



template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_difference(_InputIter1 __first1, _InputIter1 __last1,
                           _InputIter2 __first2, _InputIter2 __last2,
                           _OutputIter __result);

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_difference(_InputIter1 __first1, _InputIter1 __last1,
                           _InputIter2 __first2, _InputIter2 __last2,
                           _OutputIter __result, _Compare __comp);

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter
set_symmetric_difference(_InputIter1 __first1, _InputIter1 __last1,
                         _InputIter2 __first2, _InputIter2 __last2,
                         _OutputIter __result);


template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter
set_symmetric_difference(_InputIter1 __first1, _InputIter1 __last1,
                         _InputIter2 __first2, _InputIter2 __last2,
                         _OutputIter __result,
                         _Compare __comp);





template <class _ForwardIter>
_ForwardIter max_element(_ForwardIter __first, _ForwardIter __last);
template <class _ForwardIter, class _Compare>
_ForwardIter max_element(_ForwardIter __first, _ForwardIter __last,
                            _Compare __comp);

template <class _ForwardIter>
_ForwardIter min_element(_ForwardIter __first, _ForwardIter __last);

template <class _ForwardIter, class _Compare>
_ForwardIter min_element(_ForwardIter __first, _ForwardIter __last,
                            _Compare __comp);




template <class _BidirectionalIter>
bool next_permutation(_BidirectionalIter __first, _BidirectionalIter __last);

template <class _BidirectionalIter, class _Compare>
bool next_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                      _Compare __comp);


template <class _BidirectionalIter>
bool prev_permutation(_BidirectionalIter __first, _BidirectionalIter __last);


template <class _BidirectionalIter, class _Compare>
bool prev_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                      _Compare __comp);






template <class _RandomAccessIter>
bool is_heap(_RandomAccessIter __first, _RandomAccessIter __last);

template <class _RandomAccessIter, class _StrictWeakOrdering>
bool is_heap(_RandomAccessIter __first, _RandomAccessIter __last,
             _StrictWeakOrdering __comp);




} namespace NStlPriv {

template <class _ForwardIter, class _StrictWeakOrdering>
bool __is_sorted(_ForwardIter __first, _ForwardIter __last,
                 _StrictWeakOrdering __comp);

} namespace NStl {
template <class _ForwardIter>
inline bool is_sorted(_ForwardIter __first, _ForwardIter __last) {
  return ::NStlPriv:: __is_sorted(__first, __last,
                                ::NStlPriv:: __less((typename iterator_traits< _ForwardIter >::value_type*)0));
}

template <class _ForwardIter, class _StrictWeakOrdering>
inline bool is_sorted(_ForwardIter __first, _ForwardIter __last,
                      _StrictWeakOrdering __comp) {
  return ::NStlPriv:: __is_sorted(__first, __last, __comp);
}


}








extern "C++" {

namespace std
{
  class exception
  {
  public:
    exception() throw() { }
    virtual ~exception() throw();



    virtual const char* what() const throw();
  };



  class bad_exception : public exception
  {
  public:
    bad_exception() throw() { }



    virtual ~bad_exception() throw();


    virtual const char* what() const throw();
  };


  typedef void (*terminate_handler) ();


  typedef void (*unexpected_handler) ();


  terminate_handler set_terminate(terminate_handler) throw();



  void terminate() __attribute__ ((__noreturn__));


  unexpected_handler set_unexpected(unexpected_handler) throw();



  void unexpected() __attribute__ ((__noreturn__));
  bool uncaught_exception() throw();


}

namespace __gnu_cxx __attribute__ ((__visibility__ ("default"))) {
  void __verbose_terminate_handler();

}

}



extern "C++" {

namespace std
{






  class bad_alloc : public exception
  {
  public:
    bad_alloc() throw() { }



    virtual ~bad_alloc() throw();


    virtual const char* what() const throw();
  };

  struct nothrow_t { };

  extern const nothrow_t nothrow;



  typedef void (*new_handler)();



  new_handler set_new_handler(new_handler) throw();
}
void* operator new(std::size_t) throw (std::bad_alloc);
void* operator new[](std::size_t) throw (std::bad_alloc);
void operator delete(void*) throw();
void operator delete[](void*) throw();
void* operator new(std::size_t, const std::nothrow_t&) throw();
void* operator new[](std::size_t, const std::nothrow_t&) throw();
void operator delete(void*, const std::nothrow_t&) throw();
void operator delete[](void*, const std::nothrow_t&) throw();


inline void* operator new(std::size_t, void* __p) throw() { return __p; }
inline void* operator new[](std::size_t, void* __p) throw() { return __p; }


inline void operator delete (void*, void*) throw() { }
inline void operator delete[](void*, void*) throw() { }

}

namespace NStl {


using __std_alias::bad_alloc;



using __std_alias::nothrow_t;
using __std_alias::nothrow;




using __std_alias::new_handler;
using __std_alias::set_new_handler;



}
namespace NStl {





inline void* __stl_new(size_t __n) { return ::operator new(__n); }
inline void __stl_delete(void* __p) { ::operator delete(__p); }

}
namespace NStl {

template <class _Tp>
inline void __destroy_aux(_Tp* __pointer, const __false_type& )
{ __pointer->~_Tp(); }

template <class _Tp>
inline void __destroy_aux(_Tp*, const __true_type& ) {}

template <class _Tp>
inline void _Destroy(_Tp* __pointer) {



  typedef typename __type_traits<_Tp>::has_trivial_destructor _Trivial_destructor;
  __destroy_aux(__pointer, _Trivial_destructor());



}

template <class _Tp>
inline void _Destroy_Moved(_Tp* __pointer) {
  typedef typename __move_traits<_Tp>::complete _Trivial_destructor;
  __destroy_aux(__pointer, _Trivial_destructor());



}
template <class _T1>
inline void _Construct(_T1* __p) {






  new (__p) _T1();

}

template <class _T1>
inline void _ConstructNoFill(_T1* __p) {






    new (__p) _T1;

}

template <class _Tp, class _Targ>
inline void _Copy_Construct(_Tp* __p, const _Targ& __val) {



  new (__p) _Tp(__val);
}

template <class _T1, class _T2>
inline void _Param_Construct(_T1* __p, const _T2& __val) {



  new (__p) _T1(__val);
}

template <class _T1, class _T2>
inline void _Move_Construct_Aux(_T1* __p, _T2& __val, const __false_type& ) {
  new (__p) _T1(::NStlPriv:: _AsMoveSource(__val));
}

template <class _T1, class _T2>
inline void _Move_Construct_Aux(_T1* __p, _T2& __val, const __true_type& ) {
  new (__p) _T1(__val);
}

template <class _T1, class _T2>
inline void _Move_Construct(_T1* __p, _T2& __val) {



  _Move_Construct_Aux(__p, __val, _Is_POD(__p)._Answer());
}
template <class _ForwardIterator, class _Tp>
inline void
__destroy_range_aux(_ForwardIterator __first, _ForwardIterator __last, _Tp*, const __false_type& ) {
  for ( ; __first != __last; ++__first) {
    __destroy_aux(&(*__first), __false_type());



  }
}

template <class _ForwardIterator, class _Tp>







inline void
__destroy_range_aux(_ForwardIterator, _ForwardIterator, _Tp*, const __true_type& ) {}


template <class _ForwardIterator, class _Tp>
inline void
__destroy_range(_ForwardIterator __first, _ForwardIterator __last, _Tp *__ptr) {
  typedef typename __type_traits<_Tp>::has_trivial_destructor _Trivial_destructor;
  __destroy_range_aux(__first, __last, __ptr, _Trivial_destructor());
}

template <class _ForwardIterator>
inline void _Destroy_Range(_ForwardIterator __first, _ForwardIterator __last) {
  __destroy_range(__first, __last, (typename iterator_traits< _ForwardIterator >::value_type*)0);
}

inline void _Destroy_Range(char*, char*) {}

inline void _Destroy_Range(wchar_t*, wchar_t*) {}
inline void _Destroy_Range(const wchar_t*, const wchar_t*) {}


template <class _ForwardIterator, class _Tp>
inline void
__destroy_mv_srcs(_ForwardIterator __first, _ForwardIterator __last, _Tp *__ptr) {
  typedef typename __move_traits<_Tp>::complete _CompleteMove;
  __destroy_range_aux(__first, __last, __ptr, _CompleteMove());
}

template <class _ForwardIterator>
inline void _Destroy_Moved_Range(_ForwardIterator __first, _ForwardIterator __last) {
  __destroy_mv_srcs(__first, __last, (typename iterator_traits< _ForwardIterator >::value_type*)0);
}
template <class _T1, class _T2>
inline void construct(_T1* __p, const _T2& __val) {_Param_Construct(__p, __val); }
template <class _T1>
inline void construct(_T1* __p) { ::NStl::_Construct(__p); }
template <class _Tp>
inline void destroy(_Tp* __pointer) { ::NStl::_Destroy(__pointer); }
template <class _ForwardIterator>
inline void destroy(_ForwardIterator __first, _ForwardIterator __last) { ::NStl::_Destroy_Range(__first, __last); }


}


namespace NStl {

} namespace NStlPriv {



template <class _InputIter, class _OutputIter, class _Distance>
inline _OutputIter __ucopy(_InputIter __first, _InputIter __last,
                           _OutputIter __result, _Distance*) {
  _OutputIter __cur = __result;
  try {
    for ( ; __first != __last; ++__first, ++__cur)
      _Param_Construct(&*__cur, *__first);
    return __cur;
  }
  catch(...) { ::NStl::_Destroy_Range(__result, __cur); throw; }

}

template <class _InputIter, class _OutputIter, class _Distance>
inline _OutputIter __ucopy(_InputIter __first, _InputIter __last,
                           _OutputIter __result, const input_iterator_tag &, _Distance* __d)
{ return __ucopy(__first, __last, __result, __d); }
template <class _RandomAccessIter, class _OutputIter, class _Distance>
inline _OutputIter __ucopy(_RandomAccessIter __first, _RandomAccessIter __last,
                           _OutputIter __result, const random_access_iterator_tag &, _Distance*) {
  _OutputIter __cur = __result;
  try {
    for (_Distance __n = __last - __first; __n > 0; --__n) {
      _Param_Construct(&*__cur, *__first);
      ++__first;
      ++__cur;
    }
    return __cur;
  }
  catch(...) { ::NStl::_Destroy_Range(__result, __cur); throw; }

}


template <class _RandomAccessIter, class _OutputIter>
inline _OutputIter __ucopy(_RandomAccessIter __first, _RandomAccessIter __last, _OutputIter __result)
{ return __ucopy(__first, __last, __result, random_access_iterator_tag(), (ptrdiff_t*)0); }

inline void*
__ucopy_trivial(const void* __first, const void* __last, void* __result) {

  return (__last == __first) ? __result :
    ((char*)memcpy(__result, __first, ((const char*)__last - (const char*)__first))) +
    ((const char*)__last - (const char*)__first);
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __ucopy_ptrs(_InputIter __first, _InputIter __last, _OutputIter __result,
                                const __false_type& )
{ return __ucopy(__first, __last, __result, random_access_iterator_tag(), (ptrdiff_t*)0); }

template <class _InputIter, class _OutputIter>
inline _OutputIter __ucopy_ptrs(_InputIter __first, _InputIter __last, _OutputIter __result,
                                const __true_type& ) {


  return (_OutputIter)__ucopy_trivial(__first, __last, __result);
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __ucopy_aux(_InputIter __first, _InputIter __last, _OutputIter __result,
                               const __true_type& ) {
  return __ucopy_ptrs(__first, __last, __result,
                      _UseTrivialUCopy((typename iterator_traits< _InputIter >::value_type*)0,
                                       (typename iterator_traits< _OutputIter >::value_type*)0)._Answer());
}

template <class _InputIter, class _OutputIter>
inline _OutputIter __ucopy_aux(_InputIter __first, _InputIter __last, _OutputIter __result,
                               const __false_type& ) {
  return __ucopy(__first, __last, __result,
                 typename iterator_traits< _InputIter >::iterator_category(),
                 (typename iterator_traits< _InputIter >::difference_type*)0);
}

} namespace NStl {

template <class _InputIter, class _ForwardIter>
inline _ForwardIter
uninitialized_copy(_InputIter __first, _InputIter __last, _ForwardIter __result)
{ return ::NStlPriv:: __ucopy_aux(__first, __last, __result, _BothPtrType< _InputIter, _ForwardIter>::_Answer()); }

inline char*
uninitialized_copy(const char* __first, const char* __last, char* __result)
{ return (char*)::NStlPriv:: __ucopy_trivial(__first, __last, __result); }


inline wchar_t*
uninitialized_copy(const wchar_t* __first, const wchar_t* __last, wchar_t* __result)
{ return (wchar_t*)::NStlPriv:: __ucopy_trivial (__first, __last, __result); }



} namespace NStlPriv {

template <class _InputIter, class _Size, class _ForwardIter>
inline
pair<_InputIter, _ForwardIter>
__ucopy_n(_InputIter __first, _Size __count, _ForwardIter __result,
          const input_iterator_tag &) {
  _ForwardIter __cur = __result;
  try {
    for ( ; __count > 0 ; --__count, ++__first, ++__cur)
      _Param_Construct(&*__cur, *__first);
    return pair<_InputIter, _ForwardIter>(__first, __cur);
  }
  catch(...) { ::NStl::_Destroy_Range(__result, __cur); throw; }

}
template <class _RandomAccessIter, class _Size, class _ForwardIter>
inline pair<_RandomAccessIter, _ForwardIter>
__ucopy_n(_RandomAccessIter __first, _Size __count, _ForwardIter __result,
                       const random_access_iterator_tag &) {
  _RandomAccessIter __last = __first + __count;
  return pair<_RandomAccessIter, _ForwardIter>(__last, uninitialized_copy(__first, __last, __result));
}


template <class _InputIter, class _Size, class _ForwardIter>
inline pair<_InputIter, _ForwardIter>
__ucopy_n(_InputIter __first, _Size __count, _ForwardIter __result)
{ return ::NStlPriv:: __ucopy_n(__first, __count, __result, typename iterator_traits< _InputIter >::iterator_category()); }



} namespace NStl {

template <class _InputIter, class _Size, class _ForwardIter>
inline pair<_InputIter, _ForwardIter>
uninitialized_copy_n(_InputIter __first, _Size __count, _ForwardIter __result)
{ return ::NStlPriv:: __ucopy_n(__first, __count, __result); }

} namespace NStlPriv {



template <class _ForwardIter, class _Tp, class _Distance>
inline void __ufill(_ForwardIter __first, _ForwardIter __last, const _Tp& __x, _Distance*) {
  _ForwardIter __cur = __first;
  try {
    for ( ; __cur != __last; ++__cur)
      _Param_Construct(&*__cur, __x);
  }
  catch(...) { ::NStl::_Destroy_Range(__first, __cur); throw; }
}

template <class _ForwardIter, class _Tp, class _Distance>
inline void __ufill(_ForwardIter __first, _ForwardIter __last,
                    const _Tp& __x, const input_iterator_tag &, _Distance* __d)
{ __ufill(__first, __last, __x, __d); }
template <class _ForwardIter, class _Tp, class _Distance>
inline void __ufill(_ForwardIter __first, _ForwardIter __last,
                    const _Tp& __x, const random_access_iterator_tag &, _Distance*) {
  _ForwardIter __cur = __first;
  try {
    for (_Distance __n = __last - __first; __n > 0; --__n, ++__cur)
      _Param_Construct(&*__cur, __x);
  }
  catch(...) { ::NStl::_Destroy_Range(__first, __cur); throw; }
}

} namespace NStl {

template <class _ForwardIter, class _Tp>
inline void uninitialized_fill(_ForwardIter __first, _ForwardIter __last, const _Tp& __x) {
  ::NStlPriv:: __ufill(__first, __last, __x,
                     typename iterator_traits< _ForwardIter >::iterator_category(),
                     (typename iterator_traits< _ForwardIter >::difference_type*)0);
}


inline void uninitialized_fill(unsigned char* __first, unsigned char* __last,
                               const unsigned char& __val) {
  unsigned char __tmp = __val;
  memset(__first, __tmp, __last - __first);
}

inline void uninitialized_fill(signed char* __first, signed char* __last,
                               const signed char& __val) {
  signed char __tmp = __val;
  memset(__first, static_cast<unsigned char>(__tmp), __last - __first);
}

inline void uninitialized_fill(char* __first, char* __last, const char& __val) {
  char __tmp = __val;
  memset(__first, static_cast<unsigned char>(__tmp), __last - __first);
}

} namespace NStlPriv {

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __ufill_n(_ForwardIter __first, _Size __n, const _Tp& __x) {
  _ForwardIter __cur = __first;
  try {
    for ( ; __n > 0; --__n, ++__cur)
      _Param_Construct(&*__cur, __x);
  }
  catch(...) { ::NStl::_Destroy_Range(__first, __cur); throw; }
  return __cur;
}

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __ufill_n(_ForwardIter __first, _Size __n, const _Tp& __x,
                              const input_iterator_tag &)
{ return __ufill_n(__first, __n, __x); }
template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uninitialized_fill_n(_ForwardIter __first, _Size __n, const _Tp& __x) {
  _ForwardIter __last = __first + __n;
  __ufill(__first, __last, __x, random_access_iterator_tag(), (ptrdiff_t*)0);
  return __last;
}

template <class _ForwardIter, class _Size>
inline _ForwardIter uninitialized_fill_n_nofill(_ForwardIter __first, _Size __n) {
    _ForwardIter __cur = __first;
    for ( ; __n > 0; --__n, ++__cur)
        _ConstructNoFill(&*__cur);
    return __cur;
}

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __ufill_n(_ForwardIter __first, _Size __n, const _Tp& __x,
                              const random_access_iterator_tag &)
{ return __uninitialized_fill_n(__first, __n, __x); }





template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uinit_aux_aux(_ForwardIter __first, _Size __n, const _Tp& __val,
                                    const __false_type& )
{ return __uninitialized_fill_n(__first, __n, __val); }

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uinit_aux_aux(_ForwardIter __first, _Size __n, const _Tp& __val,
                                    const __true_type& ) {
  (void)__val;

  if (!(__builtin_constant_p(__n) && __n == 0))

    memset((unsigned char*)__first, 0, __n * sizeof(_Tp));
  return __first + __n;
}

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uinit_aux(_ForwardIter __first, _Size __n, const _Tp&,
                                const __true_type& )
{ return __first + __n; }

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uinit_aux(_ForwardIter __first, _Size __n, const _Tp& __val,
                                const __false_type& )
{ return __uinit_aux_aux(__first, __n, __val, _HasDefaultZeroValue(__first)._Answer()); }

template <class _ForwardIter, class _Size, class _Tp>
inline _ForwardIter __uninitialized_init(_ForwardIter __first, _Size __n, const _Tp& __val)
{ return __uinit_aux(__first, __n, __val, _UseTrivialInit(__first)._Answer()); }

} namespace NStl {

template <class _ForwardIter, class _Size, class _Tp>
inline void
uninitialized_fill_n(_ForwardIter __first, _Size __n, const _Tp& __x)
{ ::NStlPriv:: __ufill_n(__first, __n, __x, typename iterator_traits< _ForwardIter >::iterator_category()); }
} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _ForwardIter>
inline _ForwardIter
__uninitialized_copy_copy(_InputIter1 __first1, _InputIter1 __last1,
                          _InputIter2 __first2, _InputIter2 __last2,
                          _ForwardIter __result)
{ return uninitialized_copy(__first2, __last2, uninitialized_copy(__first1, __last1, __result)); }




template <class _ForwardIter, class _Tp, class _InputIter>
inline _ForwardIter
__uninitialized_fill_copy(_ForwardIter __result, _ForwardIter __mid, const _Tp& __x,
                          _InputIter __first, _InputIter __last) {
  uninitialized_fill(__result, __mid, __x);
  try {
    return uninitialized_copy(__first, __last, __mid);
  }
  catch(...) { ::NStl::_Destroy_Range(__result, __mid); throw; }

}




template <class _Iter, class _Tp>
inline void
__uninitialized_copy_fill(_Iter __first1, _Iter __last1, _Iter __first2, _Iter __last2,
                          const _Tp& __x) {
  _Iter __mid2 = uninitialized_copy(__first1, __last1, __first2);
  try {
    uninitialized_fill(__mid2, __last2, __x);
  }
  catch(...) { ::NStl::_Destroy_Range(__first2, __mid2); throw; }
}




template <class _InputIter, class _ForwardIter, class _TrivialUCpy>
inline _ForwardIter
__uninitialized_move(_InputIter __first, _InputIter __last, _ForwardIter __result,
                     _TrivialUCpy __trivial_ucpy, const __false_type& )
{ return __ucopy_ptrs(__first, __last, __result, __trivial_ucpy); }

template <class _InputIter, class _ForwardIter, class _TrivialUCpy>
inline
_ForwardIter
__uninitialized_move(_InputIter __first, _InputIter __last, _ForwardIter __result,
                     _TrivialUCpy , const __true_type& ) {

  for (ptrdiff_t __n = __last - __first ; __n > 0; --__n) {
    _Move_Construct(&*__result, *__first);
    ++__first; ++__result;
  }
  return __result;
}

} namespace NStl {

}


namespace NStl {

template <class _Tp>
pair<_Tp*, ptrdiff_t>
__get_temporary_buffer(ptrdiff_t __len, _Tp*);



template <class _Tp>
inline pair<_Tp*, ptrdiff_t> get_temporary_buffer(ptrdiff_t __len) {
  return __get_temporary_buffer(__len, (_Tp*) 0);
}







template <class _Tp>
inline pair<_Tp*, ptrdiff_t>
get_temporary_buffer(ptrdiff_t __len, _Tp*) {
  return __get_temporary_buffer(__len, (_Tp*) 0);
}



template <class _Tp>
inline void return_temporary_buffer(_Tp* __p) {

  free((char*)__p);
}

template <class _ForwardIterator, class _Tp>
class _Temporary_buffer {
private:
  ptrdiff_t _M_original_len;
  ptrdiff_t _M_len;
  _Tp* _M_buffer;

  void _M_allocate_buffer() {
    _M_original_len = _M_len;
    _M_buffer = 0;

    if (_M_len > (ptrdiff_t)(2147483647 / sizeof(_Tp)))
      _M_len = 2147483647 / sizeof(_Tp);

    while (_M_len > 0) {
      _M_buffer = (_Tp*) malloc(_M_len * sizeof(_Tp));
      if (_M_buffer)
        break;
      _M_len /= 2;
    }
  }

  void _M_initialize_buffer(const _Tp&, const __true_type&) {}
  void _M_initialize_buffer(const _Tp& val, const __false_type&) {
    uninitialized_fill_n(_M_buffer, _M_len, val);
  }

public:
  ptrdiff_t size() const { return _M_len; }
  ptrdiff_t requested_size() const { return _M_original_len; }
  _Tp* begin() { return _M_buffer; }
  _Tp* end() { return _M_buffer + _M_len; }

  _Temporary_buffer(_ForwardIterator __first, _ForwardIterator __last) {




    typedef typename __type_traits<_Tp>::has_trivial_default_constructor _Trivial;

    try {
      _M_len = distance(__first, __last);
      _M_allocate_buffer();
      if (_M_len > 0)
        _M_initialize_buffer(*__first, _Trivial());
    }
    catch(...) { free(_M_buffer); _M_buffer = 0; _M_len = 0; throw; }
  }

  ~_Temporary_buffer() {
    ::NStl::_Destroy_Range(_M_buffer, _M_buffer + _M_len);
    free(_M_buffer);
  }

private:

  _Temporary_buffer(const _Temporary_buffer<_ForwardIterator, _Tp>&) {}
  void operator=(const _Temporary_buffer<_ForwardIterator, _Tp>&) {}
};





template <class _ForwardIterator,
          class _Tp

                    = typename iterator_traits<_ForwardIterator>::value_type

         >
struct temporary_buffer : public _Temporary_buffer<_ForwardIterator, _Tp>
{
  temporary_buffer(_ForwardIterator __first, _ForwardIterator __last)
    : _Temporary_buffer<_ForwardIterator, _Tp>(__first, __last) {}
  ~temporary_buffer() {}
};



}


namespace NStl {

template <class _Tp>
pair<_Tp*, ptrdiff_t>
__get_temporary_buffer(ptrdiff_t __len, _Tp*)
{
  if (__len > ptrdiff_t(2147483647 / sizeof(_Tp)))
    __len = 2147483647 / sizeof(_Tp);

  while (__len > 0) {
    _Tp* __tmp = (_Tp*) malloc((size_t)__len * sizeof(_Tp));
    if (__tmp != 0)
      return pair<_Tp*, ptrdiff_t>(__tmp, __len);
    __len /= 2;
  }

  return pair<_Tp*, ptrdiff_t>((_Tp*)0, 0);
}
}


namespace NStl {

} namespace NStlPriv {

template <class _BidirectionalIter, class _Distance, class _Compare>
void __merge_without_buffer(_BidirectionalIter __first,
                            _BidirectionalIter __middle,
                            _BidirectionalIter __last,
                            _Distance __len1, _Distance __len2,
                            _Compare __comp);


template <class _BidirectionalIter1, class _BidirectionalIter2,
          class _BidirectionalIter3, class _Compare>
_BidirectionalIter3 __merge_backward(_BidirectionalIter1 __first1,
                                     _BidirectionalIter1 __last1,
                                     _BidirectionalIter2 __first2,
                                     _BidirectionalIter2 __last2,
                                     _BidirectionalIter3 __result,
                                     _Compare __comp);

template <class _Tp>

inline

const _Tp& __median(const _Tp& __a, const _Tp& __b, const _Tp& __c) {
  if (__a < __b)
    if (__b < __c)
      return __b;
    else if (__a < __c)
      return __c;
    else
      return __a;
  else if (__a < __c)
    return __a;
  else if (__b < __c)
    return __c;
  else
    return __b;
}

template <class _Tp, class _Compare>

inline

const _Tp&
__median(const _Tp& __a, const _Tp& __b, const _Tp& __c, _Compare __comp) {
  if (__comp(__a, __b)) {

    if (__comp(__b, __c)) {

      return __b;
    }
    else if (__comp(__a, __c)) {

      return __c;
    }
    else
      return __a;
  }
  else if (__comp(__a, __c)) {

    return __a;
  }
  else if (__comp(__b, __c)) {

    return __c;
  }
  else
    return __b;
}

} namespace NStl {

template <class _ForwardIter1, class _ForwardIter2>
_ForwardIter1 search(_ForwardIter1 __first1, _ForwardIter1 __last1,
                     _ForwardIter2 __first2, _ForwardIter2 __last2) {



  if (__first1 == __last1 || __first2 == __last2)
    return __first1;


  _ForwardIter2 __p1(__first2);

  if ( ++__p1 == __last2 )
    return find(__first1, __last1, *__first2);



  for ( ; ; ) {
    __first1 = find(__first1, __last1, *__first2);
    if (__first1 == __last1)
      return __last1;

    _ForwardIter2 __p = __p1;
    _ForwardIter1 __current = __first1;
    if (++__current == __last1)
      return __last1;

    while (*__current == *__p) {
      if (++__p == __last2)
        return __first1;
      if (++__current == __last1)
        return __last1;
    }

    ++__first1;
  }
  return __first1;
}

} namespace NStlPriv {

template <class _RandomAccessIter, class _Integer, class _Tp,
          class _BinaryPred, class _Distance>
_RandomAccessIter __search_n(_RandomAccessIter __first, _RandomAccessIter __last,
                             _Integer __count, const _Tp& __val, _BinaryPred __pred,
                             _Distance*, const random_access_iterator_tag &)
{
  _Distance __tailSize = __last - __first;
  const _Distance __pattSize = __count;
  const _Distance __skipOffset = __pattSize - 1;
  _RandomAccessIter __backTrack;
  _Distance __remainder, __prevRemainder;

  for ( _RandomAccessIter __lookAhead = __first + __skipOffset; __tailSize >= __pattSize; __lookAhead += __pattSize ) {

    __tailSize -= __pattSize;

    while ( !__pred(*__lookAhead, __val) ) {
      if (__tailSize < __pattSize)
        return __last;

      __lookAhead += __pattSize;
      __tailSize -= __pattSize;
    }

    if ( __skipOffset == 0 ) {
      return (__lookAhead - __skipOffset);
    }

    __remainder = __skipOffset;

    for (__backTrack = __lookAhead; __pred(*--__backTrack, __val); ) {
      if (--__remainder == 0)
        return (__lookAhead - __skipOffset);
    }

    if (__remainder > __tailSize)
      return __last;

    __lookAhead += __remainder;
    __tailSize -= __remainder;

    while ( __pred(*__lookAhead, __val) ) {
      __prevRemainder = __remainder;
      __backTrack = __lookAhead;

      do {
        if (--__remainder == 0)
          return (__lookAhead - __skipOffset);
      } while (__pred(*--__backTrack, __val));


      __remainder += __pattSize - __prevRemainder;

      if (__remainder > __tailSize)
        return __last;

      __lookAhead += __remainder;
      __tailSize -= __remainder;
    }


  }

  return __last;
}

template <class _ForwardIter, class _Integer, class _Tp,
          class _Distance, class _BinaryPred>
_ForwardIter __search_n(_ForwardIter __first, _ForwardIter __last,
                        _Integer __count, const _Tp& __val, _BinaryPred __pred,
                        _Distance*, const forward_iterator_tag &) {
  for (; (__first != __last) && !__pred(*__first, __val); ++__first) {}
  while (__first != __last) {
    _Integer __n = __count - 1;
    _ForwardIter __i = __first;
    ++__i;
    while (__i != __last && __n != 0 && __pred(*__i, __val)) {
      ++__i;
      --__n;
    }
    if (__n == 0)
      return __first;
    else if (__i != __last)
      for (__first = ++__i; (__first != __last) && !__pred(*__first, __val); ++__first) {}
    else
      break;
  }
  return __last;
}

} namespace NStl {


template <class _ForwardIter, class _Integer, class _Tp>
_ForwardIter search_n(_ForwardIter __first, _ForwardIter __last,
                      _Integer __count, const _Tp& __val) {

  if (__count <= 0)
    return __first;
  if (__count == 1)

    return find(__first, __last, __val);
  return ::NStlPriv:: __search_n(__first, __last, __count, __val, equal_to<_Tp>(),
                               (typename iterator_traits< _ForwardIter >::difference_type*)0,
                               typename iterator_traits< _ForwardIter >::iterator_category());
}

template <class _ForwardIter, class _Integer, class _Tp, class _BinaryPred>
_ForwardIter search_n(_ForwardIter __first, _ForwardIter __last,
                      _Integer __count, const _Tp& __val,
                      _BinaryPred __binary_pred) {

  if (__count <= 0)
    return __first;
  return ::NStlPriv:: __search_n(__first, __last, __count, __val, __binary_pred,
                               (typename iterator_traits< _ForwardIter >::difference_type*)0,
                               typename iterator_traits< _ForwardIter >::iterator_category());
}

template <class _ForwardIter1, class _ForwardIter2>
_ForwardIter1
find_end(_ForwardIter1 __first1, _ForwardIter1 __last1,
         _ForwardIter2 __first2, _ForwardIter2 __last2) {


  return ::NStlPriv:: __find_end(__first1, __last1, __first2, __last2,

                               typename iterator_traits< _ForwardIter1 >::iterator_category(),
                               typename iterator_traits< _ForwardIter2 >::iterator_category(),




                               ::NStlPriv:: __equal_to((typename iterator_traits< _ForwardIter1 >::value_type*)0)
    );
}


} namespace NStlPriv {

template <class _InputIterator, class _OutputIterator, class _BinaryPredicate,
          class _Tp>
inline _OutputIterator
__unique_copy(_InputIterator __first, _InputIterator __last,
              _OutputIterator __result,
              _BinaryPredicate __binary_pred, _Tp*) {
  _Tp __val = *__first;
  *__result = __val;
  while (++__first != __last)
    if (!__binary_pred(__val, *__first)) {
      __val = *__first;
      *++__result = __val;
    }
  return ++__result;
}

template <class _InputIter, class _OutputIter, class _BinaryPredicate>
inline _OutputIter
__unique_copy(_InputIter __first, _InputIter __last,_OutputIter __result,
              _BinaryPredicate __binary_pred, const output_iterator_tag &) {
  return __unique_copy(__first, __last, __result, __binary_pred, (typename iterator_traits< _InputIter >::value_type*)0);
}

template <class _InputIter, class _ForwardIter, class _BinaryPredicate>
inline _ForwardIter
__unique_copy(_InputIter __first, _InputIter __last, _ForwardIter __result,
              _BinaryPredicate __binary_pred, const forward_iterator_tag &) {
  *__result = *__first;
  while (++__first != __last)
    if (!__binary_pred(*__result, *__first)) *++__result = *__first;
  return ++__result;
}
} namespace NStl {

template <class _InputIter, class _OutputIter>
_OutputIter
unique_copy(_InputIter __first, _InputIter __last, _OutputIter __result) {

  if (__first == __last) return __result;
  return ::NStlPriv:: __unique_copy(__first, __last, __result,
                                  ::NStlPriv:: __equal_to((typename iterator_traits< _InputIter >::value_type*)0),
                                  typename iterator_traits< _OutputIter >::iterator_category());
}

template <class _InputIter, class _OutputIter, class _BinaryPredicate>
_OutputIter
unique_copy(_InputIter __first, _InputIter __last,_OutputIter __result,
            _BinaryPredicate __binary_pred) {

  if (__first == __last) return __result;
  return ::NStlPriv:: __unique_copy(__first, __last, __result, __binary_pred,
                                  typename iterator_traits< _OutputIter >::iterator_category());
}


} namespace NStlPriv {

template <class _ForwardIter, class _Distance>
_ForwardIter __rotate_aux(_ForwardIter __first,
                          _ForwardIter __middle,
                          _ForwardIter __last,
                          _Distance*,
                          const forward_iterator_tag &) {
  if (__first == __middle)
    return __last;
  if (__last == __middle)
    return __first;

  _ForwardIter __first2 = __middle;
  do {
    swap(*__first++, *__first2++);
    if (__first == __middle)
      __middle = __first2;
  } while (__first2 != __last);

  _ForwardIter __new_middle = __first;

  __first2 = __middle;

  while (__first2 != __last) {
    swap (*__first++, *__first2++);
    if (__first == __middle)
      __middle = __first2;
    else if (__first2 == __last)
      __first2 = __middle;
  }

  return __new_middle;
}

template <class _BidirectionalIter, class _Distance>
_BidirectionalIter __rotate_aux(_BidirectionalIter __first,
                                _BidirectionalIter __middle,
                                _BidirectionalIter __last,
                                _Distance*,
                                const bidirectional_iterator_tag &) {
  if (__first == __middle)
    return __last;
  if (__last == __middle)
    return __first;

  __reverse(__first, __middle, bidirectional_iterator_tag());
  __reverse(__middle, __last, bidirectional_iterator_tag());

  while (__first != __middle && __middle != __last)
    swap (*__first++, *--__last);

  if (__first == __middle) {
    __reverse(__middle, __last, bidirectional_iterator_tag());
    return __last;
  }
  else {
    __reverse(__first, __middle, bidirectional_iterator_tag());
    return __first;
  }
}

template <class _RandomAccessIter, class _Distance, class _Tp>
_RandomAccessIter __rotate_aux(_RandomAccessIter __first,
                               _RandomAccessIter __middle,
                               _RandomAccessIter __last,
                               _Distance *, _Tp *) {

  _Distance __n = __last - __first;
  _Distance __k = __middle - __first;
  _Distance __l = __n - __k;
  _RandomAccessIter __result = __first + (__last - __middle);

  if (__k == 0)
    return __last;

  if (__k == __l) {
    swap_ranges(__first, __middle, __middle);
    return __result;
  }

  _Distance __d = __gcd(__n, __k);

  for (_Distance __i = 0; __i < __d; __i++) {
    _Tp __tmp = *__first;
    _RandomAccessIter __p = __first;

    if (__k < __l) {
      for (_Distance __j = 0; __j < __l/__d; __j++) {
        if (__p > __first + __l) {
          *__p = *(__p - __l);
          __p -= __l;
        }

        *__p = *(__p + __k);
        __p += __k;
      }
    }

    else {
      for (_Distance __j = 0; __j < __k/__d - 1; __j ++) {
        if (__p < __last - __k) {
          *__p = *(__p + __k);
          __p += __k;
        }

        *__p = * (__p - __l);
        __p -= __l;
      }
    }

    *__p = __tmp;
    ++__first;
  }

  return __result;
}

template <class _RandomAccessIter, class _Distance>
inline _RandomAccessIter
__rotate_aux(_RandomAccessIter __first, _RandomAccessIter __middle, _RandomAccessIter __last,
             _Distance * __dis, const random_access_iterator_tag &) {
  return __rotate_aux(__first, __middle, __last,
                      __dis, (typename iterator_traits< _RandomAccessIter >::value_type*)0);
}

template <class _ForwardIter>
_ForwardIter
__rotate(_ForwardIter __first, _ForwardIter __middle, _ForwardIter __last) {


  return __rotate_aux(__first, __middle, __last,
                      (typename iterator_traits< _ForwardIter >::difference_type*)0,
                      typename iterator_traits< _ForwardIter >::iterator_category());
}

} namespace NStl {

template <class _ForwardIter>
void rotate(_ForwardIter __first, _ForwardIter __middle, _ForwardIter __last) {
  ::NStlPriv:: __rotate(__first, __middle, __last);
}




} namespace NStlPriv {

template <class _Distance>
inline _Distance __random_number(_Distance __n) {

  return rand() % __n;



}

} namespace NStl {

template <class _RandomAccessIter>
void random_shuffle(_RandomAccessIter __first,
                    _RandomAccessIter __last) {

  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    iter_swap(__i, __first + ::NStlPriv:: __random_number((__i - __first) + 1));
}

template <class _RandomAccessIter, class _RandomNumberGenerator>
void random_shuffle(_RandomAccessIter __first, _RandomAccessIter __last,
                    _RandomNumberGenerator &__rand) {

  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    iter_swap(__i, __first + __rand((__i - __first) + 1));
}



template <class _ForwardIter, class _OutputIter, class _Distance>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out_ite, const _Distance __n) {

  _Distance __remaining = distance(__first, __last);
  _Distance __m = (min) (__n, __remaining);

  while (__m > 0) {
    if (::NStlPriv:: __random_number(__remaining) < __m) {
      *__out_ite = *__first;
      ++__out_ite;
      --__m;
    }

    --__remaining;
    ++__first;
  }
  return __out_ite;
}


template <class _ForwardIter, class _OutputIter, class _Distance,
          class _RandomNumberGenerator>
_OutputIter random_sample_n(_ForwardIter __first, _ForwardIter __last,
                            _OutputIter __out_ite, const _Distance __n,
                            _RandomNumberGenerator& __rand) {

  _Distance __remaining = distance(__first, __last);
  _Distance __m = (min) (__n, __remaining);

  while (__m > 0) {
    if (__rand(__remaining) < __m) {
      *__out_ite = *__first;
      ++__out_ite;
      --__m;
    }

    --__remaining;
    ++__first;
  }
  return __out_ite;
}

} namespace NStlPriv {

template <class _InputIter, class _RandomAccessIter, class _Distance>
_RandomAccessIter __random_sample(_InputIter __first, _InputIter __last,
                                  _RandomAccessIter __out_ite,
                                  const _Distance __n) {
  _Distance __m = 0;
  _Distance __t = __n;
  for ( ; __first != __last && __m < __n; ++__m, ++__first)
    __out_ite[__m] = *__first;

  while (__first != __last) {
    ++__t;
    _Distance __M = __random_number(__t);
    if (__M < __n)
      __out_ite[__M] = *__first;
    ++__first;
  }

  return __out_ite + __m;
}

template <class _InputIter, class _RandomAccessIter,
          class _RandomNumberGenerator, class _Distance>
_RandomAccessIter __random_sample(_InputIter __first, _InputIter __last,
                                  _RandomAccessIter __out_ite,
                                  _RandomNumberGenerator& __rand,
                                  const _Distance __n) {
  _Distance __m = 0;
  _Distance __t = __n;
  for ( ; __first != __last && __m < __n; ++__m, ++__first)
    __out_ite[__m] = *__first;

  while (__first != __last) {
    ++__t;
    _Distance __M = __rand(__t);
    if (__M < __n)
      __out_ite[__M] = *__first;
    ++__first;
  }

  return __out_ite + __m;
}

} namespace NStl {

template <class _InputIter, class _RandomAccessIter>
_RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last) {


  return ::NStlPriv:: __random_sample(__first, __last,
                                    __out_first, __out_last - __out_first);
}

template <class _InputIter, class _RandomAccessIter, class _RandomNumberGenerator>
_RandomAccessIter
random_sample(_InputIter __first, _InputIter __last,
              _RandomAccessIter __out_first, _RandomAccessIter __out_last,
              _RandomNumberGenerator& __rand) {


  return ::NStlPriv:: __random_sample(__first, __last,
                                    __out_first, __rand,
                                    __out_last - __out_first);
}




} namespace NStlPriv {

template <class _ForwardIter, class _Predicate>
inline _ForwardIter __partition(_ForwardIter __first,
                                           _ForwardIter __last,
                                           _Predicate __pred,
                                           const forward_iterator_tag &) {
  if (__first == __last) return __first;

  while (__pred(*__first))
    if (++__first == __last) return __first;

  _ForwardIter __next = __first;

  while (++__next != __last) {
    if (__pred(*__next)) {
      swap(*__first, *__next);
      ++__first;
    }
  }
  return __first;
}

template <class _BidirectionalIter, class _Predicate>
inline _BidirectionalIter __partition(_BidirectionalIter __first,
                                                 _BidirectionalIter __last,
                                                 _Predicate __pred,
                                                 const bidirectional_iterator_tag &) {
  for (;;) {
    for (;;) {
      if (__first == __last)
        return __first;
      else if (__pred(*__first))
        ++__first;
      else
        break;
    }
    --__last;
    for (;;) {
      if (__first == __last)
        return __first;
      else if (!__pred(*__last))
        --__last;
      else
        break;
    }
    iter_swap(__first, __last);
    ++__first;
  }
}
} namespace NStl {

template <class _ForwardIter, class _Predicate>
_ForwardIter partition(_ForwardIter __first, _ForwardIter __last, _Predicate __pred) {

  return ::NStlPriv:: __partition(__first, __last, __pred, typename iterator_traits< _ForwardIter >::iterator_category());
}







} namespace NStlPriv {

template <class _ForwardIter, class _Predicate, class _Distance>
_ForwardIter __inplace_stable_partition(_ForwardIter __first,
                                        _ForwardIter __last,
                                        _Predicate __pred, _Distance __len,
                                        bool __pred_of_first, bool __pred_of_before_last) {
  if (__len == 1)
    return (__pred_of_first && (__pred_of_before_last || __pred(*__first))) ? __last : __first;
  _ForwardIter __middle = __first;
  _Distance __half_len = __len / 2;
  advance(__middle, __half_len);
  return __rotate(__inplace_stable_partition(__first, __middle, __pred, __half_len, __pred_of_first, false),
                  __middle,
                  __inplace_stable_partition(__middle, __last, __pred, __len - __half_len, true, __pred_of_before_last));
}

template <class _ForwardIter, class _Pointer, class _Predicate,
          class _Distance>
_ForwardIter __stable_partition_adaptive(_ForwardIter __first,
                                         _ForwardIter __last,
                                         _Predicate __pred, _Distance __len,
                                         _Pointer __buffer, _Distance __buffer_size,
                                         bool __pred_of_first, bool __pred_of_before_last) {
  if (__len <= __buffer_size) {
    _ForwardIter __result1 = __first;
    _Pointer __result2 = __buffer;
    if ((__first != __last) && (!__pred_of_first || __pred(*__first))) {
      *__result2 = *__first;
      ++__result2; ++__first; --__len;
    }
    for (; __first != __last ; ++__first, --__len) {
      if (((__len == 1) && (__pred_of_before_last || __pred(*__first))) ||
          ((__len != 1) && __pred(*__first))){
        *__result1 = *__first;
        ++__result1;
      }
      else {
        *__result2 = *__first;
        ++__result2;
      }
    }
    copy(__buffer, __result2, __result1);
    return __result1;
  }
  else {
    _ForwardIter __middle = __first;
    _Distance __half_len = __len / 2;
    advance(__middle, __half_len);
    return __rotate(__stable_partition_adaptive(
                          __first, __middle, __pred,
                          __half_len, __buffer, __buffer_size,
                          __pred_of_first, false),
                    __middle,
                    __stable_partition_adaptive(
                          __middle, __last, __pred,
                          __len - __half_len, __buffer, __buffer_size,
                          true, __pred_of_before_last));
  }
}

template <class _ForwardIter, class _Predicate, class _Tp, class _Distance>
inline _ForwardIter
__stable_partition_aux_aux(_ForwardIter __first, _ForwardIter __last,
                           _Predicate __pred, _Tp*, _Distance*, bool __pred_of_before_last = false) {
  _Temporary_buffer<_ForwardIter, _Tp> __buf(__first, __last);

  return (__buf.size() > 0) ?
    __stable_partition_adaptive(__first, __last, __pred,
                                _Distance(__buf.requested_size()),
                                __buf.begin(), __buf.size(),
                                false, __pred_of_before_last) :
    __inplace_stable_partition(__first, __last, __pred,
                               _Distance(__buf.requested_size()),
                               false, __pred_of_before_last);

}

template <class _ForwardIter, class _Predicate>
_ForwardIter
__stable_partition_aux(_ForwardIter __first, _ForwardIter __last, _Predicate __pred,
                       const forward_iterator_tag &) {
  return __stable_partition_aux_aux(__first, __last, __pred,
                                    (typename iterator_traits< _ForwardIter >::value_type*)0,
                                    (typename iterator_traits< _ForwardIter >::difference_type*)0);
}

template <class _BidirectIter, class _Predicate>
_BidirectIter
__stable_partition_aux(_BidirectIter __first, _BidirectIter __last, _Predicate __pred,
                       const bidirectional_iterator_tag &) {
  for (--__last;;) {
    if (__first == __last)
      return __first;
    else if (!__pred(*__last))
      --__last;
    else
      break;
  }
  ++__last;

  return __stable_partition_aux_aux(__first, __last, __pred,
                                    (typename iterator_traits< _BidirectIter >::value_type*)0,
                                    (typename iterator_traits< _BidirectIter >::difference_type*)0, true);
}
} namespace NStl {

template <class _ForwardIter, class _Predicate>
_ForwardIter
stable_partition(_ForwardIter __first, _ForwardIter __last, _Predicate __pred) {

  for (;;) {
    if (__first == __last)
      return __first;
    else if (__pred(*__first))
      ++__first;
    else
      break;
  }
  return ::NStlPriv:: __stable_partition_aux(__first, __last, __pred,
                                           typename iterator_traits< _ForwardIter >::iterator_category());
}

} namespace NStlPriv {

template <class _RandomAccessIter, class _Tp, class _Compare>
_RandomAccessIter __unguarded_partition(_RandomAccessIter __first,
                                        _RandomAccessIter __last,
                                        _Tp __pivot, _Compare __comp) {
  for (;;) {
    while (__comp(*__first, __pivot)) {

      ++__first;
    }
    --__last;
    while (__comp(__pivot, *__last)) {

      --__last;
    }
    if (!(__first < __last))
      return __first;
    iter_swap(__first, __last);
    ++__first;
  }
}





template <class _RandomAccessIter, class _Tp, class _Compare>
void __unguarded_linear_insert(_RandomAccessIter __last, const _Tp& __val_in,
                               _Compare __comp) {
  const _Tp __val(__val_in);
  _RandomAccessIter __next = __last;
  --__next;
  while (__comp(__val, *__next)) {

    *__last = *__next;
    __last = __next;
    --__next;
  }
  *__last = __val;
}

template <class _RandomAccessIter, class _Tp, class _Compare>
inline void __linear_insert(_RandomAccessIter __first,
                            _RandomAccessIter __last, const _Tp& __val_in, _Compare __comp) {
  const _Tp __val(__val_in);


  if (__comp(__val, *__first)) {

    copy_backward(__first, __last, __last + 1);
    *__first = __val;
  }
  else
    __unguarded_linear_insert(__last, __val, __comp);
}

template <class _RandomAccessIter, class _Tp, class _Compare>
void __insertion_sort(_RandomAccessIter __first,
                      _RandomAccessIter __last,
                      _Tp *, _Compare __comp) {
  if (__first == __last) return;
  for (_RandomAccessIter __i = __first + 1; __i != __last; ++__i)
    __linear_insert<_RandomAccessIter, _Tp, _Compare>(__first, __i, *__i, __comp);
}

template <class _RandomAccessIter, class _Tp, class _Compare>
void __unguarded_insertion_sort_aux(_RandomAccessIter __first,
                                    _RandomAccessIter __last,
                                    _Tp*, _Compare __comp) {
  for (_RandomAccessIter __i = __first; __i != __last; ++__i)
    __unguarded_linear_insert<_RandomAccessIter, _Tp, _Compare>(__i, *__i, __comp);
}

template <class _RandomAccessIter, class _Compare>
inline void __unguarded_insertion_sort(_RandomAccessIter __first,
                                       _RandomAccessIter __last,
                                       _Compare __comp) {
  __unguarded_insertion_sort_aux(__first, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}

template <class _RandomAccessIter, class _Compare>
void __final_insertion_sort(_RandomAccessIter __first,
                            _RandomAccessIter __last, _Compare __comp) {
  if (__last - __first > (16 * 4)) {
    __insertion_sort(__first, __first + (16 * 4), (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
    __unguarded_insertion_sort(__first + (16 * 4), __last, __comp);
  }
  else
    __insertion_sort(__first, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}

template <class _RandomAccessIter, class _Tp, class _Size, class _Compare>
void __introsort_loop(_RandomAccessIter __first,
                      _RandomAccessIter __last, _Tp*,
                      _Size __depth_limit, _Compare __comp) {
  while (__last - __first > (16 * 4)) {
    if (__depth_limit == 0) {
      partial_sort(__first, __last, __last, __comp);
      return;
    }
    --__depth_limit;
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _Tp(__median(*__first,
                                         *(__first + (__last - __first)/2),
                                         *(__last - 1), __comp)),
       __comp);
    __introsort_loop(__cut, __last, (_Tp*) 0, __depth_limit, __comp);
    __last = __cut;
  }
}

} namespace NStl {

template <class _RandomAccessIter>
void sort(_RandomAccessIter __first, _RandomAccessIter __last) {

  if (__first != __last) {
    ::NStlPriv:: __introsort_loop(__first, __last,
                                (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                                ::NStlPriv:: __lg(__last - __first) * 2,
                                ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0));
    ::NStlPriv:: __final_insertion_sort(__first, __last,
                                      ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0));
  }
}

template <class _RandomAccessIter, class _Compare>
void sort(_RandomAccessIter __first, _RandomAccessIter __last, _Compare __comp) {

  if (__first != __last) {
    ::NStlPriv:: __introsort_loop(__first, __last,
                                (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                                ::NStlPriv:: __lg(__last - __first) * 2, __comp);
    ::NStlPriv:: __final_insertion_sort(__first, __last, __comp);
  }
}


} namespace NStlPriv {

template <class _RandomAccessIter, class _Compare>
void __inplace_stable_sort(_RandomAccessIter __first,
                           _RandomAccessIter __last, _Compare __comp) {
  if (__last - __first < 15) {
    __insertion_sort(__first, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
    return;
  }
  _RandomAccessIter __middle = __first + (__last - __first) / 2;
  __inplace_stable_sort(__first, __middle, __comp);
  __inplace_stable_sort(__middle, __last, __comp);
  __merge_without_buffer(__first, __middle, __last,
                         __middle - __first,
                         __last - __middle,
                         __comp);
}

template <class _RandomAccessIter1, class _RandomAccessIter2,
          class _Distance, class _Compare>
void __merge_sort_loop(_RandomAccessIter1 __first,
                       _RandomAccessIter1 __last,
                       _RandomAccessIter2 __result, _Distance __step_size,
                       _Compare __comp) {
  _Distance __two_step = 2 * __step_size;

  while (__last - __first >= __two_step) {
    __result = merge(__first, __first + __step_size,
                     __first + __step_size, __first + __two_step,
                     __result,
                     __comp);
    __first += __two_step;
  }
  __step_size = (min) (_Distance(__last - __first), __step_size);

  merge(__first, __first + __step_size,
        __first + __step_size, __last,
        __result,
        __comp);
}

const int __stl_chunk_size = 7;

template <class _RandomAccessIter, class _Distance, class _Compare>
void __chunk_insertion_sort(_RandomAccessIter __first,
                            _RandomAccessIter __last,
                            _Distance __chunk_size, _Compare __comp) {
  while (__last - __first >= __chunk_size) {
    __insertion_sort(__first, __first + __chunk_size,
                     (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
    __first += __chunk_size;
  }
  __insertion_sort(__first, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}

template <class _RandomAccessIter, class _Pointer, class _Distance,
          class _Compare>
void __merge_sort_with_buffer(_RandomAccessIter __first,
                              _RandomAccessIter __last, _Pointer __buffer,
                              _Distance*, _Compare __comp) {
  _Distance __len = __last - __first;
  _Pointer __buffer_last = __buffer + __len;

  _Distance __step_size = __stl_chunk_size;
  __chunk_insertion_sort(__first, __last, __step_size, __comp);

  while (__step_size < __len) {
    __merge_sort_loop(__first, __last, __buffer, __step_size, __comp);
    __step_size *= 2;
    __merge_sort_loop(__buffer, __buffer_last, __first, __step_size, __comp);
    __step_size *= 2;
  }
}

template <class _BidirectionalIter1, class _BidirectionalIter2,
          class _Distance>
_BidirectionalIter1 __rotate_adaptive(_BidirectionalIter1 __first,
                                      _BidirectionalIter1 __middle,
                                      _BidirectionalIter1 __last,
                                      _Distance __len1, _Distance __len2,
                                      _BidirectionalIter2 __buffer,
                                      _Distance __buffer_size) {
  if (__len1 > __len2 && __len2 <= __buffer_size) {
    _BidirectionalIter2 __buffer_end = copy(__middle, __last, __buffer);
    copy_backward(__first, __middle, __last);
    return copy(__buffer, __buffer_end, __first);
  }
  else if (__len1 <= __buffer_size) {
    _BidirectionalIter2 __buffer_end = copy(__first, __middle, __buffer);
    copy(__middle, __last, __first);
    return copy_backward(__buffer, __buffer_end, __last);
  }
  else
    return __rotate(__first, __middle, __last);
}

template <class _BidirectionalIter, class _Distance, class _Pointer,
          class _Compare>
void __merge_adaptive(_BidirectionalIter __first,
                      _BidirectionalIter __middle,
                      _BidirectionalIter __last,
                      _Distance __len1, _Distance __len2,
                      _Pointer __buffer, _Distance __buffer_size,
                      _Compare __comp) {
  if (__len1 <= __len2 && __len1 <= __buffer_size) {
    _Pointer __buffer_end = copy(__first, __middle, __buffer);
    merge(__buffer, __buffer_end, __middle, __last, __first, __comp);
  }
  else if (__len2 <= __buffer_size) {
    _Pointer __buffer_end = copy(__middle, __last, __buffer);
    __merge_backward(__first, __middle, __buffer, __buffer_end, __last,
                     __comp);
  }
  else {
    _BidirectionalIter __first_cut = __first;
    _BidirectionalIter __second_cut = __middle;
    _Distance __len11 = 0;
    _Distance __len22 = 0;
    if (__len1 > __len2) {
      __len11 = __len1 / 2;
      advance(__first_cut, __len11);
      __second_cut = lower_bound(__middle, __last, *__first_cut, __comp);
      __len22 += distance(__middle, __second_cut);
    }
    else {
      __len22 = __len2 / 2;
      advance(__second_cut, __len22);
      __first_cut = upper_bound(__first, __middle, *__second_cut, __comp);
      __len11 += distance(__first, __first_cut);
    }
    _BidirectionalIter __new_middle =
      __rotate_adaptive(__first_cut, __middle, __second_cut, __len1 - __len11,
                        __len22, __buffer, __buffer_size);
    __merge_adaptive(__first, __first_cut, __new_middle, __len11,
                     __len22, __buffer, __buffer_size, __comp);
    __merge_adaptive(__new_middle, __second_cut, __last, __len1 - __len11,
                     __len2 - __len22, __buffer, __buffer_size, __comp);
  }
}

template <class _RandomAccessIter, class _Pointer, class _Distance,
          class _Compare>
void __stable_sort_adaptive(_RandomAccessIter __first,
                            _RandomAccessIter __last, _Pointer __buffer,
                            _Distance __buffer_size, _Compare __comp) {
  _Distance __len = (__last - __first + 1) / 2;
  _RandomAccessIter __middle = __first + __len;
  if (__len > __buffer_size) {
    __stable_sort_adaptive(__first, __middle, __buffer, __buffer_size,
                           __comp);
    __stable_sort_adaptive(__middle, __last, __buffer, __buffer_size,
                           __comp);
  }
  else {
    __merge_sort_with_buffer(__first, __middle, __buffer, (_Distance*)0,
                               __comp);
    __merge_sort_with_buffer(__middle, __last, __buffer, (_Distance*)0,
                               __comp);
  }
  __merge_adaptive(__first, __middle, __last, _Distance(__middle - __first),
                   _Distance(__last - __middle), __buffer, __buffer_size,
                   __comp);
}

template <class _RandomAccessIter, class _Tp, class _Distance, class _Compare>
void __stable_sort_aux(_RandomAccessIter __first,
                       _RandomAccessIter __last, _Tp*, _Distance*,
                       _Compare __comp) {
  _Temporary_buffer<_RandomAccessIter, _Tp> buf(__first, __last);
  if (buf.begin() == 0)
    __inplace_stable_sort(__first, __last, __comp);
  else
    __stable_sort_adaptive(__first, __last, buf.begin(),
                           _Distance(buf.size()),
                           __comp);
}

} namespace NStl {

template <class _RandomAccessIter>
void stable_sort(_RandomAccessIter __first,
                 _RandomAccessIter __last) {

  ::NStlPriv:: __stable_sort_aux(__first, __last,
                               (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                               (typename iterator_traits< _RandomAccessIter >::difference_type*)0,
                               ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0));
}

template <class _RandomAccessIter, class _Compare>
void stable_sort(_RandomAccessIter __first,
                 _RandomAccessIter __last, _Compare __comp) {

  ::NStlPriv:: __stable_sort_aux(__first, __last,
                               (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                               (typename iterator_traits< _RandomAccessIter >::difference_type*)0,
                               __comp);
}


} namespace NStlPriv {

template <class _RandomAccessIter, class _Tp, class _Compare>
void __partial_sort(_RandomAccessIter __first, _RandomAccessIter __middle,
                    _RandomAccessIter __last, _Tp*, _Compare __comp) {
  make_heap(__first, __middle, __comp);
  for (_RandomAccessIter __i = __middle; __i < __last; ++__i) {
    if (__comp(*__i, *__first)) {

      __pop_heap(__first, __middle, __i, _Tp(*__i), __comp,
                 (typename iterator_traits< _RandomAccessIter >::difference_type*)0);
    }
  }
  sort_heap(__first, __middle, __comp);
}

} namespace NStl {

template <class _RandomAccessIter>
void partial_sort(_RandomAccessIter __first,_RandomAccessIter __middle,
                  _RandomAccessIter __last) {


  ::NStlPriv:: __partial_sort(__first, __middle, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                            ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0));
}

template <class _RandomAccessIter, class _Compare>
void partial_sort(_RandomAccessIter __first,_RandomAccessIter __middle,
                  _RandomAccessIter __last, _Compare __comp) {


  ::NStlPriv:: __partial_sort(__first, __middle, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}

} namespace NStlPriv {

template <class _InputIter, class _RandomAccessIter, class _Compare,
          class _Distance, class _Tp>
_RandomAccessIter __partial_sort_copy(_InputIter __first,
                                      _InputIter __last,
                                      _RandomAccessIter __result_first,
                                      _RandomAccessIter __result_last,
                                      _Compare __comp, _Distance*, _Tp*) {
  if (__result_first == __result_last) return __result_last;
  _RandomAccessIter __result_real_last = __result_first;
  while(__first != __last && __result_real_last != __result_last) {
    *__result_real_last = *__first;
    ++__result_real_last;
    ++__first;
  }
  make_heap(__result_first, __result_real_last, __comp);
  while (__first != __last) {
    if (__comp(*__first, *__result_first)) {

      __adjust_heap(__result_first, _Distance(0),
                    _Distance(__result_real_last - __result_first),
                    _Tp(*__first),
                    __comp);
    }
    ++__first;
  }
  sort_heap(__result_first, __result_real_last, __comp);
  return __result_real_last;
}

} namespace NStl {

template <class _InputIter, class _RandomAccessIter>
_RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first, _RandomAccessIter __result_last) {


  return ::NStlPriv:: __partial_sort_copy(__first, __last, __result_first, __result_last,
                                        ::NStlPriv:: __less((typename iterator_traits< _InputIter >::value_type*)0),
                                        (typename iterator_traits< _RandomAccessIter >::difference_type*)0,
                                        (typename iterator_traits< _InputIter >::value_type*)0);
}

template <class _InputIter, class _RandomAccessIter, class _Compare>
_RandomAccessIter
partial_sort_copy(_InputIter __first, _InputIter __last,
                  _RandomAccessIter __result_first,
                  _RandomAccessIter __result_last, _Compare __comp) {


  return ::NStlPriv:: __partial_sort_copy(__first, __last, __result_first, __result_last,
                                        __comp,
                                        (typename iterator_traits< _RandomAccessIter >::difference_type*)0,
                                        (typename iterator_traits< _InputIter >::value_type*)0);
}


} namespace NStlPriv {

template <class _RandomAccessIter, class _Tp, class _Compare>
void __nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                   _RandomAccessIter __last, _Tp*, _Compare __comp) {
  while (__last - __first > 3) {
    _RandomAccessIter __cut =
      __unguarded_partition(__first, __last,
                            _Tp(__median(*__first,
                                         *(__first + (__last - __first)/2),
                                         *(__last - 1),
                                         __comp)),
                            __comp);
    if (__cut <= __nth)
      __first = __cut;
    else
      __last = __cut;
  }
  __insertion_sort(__first, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}

} namespace NStl {

template <class _RandomAccessIter>
void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                 _RandomAccessIter __last) {


  ::NStlPriv:: __nth_element(__first, __nth, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0,
                           ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0));
}

template <class _RandomAccessIter, class _Compare>
void nth_element(_RandomAccessIter __first, _RandomAccessIter __nth,
                 _RandomAccessIter __last, _Compare __comp) {


  ::NStlPriv:: __nth_element(__first, __nth, __last, (typename iterator_traits< _RandomAccessIter >::value_type*)0, __comp);
}


} namespace NStlPriv {

template <class _ForwardIter, class _Tp,
          class _Compare1, class _Compare2, class _Distance>
_ForwardIter __upper_bound(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
                           _Compare1 __comp1, _Compare2 __comp2, _Distance*) {
  (void)__comp2;
  (void)__comp1;
  _Distance __len = distance(__first, __last);
  _Distance __half;

  while (__len > 0) {
    __half = __len >> 1;
    _ForwardIter __middle = __first;
    advance(__middle, __half);
    if (__comp2(__val, *__middle)) {

      __len = __half;
    }
    else {
      __first = __middle;
      ++__first;
      __len = __len - __half - 1;
    }
  }
  return __first;
}

template <class _ForwardIter, class _Tp,
          class _Compare1, class _Compare2, class _Distance>
pair<_ForwardIter, _ForwardIter>
__equal_range(_ForwardIter __first, _ForwardIter __last, const _Tp& __val,
              _Compare1 __comp1, _Compare2 __comp2, _Distance* __dist) {
  _Distance __len = distance(__first, __last);
  _Distance __half;

  while (__len > 0) {
    __half = __len >> 1;
    _ForwardIter __middle = __first;
    advance(__middle, __half);
    if (__comp1(*__middle, __val)) {

      __first = __middle;
      ++__first;
      __len = __len - __half - 1;
    }
    else if (__comp2(__val, *__middle)) {

      __len = __half;
    }
    else {
      _ForwardIter __left = __lower_bound(__first, __middle, __val, __comp1, __comp2, __dist);


      if (__comp1(*__left, __val)) {

        return pair<_ForwardIter, _ForwardIter>(__left, __left);
      }
      advance(__first, __len);
      _ForwardIter __right = __upper_bound(++__middle, __first, __val, __comp1, __comp2, __dist);
      return pair<_ForwardIter, _ForwardIter>(__left, __right);
    }
  }
  return pair<_ForwardIter, _ForwardIter>(__first, __first);
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result) {


  while (__first1 != __last1 && __first2 != __last2) {
    if (*__first2 < *__first1) {
      *__result = *__first2;
      ++__first2;
    }
    else {
      *__result = *__first1;
      ++__first1;
    }
    ++__result;
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter merge(_InputIter1 __first1, _InputIter1 __last1,
                  _InputIter2 __first2, _InputIter2 __last2,
                  _OutputIter __result, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2) {
    if (__comp(*__first2, *__first1)) {

      *__result = *__first2;
      ++__first2;
    }
    else {
      *__result = *__first1;
      ++__first1;
    }
    ++__result;
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

} namespace NStlPriv {

template <class _BidirectionalIter, class _Distance, class _Compare>
void __merge_without_buffer(_BidirectionalIter __first,
                            _BidirectionalIter __middle,
                            _BidirectionalIter __last,
                            _Distance __len1, _Distance __len2,
                            _Compare __comp) {
  if (__len1 == 0 || __len2 == 0)
    return;
  if (__len1 + __len2 == 2) {
    if (__comp(*__middle, *__first)) {

      iter_swap(__first, __middle);
    }
    return;
  }
  _BidirectionalIter __first_cut = __first;
  _BidirectionalIter __second_cut = __middle;
  _Distance __len11 = 0;
  _Distance __len22 = 0;
  if (__len1 > __len2) {
    __len11 = __len1 / 2;
    advance(__first_cut, __len11);
    __second_cut = lower_bound(__middle, __last, *__first_cut, __comp);
    __len22 += distance(__middle, __second_cut);
  }
  else {
    __len22 = __len2 / 2;
    advance(__second_cut, __len22);
    __first_cut = upper_bound(__first, __middle, *__second_cut, __comp);
    __len11 +=distance(__first, __first_cut);
  }
  _BidirectionalIter __new_middle
    = __rotate(__first_cut, __middle, __second_cut);
  __merge_without_buffer(__first, __first_cut, __new_middle, __len11, __len22,
                         __comp);
  __merge_without_buffer(__new_middle, __second_cut, __last, __len1 - __len11,
                         __len2 - __len22, __comp);
}

template <class _BidirectionalIter1, class _BidirectionalIter2,
          class _BidirectionalIter3, class _Compare>
_BidirectionalIter3 __merge_backward(_BidirectionalIter1 __first1,
                                     _BidirectionalIter1 __last1,
                                     _BidirectionalIter2 __first2,
                                     _BidirectionalIter2 __last2,
                                     _BidirectionalIter3 __result,
                                     _Compare __comp) {
  if (__first1 == __last1)
    return copy_backward(__first2, __last2, __result);
  if (__first2 == __last2)
    return copy_backward(__first1, __last1, __result);
  --__last1;
  --__last2;
  for (;;) {
    if (__comp(*__last2, *__last1)) {

      *--__result = *__last1;
      if (__first1 == __last1)
        return copy_backward(__first2, ++__last2, __result);
      --__last1;
    }
    else {
      *--__result = *__last2;
      if (__first2 == __last2)
        return copy_backward(__first1, ++__last1, __result);
      --__last2;
    }
  }
}

template <class _BidirectionalIter, class _Tp,
          class _Distance, class _Compare>
inline void __inplace_merge_aux(_BidirectionalIter __first,
                                _BidirectionalIter __middle,
                                _BidirectionalIter __last, _Tp*, _Distance*,
                                _Compare __comp) {
  _Distance __len1 = distance(__first, __middle);
  _Distance __len2 = distance(__middle, __last);

  _Temporary_buffer<_BidirectionalIter, _Tp> __buf(__first, __last);
  if (__buf.begin() == 0)
    __merge_without_buffer(__first, __middle, __last, __len1, __len2, __comp);
  else
    __merge_adaptive(__first, __middle, __last, __len1, __len2,
                     __buf.begin(), _Distance(__buf.size()),
                     __comp);
}

} namespace NStl {

template <class _BidirectionalIter>
void inplace_merge(_BidirectionalIter __first,
                   _BidirectionalIter __middle,
                   _BidirectionalIter __last) {


  if (__first == __middle || __middle == __last)
    return;
  ::NStlPriv:: __inplace_merge_aux(__first, __middle, __last,
                                 (typename iterator_traits< _BidirectionalIter >::value_type*)0, (typename iterator_traits< _BidirectionalIter >::difference_type*)0,
                                 ::NStlPriv:: __less((typename iterator_traits< _BidirectionalIter >::value_type*)0));
}

template <class _BidirectionalIter, class _Compare>
void inplace_merge(_BidirectionalIter __first,
                   _BidirectionalIter __middle,
                   _BidirectionalIter __last, _Compare __comp) {


  if (__first == __middle || __middle == __last)
    return;
  ::NStlPriv:: __inplace_merge_aux(__first, __middle, __last,
                                 (typename iterator_traits< _BidirectionalIter >::value_type*)0, (typename iterator_traits< _BidirectionalIter >::difference_type*)0,
                                 __comp);
}

} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _Compare>
bool __includes(_InputIter1 __first1, _InputIter1 __last1,
                _InputIter2 __first2, _InputIter2 __last2, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2)
    if (__comp(*__first2, *__first1)) {

      return false;
    }
    else if (__comp(*__first1, *__first2))
      ++__first1;
    else
      ++__first1, ++__first2;

  return __first2 == __last2;
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _Compare>
bool includes(_InputIter1 __first1, _InputIter1 __last1,
              _InputIter2 __first2, _InputIter2 __last2, _Compare __comp) {
  return ::NStlPriv:: __includes(__first1, __last1, __first2, __last2, __comp);
}

template <class _InputIter1, class _InputIter2>
bool includes(_InputIter1 __first1, _InputIter1 __last1,
              _InputIter2 __first2, _InputIter2 __last2) {
  return ::NStlPriv:: __includes(__first1, __last1, __first2, __last2,
                               ::NStlPriv:: __less((typename iterator_traits< _InputIter1 >::value_type*)0));
}

} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter __set_union(_InputIter1 __first1, _InputIter1 __last1,
                        _InputIter2 __first2, _InputIter2 __last2,
                        _OutputIter __result, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2) {
    if (__comp(*__first1, *__first2)) {

      *__result = *__first1;
      ++__first1;
    }
    else if (__comp(*__first2, *__first1)) {

      *__result = *__first2;
      ++__first2;
    }
    else {
      *__result = *__first1;
      ++__first1;
      ++__first2;
    }
    ++__result;
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_union(_InputIter1 __first1, _InputIter1 __last1,
                      _InputIter2 __first2, _InputIter2 __last2,
                      _OutputIter __result) {
  return ::NStlPriv:: __set_union(__first1, __last1, __first2, __last2, __result,
                                ::NStlPriv:: __less((typename iterator_traits< _InputIter1 >::value_type*)0));
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_union(_InputIter1 __first1, _InputIter1 __last1,
                      _InputIter2 __first2, _InputIter2 __last2,
                      _OutputIter __result, _Compare __comp) {
  return ::NStlPriv:: __set_union(__first1, __last1, __first2, __last2, __result, __comp);
}

} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter __set_intersection(_InputIter1 __first1, _InputIter1 __last1,
                               _InputIter2 __first2, _InputIter2 __last2,
                               _OutputIter __result, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2)
    if (__comp(*__first1, *__first2)) {

      ++__first1;
    }
    else if (__comp(*__first2, *__first1))
      ++__first2;
    else {
      *__result = *__first1;
      ++__first1;
      ++__first2;
      ++__result;
    }
  return __result;
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_intersection(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _OutputIter __result) {
  return ::NStlPriv:: __set_intersection(__first1, __last1, __first2, __last2, __result,
                                       ::NStlPriv:: __less((typename iterator_traits< _InputIter1 >::value_type*)0));
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_intersection(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _OutputIter __result, _Compare __comp) {
  return ::NStlPriv:: __set_intersection(__first1, __last1, __first2, __last2, __result, __comp);
}

} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter __set_difference(_InputIter1 __first1, _InputIter1 __last1,
                             _InputIter2 __first2, _InputIter2 __last2,
                             _OutputIter __result, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2)
    if (__comp(*__first1, *__first2)) {

      *__result = *__first1;
      ++__first1;
      ++__result;
    }
    else if (__comp(*__first2, *__first1))
      ++__first2;
    else {
      ++__first1;
      ++__first2;
    }
  return copy(__first1, __last1, __result);
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter set_difference(_InputIter1 __first1, _InputIter1 __last1,
                           _InputIter2 __first2, _InputIter2 __last2,
                           _OutputIter __result) {
  return ::NStlPriv:: __set_difference(__first1, __last1, __first2, __last2, __result,
                                     ::NStlPriv:: __less((typename iterator_traits< _InputIter1 >::value_type*)0));
}

template <class _InputIter1, class _InputIter2, class _OutputIter,
          class _Compare>
_OutputIter set_difference(_InputIter1 __first1, _InputIter1 __last1,
                           _InputIter2 __first2, _InputIter2 __last2,
                           _OutputIter __result, _Compare __comp) {
  return ::NStlPriv:: __set_difference(__first1, __last1, __first2, __last2, __result, __comp);
}

} namespace NStlPriv {

template <class _InputIter1, class _InputIter2, class _OutputIter, class _Compare>
_OutputIter
__set_symmetric_difference(_InputIter1 __first1, _InputIter1 __last1,
                           _InputIter2 __first2, _InputIter2 __last2,
                           _OutputIter __result, _Compare __comp) {


  while (__first1 != __last1 && __first2 != __last2) {
    if (__comp(*__first1, *__first2)) {

      *__result = *__first1;
      ++__first1;
      ++__result;
    }
    else if (__comp(*__first2, *__first1)) {
      *__result = *__first2;
      ++__first2;
      ++__result;
    }
    else {
      ++__first1;
      ++__first2;
    }
  }
  return copy(__first2, __last2, copy(__first1, __last1, __result));
}

} namespace NStl {

template <class _InputIter1, class _InputIter2, class _OutputIter>
_OutputIter
set_symmetric_difference(_InputIter1 __first1, _InputIter1 __last1,
                         _InputIter2 __first2, _InputIter2 __last2,
                         _OutputIter __result) {
  return ::NStlPriv:: __set_symmetric_difference(__first1, __last1, __first2, __last2, __result,
                                               ::NStlPriv:: __less((typename iterator_traits< _InputIter1 >::value_type*)0));
}

template <class _InputIter1, class _InputIter2, class _OutputIter, class _Compare>
_OutputIter
set_symmetric_difference(_InputIter1 __first1, _InputIter1 __last1,
                         _InputIter2 __first2, _InputIter2 __last2,
                         _OutputIter __result,
                         _Compare __comp) {
  return ::NStlPriv:: __set_symmetric_difference(__first1, __last1, __first2, __last2, __result, __comp);
}




template <class _ForwardIter>
_ForwardIter max_element(_ForwardIter __first, _ForwardIter __last) {

  if (__first == __last) return __first;
  _ForwardIter __result = __first;
  while (++__first != __last)
    if (*__result < *__first)
      __result = __first;
  return __result;
}

template <class _ForwardIter, class _Compare>
_ForwardIter max_element(_ForwardIter __first, _ForwardIter __last,
                         _Compare __comp) {

  if (__first == __last) return __first;
  _ForwardIter __result = __first;
  while (++__first != __last) {
    if (__comp(*__result, *__first)) {

      __result = __first;
    }
  }
  return __result;
}

template <class _ForwardIter>
_ForwardIter min_element(_ForwardIter __first, _ForwardIter __last) {

  if (__first == __last) return __first;
  _ForwardIter __result = __first;
  while (++__first != __last)
    if (*__first < *__result)
      __result = __first;
  return __result;
}

template <class _ForwardIter, class _Compare>
_ForwardIter min_element(_ForwardIter __first, _ForwardIter __last,
                         _Compare __comp) {

  if (__first == __last) return __first;
  _ForwardIter __result = __first;
  while (++__first != __last) {
    if (__comp(*__first, *__result)) {

      __result = __first;
    }
  }
  return __result;
}



} namespace NStlPriv {

template <class _BidirectionalIter, class _Compare>
bool __next_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                        _Compare __comp) {

  if (__first == __last)
    return false;
  _BidirectionalIter __i = __first;
  ++__i;
  if (__i == __last)
    return false;
  __i = __last;
  --__i;

  for(;;) {
    _BidirectionalIter __ii = __i;
    --__i;
    if (__comp(*__i, *__ii)) {

      _BidirectionalIter __j = __last;
      while (!__comp(*__i, *--__j)) {}
      iter_swap(__i, __j);
      reverse(__ii, __last);
      return true;
    }
    if (__i == __first) {
      reverse(__first, __last);
      return false;
    }
  }



}

} namespace NStl {

template <class _BidirectionalIter>
bool next_permutation(_BidirectionalIter __first, _BidirectionalIter __last) {

  return ::NStlPriv:: __next_permutation(__first, __last,
                                       ::NStlPriv:: __less((typename iterator_traits< _BidirectionalIter >::value_type*)0));
}

template <class _BidirectionalIter, class _Compare>
bool next_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                      _Compare __comp) {

  return ::NStlPriv:: __next_permutation(__first, __last, __comp);
}

} namespace NStlPriv {

template <class _BidirectionalIter, class _Compare>
bool __prev_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                        _Compare __comp) {
  if (__first == __last)
    return false;
  _BidirectionalIter __i = __first;
  ++__i;
  if (__i == __last)
    return false;
  __i = __last;
  --__i;

  for(;;) {
    _BidirectionalIter __ii = __i;
    --__i;
    if (__comp(*__ii, *__i)) {

      _BidirectionalIter __j = __last;
      while (!__comp(*--__j, *__i)) {}
      iter_swap(__i, __j);
      reverse(__ii, __last);
      return true;
    }
    if (__i == __first) {
      reverse(__first, __last);
      return false;
    }
  }



}

} namespace NStl {

template <class _BidirectionalIter>
bool prev_permutation(_BidirectionalIter __first, _BidirectionalIter __last) {

  return ::NStlPriv:: __prev_permutation(__first, __last,
                                       ::NStlPriv:: __less((typename iterator_traits< _BidirectionalIter >::value_type*)0));
}

template <class _BidirectionalIter, class _Compare>
bool prev_permutation(_BidirectionalIter __first, _BidirectionalIter __last,
                      _Compare __comp) {

  return ::NStlPriv:: __prev_permutation(__first, __last, __comp);
}






} namespace NStlPriv {

template <class _RandomAccessIter, class _Distance, class _StrictWeakOrdering>
bool __is_heap(_RandomAccessIter __first, _StrictWeakOrdering __comp,
               _Distance __n) {
  _Distance __parent = 0;
  for (_Distance __child = 1; __child < __n; ++__child) {
    if (__comp(__first[__parent], __first[__child])) {

      return false;
    }
    if ((__child & 1) == 0)
      ++__parent;
  }
  return true;
}

} namespace NStl {

template <class _RandomAccessIter>
bool is_heap(_RandomAccessIter __first, _RandomAccessIter __last) {

  return ::NStlPriv:: __is_heap(__first, ::NStlPriv:: __less((typename iterator_traits< _RandomAccessIter >::value_type*)0), __last - __first);
}

template <class _RandomAccessIter, class _StrictWeakOrdering>
bool is_heap(_RandomAccessIter __first, _RandomAccessIter __last,
             _StrictWeakOrdering __comp) {

  return ::NStlPriv:: __is_heap(__first, __comp, __last - __first);
}


} namespace NStlPriv {

template <class _ForwardIter, class _StrictWeakOrdering>
bool __is_sorted(_ForwardIter __first, _ForwardIter __last,
                 _StrictWeakOrdering __comp) {

  if (__first == __last)
    return true;

  _ForwardIter __next = __first;
  for (++__next; __next != __last; __first = __next, ++__next) {
    if (__comp(*__next, *__first)) {

      return false;
    }
  }

  return true;
}

}

using namespace NStl;



static const uint64 k0 = 0xc3a5c85c97cb3127ULL;
static const uint64 k1 = 0xb492b66fbe98f273ULL;
static const uint64 k2 = 0x9ae16a3b2f90404fULL;
static const uint64 k3 = 0xc949d7c7509e6557ULL;



static uint64 Rotate(uint64 val, int shift) {

  return shift == 0 ? val : ((val >> shift) | (val << (64 - shift)));
}




static uint64 RotateByAtLeast1(uint64 val, int shift) {
  return (val >> shift) | (val << (64 - shift));
}

static uint64 ShiftMix(uint64 val) {
  return val ^ (val >> 47);
}

static uint64 HashLen16(uint64 u, uint64 v) {
  return Hash128to64(uint128(u, v));
}

static uint64 HashLen0to16(const char *s, size_t len) {
  if (len > 8) {
    uint64 a = (*(const uint64*)(s));
    uint64 b = (*(const uint64*)(s + len - 8));
    return HashLen16(a, RotateByAtLeast1(b + len, static_cast<int>(len))) ^ b;
  }
  if (len >= 4) {
    uint64 a = (*(const uint32*)(s));
    return HashLen16(len + (a << 3), (*(const uint32*)(s + len - 4)));
  }
  if (len > 0) {
    uint8 a = s[0];
    uint8 b = s[len >> 1];
    uint8 c = s[len - 1];
    uint32 y = static_cast<uint32>(a) + (static_cast<uint32>(b) << 8);
    uint32 z = static_cast<uint32>(len) + (static_cast<uint32>(c) << 2);
    return ShiftMix(y * k2 ^ z * k3) * k2;
  }
  return k2;
}



static uint64 HashLen17to32(const char *s, size_t len) {
  uint64 a = (*(const uint64*)(s)) * k1;
  uint64 b = (*(const uint64*)(s + 8));
  uint64 c = (*(const uint64*)(s + len - 8)) * k2;
  uint64 d = (*(const uint64*)(s + len - 16)) * k0;
  return HashLen16(Rotate(a - b, 43) + Rotate(c, 30) + d,
                   a + Rotate(b ^ k3, 20) - c + len);
}



static pair<uint64, uint64> WeakHashLen32WithSeeds(
    uint64 w, uint64 x, uint64 y, uint64 z, uint64 a, uint64 b) {
  a += w;
  b = Rotate(b + a + z, 21);
  uint64 c = a;
  a += x;
  a += y;
  b += Rotate(a, 44);
  return make_pair(a + z, b + c);
}


static pair<uint64, uint64> WeakHashLen32WithSeeds(
    const char* s, uint64 a, uint64 b) {
  return WeakHashLen32WithSeeds((*(const uint64*)(s)),
                                (*(const uint64*)(s + 8)),
                                (*(const uint64*)(s + 16)),
                                (*(const uint64*)(s + 24)),
                                a,
                                b);
}


static uint64 HashLen33to64(const char *s, size_t len) {
  uint64 z = (*(const uint64*)(s + 24));
  uint64 a = (*(const uint64*)(s)) + (len + (*(const uint64*)(s + len - 16))) * k0;
  uint64 b = Rotate(a + z, 52);
  uint64 c = Rotate(a, 37);
  a += (*(const uint64*)(s + 8));
  c += Rotate(a, 7);
  a += (*(const uint64*)(s + 16));
  uint64 vf = a + z;
  uint64 vs = b + Rotate(a, 31) + c;
  a = (*(const uint64*)(s + 16)) + (*(const uint64*)(s + len - 32));
  z = (*(const uint64*)(s + len - 8));
  b = Rotate(a + z, 52);
  c = Rotate(a, 37);
  a += (*(const uint64*)(s + len - 24));
  c += Rotate(a, 7);
  a += (*(const uint64*)(s + len - 16));
  uint64 wf = a + z;
  uint64 ws = b + Rotate(a, 31) + c;
  uint64 r = ShiftMix((vf + ws) * k2 + (wf + vs) * k0);
  return ShiftMix(r * k0 + vs) * k2;
}

template <class T>
static inline void DoSwap(T& l, T& r) {
    const T tmp(l); l = r; r = tmp;
}

uint64 CityHash64(const char *s, size_t len) {
  if (len <= 32) {
    if (len <= 16) {
      return HashLen0to16(s, len);
    } else {
      return HashLen17to32(s, len);
    }
  } else if (len <= 64) {
    return HashLen33to64(s, len);
  }



  uint64 x = (*(const uint64*)(s));
  uint64 y = (*(const uint64*)(s + len - 16)) ^ k1;
  uint64 z = (*(const uint64*)(s + len - 56)) ^ k0;
  pair<uint64, uint64> v = WeakHashLen32WithSeeds(s + len - 64, len, y);
  pair<uint64, uint64> w = WeakHashLen32WithSeeds(s + len - 32, len * k1, k0);
  z += ShiftMix(v.second) * k1;
  x = Rotate(z + x, 39) * k1;
  y = Rotate(y, 33) * k1;


  len = (len - 1) & ~static_cast<size_t>(63);
  do {
    x = Rotate(x + y + v.first + (*(const uint64*)(s + 16)), 37) * k1;
    y = Rotate(y + v.second + (*(const uint64*)(s + 48)), 42) * k1;
    x ^= w.second;
    y ^= v.first;
    z = Rotate(z ^ w.first, 33);
    v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
    w = WeakHashLen32WithSeeds(s + 32, z + w.second, y);
    DoSwap(z, x);
    s += 64;
    len -= 64;
  } while (len != 0);
  return HashLen16(HashLen16(v.first, w.first) + ShiftMix(y) * k1 + z,
                   HashLen16(v.second, w.second) + x);
}

uint64 CityHash64WithSeed(const char *s, size_t len, uint64 seed) {
  return CityHash64WithSeeds(s, len, k2, seed);
}

uint64 CityHash64WithSeeds(const char *s, size_t len,
                           uint64 seed0, uint64 seed1) {
  return HashLen16(CityHash64(s, len) - seed0, seed1);
}



static uint128 CityMurmur(const char *s, size_t len, uint128 seed) {
  uint64 a = Uint128Low64(seed);
  uint64 b = Uint128High64(seed);
  uint64 c = 0;
  uint64 d = 0;
  ssize_t l = len - 16;
  if (l <= 0) {
    c = b * k1 + HashLen0to16(s, len);
    d = Rotate(a + (len >= 8 ? (*(const uint64*)(s)) : c), 32);
  } else {
    c = HashLen16((*(const uint64*)(s + len - 8)) + k1, a);
    d = HashLen16(b + len, c + (*(const uint64*)(s + len - 16)));
    a += d;
    do {
      a ^= ShiftMix((*(const uint64*)(s)) * k1) * k1;
      a *= k1;
      b ^= a;
      c ^= ShiftMix((*(const uint64*)(s + 8)) * k1) * k1;
      c *= k1;
      d ^= c;
      s += 16;
      l -= 16;
    } while (l > 0);
  }
  a = HashLen16(a, c);
  b = HashLen16(d, b);
  return uint128(a ^ b, HashLen16(b, a));
}

uint128 CityHash128WithSeed(const char *s, size_t len, uint128 seed) {
  if (len < 128) {
    return CityMurmur(s, len, seed);
  }



  pair<uint64, uint64> v, w;
  uint64 x = Uint128Low64(seed);
  uint64 y = Uint128High64(seed);
  uint64 z = len * k1;
  v.first = Rotate(y ^ k1, 49) * k1 + (*(const uint64*)(s));
  v.second = Rotate(v.first, 42) * k1 + (*(const uint64*)(s + 8));
  w.first = Rotate(y + z, 35) * k1 + x;
  w.second = Rotate(x + (*(const uint64*)(s + 88)), 53) * k1;


  do {
    x = Rotate(x + y + v.first + (*(const uint64*)(s + 16)), 37) * k1;
    y = Rotate(y + v.second + (*(const uint64*)(s + 48)), 42) * k1;
    x ^= w.second;
    y ^= v.first;
    z = Rotate(z ^ w.first, 33);
    v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
    w = WeakHashLen32WithSeeds(s + 32, z + w.second, y);
    DoSwap(z, x);
    s += 64;
    x = Rotate(x + y + v.first + (*(const uint64*)(s + 16)), 37) * k1;
    y = Rotate(y + v.second + (*(const uint64*)(s + 48)), 42) * k1;
    x ^= w.second;
    y ^= v.first;
    z = Rotate(z ^ w.first, 33);
    v = WeakHashLen32WithSeeds(s, v.second * k1, x + w.first);
    w = WeakHashLen32WithSeeds(s + 32, z + w.second, y);
    DoSwap(z, x);
    s += 64;
    len -= 128;
  } while (__builtin_expect(!!(len >= 128), 1));
  y += Rotate(w.first, 37) * k0 + z;
  x += Rotate(v.first + z, 49) * k0;

  for (size_t tail_done = 0; tail_done < len; ) {
    tail_done += 32;
    y = Rotate(y - x, 42) * k0 + v.second;
    w.first += (*(const uint64*)(s + len - tail_done + 16));
    x = Rotate(x, 49) * k0 + w.first;
    w.first += v.first;
    v = WeakHashLen32WithSeeds(s + len - tail_done, v.first, v.second);
  }



  x = HashLen16(x, v.first);
  y = HashLen16(y, w.first);
  return uint128(HashLen16(x + v.second, w.second) + y,
                 HashLen16(x + w.second, y + v.second));
}

uint128 CityHash128(const char *s, size_t len) {
  if (len >= 16) {
    return CityHash128WithSeed(s + 16,
                               len - 16,
                               uint128((*(const uint64*)(s)) ^ k3,
                                       (*(const uint64*)(s + 8))));
  } else if (len >= 8) {
    return CityHash128WithSeed(__null,
                               0,
                               uint128((*(const uint64*)(s)) ^ (len * k0),
                                       (*(const uint64*)(s + len - 8)) ^ k1));
  } else {
    return CityHash128WithSeed(s, len, uint128(k0, k1));
  }
}