extern void __VERIFIER_error() __attribute__ ((__noreturn__));
extern int __VERIFIER_nondet_int(void);

typedef unsigned int size_t;
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;
__extension__ typedef signed long long int __int64_t;
__extension__ typedef unsigned long long int __uint64_t;
__extension__ typedef long long int __quad_t;
__extension__ typedef unsigned long long int __u_quad_t;
__extension__ typedef __u_quad_t __dev_t;
__extension__ typedef unsigned int __uid_t;
__extension__ typedef unsigned int __gid_t;
__extension__ typedef unsigned long int __ino_t;
__extension__ typedef __u_quad_t __ino64_t;
__extension__ typedef unsigned int __mode_t;
__extension__ typedef unsigned int __nlink_t;
__extension__ typedef long int __off_t;
__extension__ typedef __quad_t __off64_t;
__extension__ typedef int __pid_t;
__extension__ typedef struct { int __val[2]; } __fsid_t;
__extension__ typedef long int __clock_t;
__extension__ typedef unsigned long int __rlim_t;
__extension__ typedef __u_quad_t __rlim64_t;
__extension__ typedef unsigned int __id_t;
__extension__ typedef long int __time_t;
__extension__ typedef unsigned int __useconds_t;
__extension__ typedef long int __suseconds_t;
__extension__ typedef int __daddr_t;
__extension__ typedef int __key_t;
__extension__ typedef int __clockid_t;
__extension__ typedef void * __timer_t;
__extension__ typedef long int __blksize_t;
__extension__ typedef long int __blkcnt_t;
__extension__ typedef __quad_t __blkcnt64_t;
__extension__ typedef unsigned long int __fsblkcnt_t;
__extension__ typedef __u_quad_t __fsblkcnt64_t;
__extension__ typedef unsigned long int __fsfilcnt_t;
__extension__ typedef __u_quad_t __fsfilcnt64_t;
__extension__ typedef int __fsword_t;
__extension__ typedef int __ssize_t;
__extension__ typedef long int __syscall_slong_t;
__extension__ typedef unsigned long int __syscall_ulong_t;
typedef __off64_t __loff_t;
typedef __quad_t *__qaddr_t;
typedef char *__caddr_t;
__extension__ typedef int __intptr_t;
__extension__ typedef unsigned int __socklen_t;
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 __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)];
};
typedef struct _IO_FILE _IO_FILE;
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);
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) __attribute__ ((__nothrow__ , __leaf__));
extern int _IO_ferror (_IO_FILE *__fp) __attribute__ ((__nothrow__ , __leaf__));
extern int _IO_peekc_locked (_IO_FILE *__fp);
extern void _IO_flockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
extern void _IO_funlockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
extern int _IO_ftrylockfile (_IO_FILE *) __attribute__ ((__nothrow__ , __leaf__));
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 *) __attribute__ ((__nothrow__ , __leaf__));
typedef __gnuc_va_list va_list;
typedef __off_t off_t;
typedef __ssize_t ssize_t;

typedef _G_fpos_t fpos_t;

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

extern int remove (const char *__filename) __attribute__ ((__nothrow__ , __leaf__));
extern int rename (const char *__old, const char *__new) __attribute__ ((__nothrow__ , __leaf__));

extern int renameat (int __oldfd, const char *__old, int __newfd,
       const char *__new) __attribute__ ((__nothrow__ , __leaf__));

extern FILE *tmpfile (void) ;
extern char *tmpnam (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;

extern char *tmpnam_r (char *__s) __attribute__ ((__nothrow__ , __leaf__)) ;
extern char *tempnam (const char *__dir, const char *__pfx)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;

extern int fclose (FILE *__stream);
extern int fflush (FILE *__stream);

extern int fflush_unlocked (FILE *__stream);

extern FILE *fopen (const char *__restrict __filename,
      const char *__restrict __modes) ;
extern FILE *freopen (const char *__restrict __filename,
        const char *__restrict __modes,
        FILE *__restrict __stream) ;

extern FILE *fdopen (int __fd, const char *__modes) __attribute__ ((__nothrow__ , __leaf__)) ;
extern FILE *fmemopen (void *__s, size_t __len, const char *__modes)
  __attribute__ ((__nothrow__ , __leaf__)) ;
extern FILE *open_memstream (char **__bufloc, size_t *__sizeloc) __attribute__ ((__nothrow__ , __leaf__)) ;

extern void setbuf (FILE *__restrict __stream, char *__restrict __buf) __attribute__ ((__nothrow__ , __leaf__));
extern int setvbuf (FILE *__restrict __stream, char *__restrict __buf,
      int __modes, size_t __n) __attribute__ ((__nothrow__ , __leaf__));

extern void setbuffer (FILE *__restrict __stream, char *__restrict __buf,
         size_t __size) __attribute__ ((__nothrow__ , __leaf__));
extern void setlinebuf (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));

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, ...) __attribute__ ((__nothrow__));
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) __attribute__ ((__nothrow__));


extern int snprintf (char *__restrict __s, size_t __maxlen,
       const char *__restrict __format, ...)
     __attribute__ ((__nothrow__)) __attribute__ ((__format__ (__printf__, 3, 4)));
extern int vsnprintf (char *__restrict __s, size_t __maxlen,
        const char *__restrict __format, __gnuc_va_list __arg)
     __attribute__ ((__nothrow__)) __attribute__ ((__format__ (__printf__, 3, 0)));

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, ...) __attribute__ ((__nothrow__ , __leaf__));
extern int fscanf (FILE *__restrict __stream, const char *__restrict __format, ...) __asm__ ("" "__isoc99_fscanf") ;
extern int scanf (const char *__restrict __format, ...) __asm__ ("" "__isoc99_scanf") ;
extern int sscanf (const char *__restrict __s, const char *__restrict __format, ...) __asm__ ("" "__isoc99_sscanf") __attribute__ ((__nothrow__ , __leaf__));


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)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__format__ (__scanf__, 2, 0)));
extern int vfscanf (FILE *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vfscanf")
     __attribute__ ((__format__ (__scanf__, 2, 0))) ;
extern int vscanf (const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vscanf")
     __attribute__ ((__format__ (__scanf__, 1, 0))) ;
extern int vsscanf (const char *__restrict __s, const char *__restrict __format, __gnuc_va_list __arg) __asm__ ("" "__isoc99_vsscanf") __attribute__ ((__nothrow__ , __leaf__))
     __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 __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 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, __off_t __off, int __whence);
extern __off_t ftello (FILE *__stream) ;

extern int fgetpos (FILE *__restrict __stream, fpos_t *__restrict __pos);
extern int fsetpos (FILE *__stream, const fpos_t *__pos);


extern void clearerr (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int feof (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int ferror (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;

extern void clearerr_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int feof_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int ferror_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;

extern void perror (const char *__s);

extern int sys_nerr;
extern const char *const sys_errlist[];
extern int fileno (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int fileno_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern FILE *popen (const char *__command, const char *__modes) ;
extern int pclose (FILE *__stream);
extern char *ctermid (char *__s) __attribute__ ((__nothrow__ , __leaf__));
extern void flockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int ftrylockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern void funlockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));

typedef long int wchar_t;

typedef enum
{
  P_ALL,
  P_PID,
  P_PGID
} idtype_t;
static __inline unsigned int
__bswap_32 (unsigned int __bsx)
{
  return __builtin_bswap32 (__bsx);
}
static __inline __uint64_t
__bswap_64 (__uint64_t __bsx)
{
  return __builtin_bswap64 (__bsx);
}
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 union
  {
    union wait *__uptr;
    int *__iptr;
  } __WAIT_STATUS __attribute__ ((__transparent_union__));

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) __attribute__ ((__nothrow__ , __leaf__)) ;

extern double atof (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
extern int atoi (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;
extern long int atol (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;


__extension__ extern long long int atoll (const char *__nptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;


extern double strtod (const char *__restrict __nptr,
        char **__restrict __endptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern float strtof (const char *__restrict __nptr,
       char **__restrict __endptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern long double strtold (const char *__restrict __nptr,
       char **__restrict __endptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));


extern long int strtol (const char *__restrict __nptr,
   char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern unsigned long int strtoul (const char *__restrict __nptr,
      char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

__extension__
extern long long int strtoq (const char *__restrict __nptr,
        char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
__extension__
extern unsigned long long int strtouq (const char *__restrict __nptr,
           char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

__extension__
extern long long int strtoll (const char *__restrict __nptr,
         char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
__extension__
extern unsigned long long int strtoull (const char *__restrict __nptr,
     char **__restrict __endptr, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

extern char *l64a (long int __n) __attribute__ ((__nothrow__ , __leaf__)) ;
extern long int a64l (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1))) ;

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 __ino_t ino_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 __pid_t pid_t;
typedef __id_t id_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 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;
    __syscall_slong_t tv_nsec;
  };
struct timeval
  {
    __time_t tv_sec;
    __suseconds_t tv_usec;
  };
typedef __suseconds_t suseconds_t;
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 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)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__
extern unsigned int gnu_dev_minor (unsigned long long int __dev)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__
extern unsigned long long int gnu_dev_makedev (unsigned int __major,
            unsigned int __minor)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));

typedef __blksize_t blksize_t;
typedef __blkcnt_t blkcnt_t;
typedef __fsblkcnt_t fsblkcnt_t;
typedef __fsfilcnt_t fsfilcnt_t;
typedef unsigned long int pthread_t;
union pthread_attr_t
{
  char __size[36];
  long int __align;
};
typedef union pthread_attr_t pthread_attr_t;
typedef struct __pthread_internal_slist
{
  struct __pthread_internal_slist *__next;
} __pthread_slist_t;
typedef union
{
  struct __pthread_mutex_s
  {
    int __lock;
    unsigned int __count;
    int __owner;
    int __kind;
    unsigned int __nusers;
    __extension__ union
    {
      struct
      {
 short __espins;
 short __elision;
      } __elision_data;
      __pthread_slist_t __list;
    };
  } __data;
  char __size[24];
  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;
    unsigned char __flags;
    unsigned char __shared;
    signed char __rwelision;
    unsigned char __pad2;
    int __writer;
  } __data;
  char __size[32];
  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[20];
  long int __align;
} pthread_barrier_t;
typedef union
{
  char __size[4];
  int __align;
} pthread_barrierattr_t;

extern long int random (void) __attribute__ ((__nothrow__ , __leaf__));
extern void srandom (unsigned int __seed) __attribute__ ((__nothrow__ , __leaf__));
extern char *initstate (unsigned int __seed, char *__statebuf,
   size_t __statelen) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern char *setstate (char *__statebuf) __attribute__ ((__nothrow__ , __leaf__)) __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) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int srandom_r (unsigned int __seed, struct random_data *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern int initstate_r (unsigned int __seed, char *__restrict __statebuf,
   size_t __statelen,
   struct random_data *__restrict __buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 4)));
extern int setstate_r (char *__restrict __statebuf,
         struct random_data *__restrict __buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern int rand (void) __attribute__ ((__nothrow__ , __leaf__));
extern void srand (unsigned int __seed) __attribute__ ((__nothrow__ , __leaf__));

extern int rand_r (unsigned int *__seed) __attribute__ ((__nothrow__ , __leaf__));
extern double drand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern double erand48 (unsigned short int __xsubi[3]) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern long int lrand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern long int nrand48 (unsigned short int __xsubi[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern long int mrand48 (void) __attribute__ ((__nothrow__ , __leaf__));
extern long int jrand48 (unsigned short int __xsubi[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern void srand48 (long int __seedval) __attribute__ ((__nothrow__ , __leaf__));
extern unsigned short int *seed48 (unsigned short int __seed16v[3])
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern void lcong48 (unsigned short int __param[7]) __attribute__ ((__nothrow__ , __leaf__)) __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;
    __extension__ unsigned long long int __a;
  };
extern int drand48_r (struct drand48_data *__restrict __buffer,
        double *__restrict __result) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int erand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        double *__restrict __result) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int lrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int nrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int mrand48_r (struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int jrand48_r (unsigned short int __xsubi[3],
        struct drand48_data *__restrict __buffer,
        long int *__restrict __result)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int srand48_r (long int __seedval, struct drand48_data *__buffer)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern int seed48_r (unsigned short int __seed16v[3],
       struct drand48_data *__buffer) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int lcong48_r (unsigned short int __param[7],
        struct drand48_data *__buffer)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern void *malloc (size_t __size) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;
extern void *calloc (size_t __nmemb, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;


extern void *realloc (void *__ptr, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__warn_unused_result__));
extern void free (void *__ptr) __attribute__ ((__nothrow__ , __leaf__));

extern void cfree (void *__ptr) __attribute__ ((__nothrow__ , __leaf__));

extern void *alloca (size_t __size) __attribute__ ((__nothrow__ , __leaf__));

extern void *valloc (size_t __size) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) ;
extern int posix_memalign (void **__memptr, size_t __alignment, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;
extern void *aligned_alloc (size_t __alignment, size_t __size)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) __attribute__ ((__alloc_size__ (2))) ;

extern void abort (void) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));
extern int atexit (void (*__func) (void)) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int at_quick_exit (void (*__func) (void)) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

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

extern void exit (int __status) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));
extern void quick_exit (int __status) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));


extern void _Exit (int __status) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));


extern char *getenv (const char *__name) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;

extern int putenv (char *__string) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int setenv (const char *__name, const char *__value, int __replace)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern int unsetenv (const char *__name) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int clearenv (void) __attribute__ ((__nothrow__ , __leaf__));
extern char *mktemp (char *__template) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int mkstemp (char *__template) __attribute__ ((__nonnull__ (1))) ;
extern int mkstemps (char *__template, int __suffixlen) __attribute__ ((__nonnull__ (1))) ;
extern char *mkdtemp (char *__template) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;

extern int system (const char *__command) ;

extern char *realpath (const char *__restrict __name,
         char *__restrict __resolved) __attribute__ ((__nothrow__ , __leaf__)) ;
typedef int (*__compar_fn_t) (const void *, const 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 int abs (int __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;
extern long int labs (long int __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;

__extension__ extern long long int llabs (long long int __x)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)) ;

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


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

extern char *ecvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *fcvt (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *gcvt (double __value, int __ndigit, char *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3))) ;
extern char *qecvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qfcvt (long double __value, int __ndigit,
      int *__restrict __decpt, int *__restrict __sign)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4))) ;
extern char *qgcvt (long double __value, int __ndigit, char *__buf)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3))) ;
extern int ecvt_r (double __value, int __ndigit, int *__restrict __decpt,
     int *__restrict __sign, char *__restrict __buf,
     size_t __len) __attribute__ ((__nothrow__ , __leaf__)) __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) __attribute__ ((__nothrow__ , __leaf__)) __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)
     __attribute__ ((__nothrow__ , __leaf__)) __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)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3, 4, 5)));

extern int mblen (const char *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__));
extern int mbtowc (wchar_t *__restrict __pwc,
     const char *__restrict __s, size_t __n) __attribute__ ((__nothrow__ , __leaf__));
extern int wctomb (char *__s, wchar_t __wchar) __attribute__ ((__nothrow__ , __leaf__));
extern size_t mbstowcs (wchar_t *__restrict __pwcs,
   const char *__restrict __s, size_t __n) __attribute__ ((__nothrow__ , __leaf__));
extern size_t wcstombs (char *__restrict __s,
   const wchar_t *__restrict __pwcs, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__));

extern int rpmatch (const char *__response) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) ;
extern int getsubopt (char **__restrict __optionp,
        char *const *__restrict __tokens,
        char **__restrict __valuep)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2, 3))) ;
extern int getloadavg (double __loadavg[], int __nelem)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));



extern void *memcpy (void *__restrict __dest, const void *__restrict __src,
       size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern void *memmove (void *__dest, const void *__src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern void *memccpy (void *__restrict __dest, const void *__restrict __src,
        int __c, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));

extern void *memset (void *__s, int __c, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int memcmp (const void *__s1, const void *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern void *memchr (const void *__s, int __c, size_t __n)
      __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));


extern char *strcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strncpy (char *__restrict __dest,
        const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strcat (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strncat (char *__restrict __dest, const char *__restrict __src,
        size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int strcmp (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern int strncmp (const char *__s1, const char *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern int strcoll (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern size_t strxfrm (char *__restrict __dest,
         const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __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)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));
extern size_t strxfrm_l (char *__dest, const char *__src, size_t __n,
    __locale_t __l) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 4)));
extern char *strdup (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));
extern char *strndup (const char *__string, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__malloc__)) __attribute__ ((__nonnull__ (1)));

extern char *strchr (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern char *strrchr (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));


extern size_t strcspn (const char *__s, const char *__reject)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern size_t strspn (const char *__s, const char *__accept)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strpbrk (const char *__s, const char *__accept)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strstr (const char *__haystack, const char *__needle)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strtok (char *__restrict __s, const char *__restrict __delim)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));

extern char *__strtok_r (char *__restrict __s,
    const char *__restrict __delim,
    char **__restrict __save_ptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 3)));
extern char *strtok_r (char *__restrict __s, const char *__restrict __delim,
         char **__restrict __save_ptr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 3)));

extern size_t strlen (const char *__s)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));

extern size_t strnlen (const char *__string, size_t __maxlen)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));

extern char *strerror (int __errnum) __attribute__ ((__nothrow__ , __leaf__));

extern int strerror_r (int __errnum, char *__buf, size_t __buflen) __asm__ ("" "__xpg_strerror_r") __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern char *strerror_l (int __errnum, __locale_t __l) __attribute__ ((__nothrow__ , __leaf__));
extern void __bzero (void *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern void bcopy (const void *__src, void *__dest, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern void bzero (void *__s, size_t __n) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int bcmp (const void *__s1, const void *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *index (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern char *rindex (const char *__s, int __c)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1)));
extern int ffs (int __i) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern int strcasecmp (const char *__s1, const char *__s2)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern int strncasecmp (const char *__s1, const char *__s2, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strsep (char **__restrict __stringp,
       const char *__restrict __delim)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *strsignal (int __sig) __attribute__ ((__nothrow__ , __leaf__));
extern char *__stpcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *stpcpy (char *__restrict __dest, const char *__restrict __src)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *__stpncpy (char *__restrict __dest,
   const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern char *stpncpy (char *__restrict __dest,
        const char *__restrict __src, size_t __n)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));


extern int *__errno_location (void) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));

struct sched_param
  {
    int __sched_priority;
  };


struct __sched_param
  {
    int __sched_priority;
  };
typedef unsigned long int __cpu_mask;
typedef struct
{
  __cpu_mask __bits[1024 / (8 * sizeof (__cpu_mask))];
} cpu_set_t;

extern int __sched_cpucount (size_t __setsize, const cpu_set_t *__setp)
  __attribute__ ((__nothrow__ , __leaf__));
extern cpu_set_t *__sched_cpualloc (size_t __count) __attribute__ ((__nothrow__ , __leaf__)) ;
extern void __sched_cpufree (cpu_set_t *__set) __attribute__ ((__nothrow__ , __leaf__));


extern int sched_setparam (__pid_t __pid, const struct sched_param *__param)
     __attribute__ ((__nothrow__ , __leaf__));
extern int sched_getparam (__pid_t __pid, struct sched_param *__param) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_setscheduler (__pid_t __pid, int __policy,
          const struct sched_param *__param) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_getscheduler (__pid_t __pid) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_yield (void) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_get_priority_max (int __algorithm) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_get_priority_min (int __algorithm) __attribute__ ((__nothrow__ , __leaf__));
extern int sched_rr_get_interval (__pid_t __pid, struct timespec *__t) __attribute__ ((__nothrow__ , __leaf__));



struct tm
{
  int tm_sec;
  int tm_min;
  int tm_hour;
  int tm_mday;
  int tm_mon;
  int tm_year;
  int tm_wday;
  int tm_yday;
  int tm_isdst;
  long int tm_gmtoff;
  const char *tm_zone;
};


struct itimerspec
  {
    struct timespec it_interval;
    struct timespec it_value;
  };
struct sigevent;

extern clock_t clock (void) __attribute__ ((__nothrow__ , __leaf__));
extern time_t time (time_t *__timer) __attribute__ ((__nothrow__ , __leaf__));
extern double difftime (time_t __time1, time_t __time0)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern time_t mktime (struct tm *__tp) __attribute__ ((__nothrow__ , __leaf__));
extern size_t strftime (char *__restrict __s, size_t __maxsize,
   const char *__restrict __format,
   const struct tm *__restrict __tp) __attribute__ ((__nothrow__ , __leaf__));

extern size_t strftime_l (char *__restrict __s, size_t __maxsize,
     const char *__restrict __format,
     const struct tm *__restrict __tp,
     __locale_t __loc) __attribute__ ((__nothrow__ , __leaf__));

extern struct tm *gmtime (const time_t *__timer) __attribute__ ((__nothrow__ , __leaf__));
extern struct tm *localtime (const time_t *__timer) __attribute__ ((__nothrow__ , __leaf__));

extern struct tm *gmtime_r (const time_t *__restrict __timer,
       struct tm *__restrict __tp) __attribute__ ((__nothrow__ , __leaf__));
extern struct tm *localtime_r (const time_t *__restrict __timer,
          struct tm *__restrict __tp) __attribute__ ((__nothrow__ , __leaf__));

extern char *asctime (const struct tm *__tp) __attribute__ ((__nothrow__ , __leaf__));
extern char *ctime (const time_t *__timer) __attribute__ ((__nothrow__ , __leaf__));

extern char *asctime_r (const struct tm *__restrict __tp,
   char *__restrict __buf) __attribute__ ((__nothrow__ , __leaf__));
extern char *ctime_r (const time_t *__restrict __timer,
        char *__restrict __buf) __attribute__ ((__nothrow__ , __leaf__));
extern char *__tzname[2];
extern int __daylight;
extern long int __timezone;
extern char *tzname[2];
extern void tzset (void) __attribute__ ((__nothrow__ , __leaf__));
extern int daylight;
extern long int timezone;
extern int stime (const time_t *__when) __attribute__ ((__nothrow__ , __leaf__));
extern time_t timegm (struct tm *__tp) __attribute__ ((__nothrow__ , __leaf__));
extern time_t timelocal (struct tm *__tp) __attribute__ ((__nothrow__ , __leaf__));
extern int dysize (int __year) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern int nanosleep (const struct timespec *__requested_time,
        struct timespec *__remaining);
extern int clock_getres (clockid_t __clock_id, struct timespec *__res) __attribute__ ((__nothrow__ , __leaf__));
extern int clock_gettime (clockid_t __clock_id, struct timespec *__tp) __attribute__ ((__nothrow__ , __leaf__));
extern int clock_settime (clockid_t __clock_id, const struct timespec *__tp)
     __attribute__ ((__nothrow__ , __leaf__));
extern int clock_nanosleep (clockid_t __clock_id, int __flags,
       const struct timespec *__req,
       struct timespec *__rem);
extern int clock_getcpuclockid (pid_t __pid, clockid_t *__clock_id) __attribute__ ((__nothrow__ , __leaf__));
extern int timer_create (clockid_t __clock_id,
    struct sigevent *__restrict __evp,
    timer_t *__restrict __timerid) __attribute__ ((__nothrow__ , __leaf__));
extern int timer_delete (timer_t __timerid) __attribute__ ((__nothrow__ , __leaf__));
extern int timer_settime (timer_t __timerid, int __flags,
     const struct itimerspec *__restrict __value,
     struct itimerspec *__restrict __ovalue) __attribute__ ((__nothrow__ , __leaf__));
extern int timer_gettime (timer_t __timerid, struct itimerspec *__value)
     __attribute__ ((__nothrow__ , __leaf__));
extern int timer_getoverrun (timer_t __timerid) __attribute__ ((__nothrow__ , __leaf__));
extern int timespec_get (struct timespec *__ts, int __base)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));

typedef int __jmp_buf[6];
enum
{
  PTHREAD_CREATE_JOINABLE,
  PTHREAD_CREATE_DETACHED
};
enum
{
  PTHREAD_MUTEX_TIMED_NP,
  PTHREAD_MUTEX_RECURSIVE_NP,
  PTHREAD_MUTEX_ERRORCHECK_NP,
  PTHREAD_MUTEX_ADAPTIVE_NP
  ,
  PTHREAD_MUTEX_NORMAL = PTHREAD_MUTEX_TIMED_NP,
  PTHREAD_MUTEX_RECURSIVE = PTHREAD_MUTEX_RECURSIVE_NP,
  PTHREAD_MUTEX_ERRORCHECK = PTHREAD_MUTEX_ERRORCHECK_NP,
  PTHREAD_MUTEX_DEFAULT = PTHREAD_MUTEX_NORMAL
};
enum
{
  PTHREAD_MUTEX_STALLED,
  PTHREAD_MUTEX_STALLED_NP = PTHREAD_MUTEX_STALLED,
  PTHREAD_MUTEX_ROBUST,
  PTHREAD_MUTEX_ROBUST_NP = PTHREAD_MUTEX_ROBUST
};
enum
{
  PTHREAD_PRIO_NONE,
  PTHREAD_PRIO_INHERIT,
  PTHREAD_PRIO_PROTECT
};
enum
{
  PTHREAD_RWLOCK_PREFER_READER_NP,
  PTHREAD_RWLOCK_PREFER_WRITER_NP,
  PTHREAD_RWLOCK_PREFER_WRITER_NONRECURSIVE_NP,
  PTHREAD_RWLOCK_DEFAULT_NP = PTHREAD_RWLOCK_PREFER_READER_NP
};
enum
{
  PTHREAD_INHERIT_SCHED,
  PTHREAD_EXPLICIT_SCHED
};
enum
{
  PTHREAD_SCOPE_SYSTEM,
  PTHREAD_SCOPE_PROCESS
};
enum
{
  PTHREAD_PROCESS_PRIVATE,
  PTHREAD_PROCESS_SHARED
};
struct _pthread_cleanup_buffer
{
  void (*__routine) (void *);
  void *__arg;
  int __canceltype;
  struct _pthread_cleanup_buffer *__prev;
};
enum
{
  PTHREAD_CANCEL_ENABLE,
  PTHREAD_CANCEL_DISABLE
};
enum
{
  PTHREAD_CANCEL_DEFERRED,
  PTHREAD_CANCEL_ASYNCHRONOUS
};

extern int pthread_create (pthread_t *__restrict __newthread,
      const pthread_attr_t *__restrict __attr,
      void *(*__start_routine) (void *),
      void *__restrict __arg) __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1, 3)));
extern void pthread_exit (void *__retval) __attribute__ ((__noreturn__));
extern int pthread_join (pthread_t __th, void **__thread_return);
extern int pthread_detach (pthread_t __th) __attribute__ ((__nothrow__ , __leaf__));
extern pthread_t pthread_self (void) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern int pthread_equal (pthread_t __thread1, pthread_t __thread2)
  __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern int pthread_attr_init (pthread_attr_t *__attr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_destroy (pthread_attr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getdetachstate (const pthread_attr_t *__attr,
     int *__detachstate)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setdetachstate (pthread_attr_t *__attr,
     int __detachstate)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getguardsize (const pthread_attr_t *__attr,
          size_t *__guardsize)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setguardsize (pthread_attr_t *__attr,
          size_t __guardsize)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getschedparam (const pthread_attr_t *__restrict __attr,
           struct sched_param *__restrict __param)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setschedparam (pthread_attr_t *__restrict __attr,
           const struct sched_param *__restrict
           __param) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_getschedpolicy (const pthread_attr_t *__restrict
     __attr, int *__restrict __policy)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setschedpolicy (pthread_attr_t *__attr, int __policy)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getinheritsched (const pthread_attr_t *__restrict
      __attr, int *__restrict __inherit)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setinheritsched (pthread_attr_t *__attr,
      int __inherit)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getscope (const pthread_attr_t *__restrict __attr,
      int *__restrict __scope)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setscope (pthread_attr_t *__attr, int __scope)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getstackaddr (const pthread_attr_t *__restrict
          __attr, void **__restrict __stackaddr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2))) __attribute__ ((__deprecated__));
extern int pthread_attr_setstackaddr (pthread_attr_t *__attr,
          void *__stackaddr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1))) __attribute__ ((__deprecated__));
extern int pthread_attr_getstacksize (const pthread_attr_t *__restrict
          __attr, size_t *__restrict __stacksize)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_attr_setstacksize (pthread_attr_t *__attr,
          size_t __stacksize)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_attr_getstack (const pthread_attr_t *__restrict __attr,
      void **__restrict __stackaddr,
      size_t *__restrict __stacksize)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2, 3)));
extern int pthread_attr_setstack (pthread_attr_t *__attr, void *__stackaddr,
      size_t __stacksize) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_setschedparam (pthread_t __target_thread, int __policy,
      const struct sched_param *__param)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (3)));
extern int pthread_getschedparam (pthread_t __target_thread,
      int *__restrict __policy,
      struct sched_param *__restrict __param)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2, 3)));
extern int pthread_setschedprio (pthread_t __target_thread, int __prio)
     __attribute__ ((__nothrow__ , __leaf__));
extern int pthread_once (pthread_once_t *__once_control,
    void (*__init_routine) (void)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_setcancelstate (int __state, int *__oldstate);
extern int pthread_setcanceltype (int __type, int *__oldtype);
extern int pthread_cancel (pthread_t __th);
extern void pthread_testcancel (void);
typedef struct
{
  struct
  {
    __jmp_buf __cancel_jmp_buf;
    int __mask_was_saved;
  } __cancel_jmp_buf[1];
  void *__pad[4];
} __pthread_unwind_buf_t __attribute__ ((__aligned__));
struct __pthread_cleanup_frame
{
  void (*__cancel_routine) (void *);
  void *__cancel_arg;
  int __do_it;
  int __cancel_type;
};
extern void __pthread_register_cancel (__pthread_unwind_buf_t *__buf)
     __attribute__ ((__regparm__ (1)));
extern void __pthread_unregister_cancel (__pthread_unwind_buf_t *__buf)
  __attribute__ ((__regparm__ (1)));
extern void __pthread_unwind_next (__pthread_unwind_buf_t *__buf)
     __attribute__ ((__regparm__ (1))) __attribute__ ((__noreturn__))
     __attribute__ ((__weak__))
     ;
struct __jmp_buf_tag;
extern int __sigsetjmp (struct __jmp_buf_tag *__env, int __savemask) __attribute__ ((__nothrow__));
extern int pthread_mutex_init (pthread_mutex_t *__mutex,
          const pthread_mutexattr_t *__mutexattr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutex_destroy (pthread_mutex_t *__mutex)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutex_trylock (pthread_mutex_t *__mutex)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutex_lock (pthread_mutex_t *__mutex)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutex_timedlock (pthread_mutex_t *__restrict __mutex,
        const struct timespec *__restrict
        __abstime) __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutex_unlock (pthread_mutex_t *__mutex)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutex_getprioceiling (const pthread_mutex_t *
      __restrict __mutex,
      int *__restrict __prioceiling)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutex_setprioceiling (pthread_mutex_t *__restrict __mutex,
      int __prioceiling,
      int *__restrict __old_ceiling)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 3)));
extern int pthread_mutex_consistent (pthread_mutex_t *__mutex)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_init (pthread_mutexattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_destroy (pthread_mutexattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_getpshared (const pthread_mutexattr_t *
      __restrict __attr,
      int *__restrict __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutexattr_setpshared (pthread_mutexattr_t *__attr,
      int __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_gettype (const pthread_mutexattr_t *__restrict
          __attr, int *__restrict __kind)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutexattr_settype (pthread_mutexattr_t *__attr, int __kind)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_getprotocol (const pthread_mutexattr_t *
       __restrict __attr,
       int *__restrict __protocol)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutexattr_setprotocol (pthread_mutexattr_t *__attr,
       int __protocol)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_getprioceiling (const pthread_mutexattr_t *
          __restrict __attr,
          int *__restrict __prioceiling)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutexattr_setprioceiling (pthread_mutexattr_t *__attr,
          int __prioceiling)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_mutexattr_getrobust (const pthread_mutexattr_t *__attr,
     int *__robustness)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_mutexattr_setrobust (pthread_mutexattr_t *__attr,
     int __robustness)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_init (pthread_rwlock_t *__restrict __rwlock,
    const pthread_rwlockattr_t *__restrict
    __attr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_destroy (pthread_rwlock_t *__rwlock)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_rdlock (pthread_rwlock_t *__rwlock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_tryrdlock (pthread_rwlock_t *__rwlock)
  __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_timedrdlock (pthread_rwlock_t *__restrict __rwlock,
           const struct timespec *__restrict
           __abstime) __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_rwlock_wrlock (pthread_rwlock_t *__rwlock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_trywrlock (pthread_rwlock_t *__rwlock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlock_timedwrlock (pthread_rwlock_t *__restrict __rwlock,
           const struct timespec *__restrict
           __abstime) __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_rwlock_unlock (pthread_rwlock_t *__rwlock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlockattr_init (pthread_rwlockattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlockattr_destroy (pthread_rwlockattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlockattr_getpshared (const pthread_rwlockattr_t *
       __restrict __attr,
       int *__restrict __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_rwlockattr_setpshared (pthread_rwlockattr_t *__attr,
       int __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_rwlockattr_getkind_np (const pthread_rwlockattr_t *
       __restrict __attr,
       int *__restrict __pref)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_rwlockattr_setkind_np (pthread_rwlockattr_t *__attr,
       int __pref) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_cond_init (pthread_cond_t *__restrict __cond,
         const pthread_condattr_t *__restrict __cond_attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_cond_destroy (pthread_cond_t *__cond)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_cond_signal (pthread_cond_t *__cond)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_cond_broadcast (pthread_cond_t *__cond)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_cond_wait (pthread_cond_t *__restrict __cond,
         pthread_mutex_t *__restrict __mutex)
     __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_cond_timedwait (pthread_cond_t *__restrict __cond,
       pthread_mutex_t *__restrict __mutex,
       const struct timespec *__restrict __abstime)
     __attribute__ ((__nonnull__ (1, 2, 3)));
extern int pthread_condattr_init (pthread_condattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_condattr_destroy (pthread_condattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_condattr_getpshared (const pthread_condattr_t *
     __restrict __attr,
     int *__restrict __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_condattr_setpshared (pthread_condattr_t *__attr,
     int __pshared) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_condattr_getclock (const pthread_condattr_t *
          __restrict __attr,
          __clockid_t *__restrict __clock_id)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_condattr_setclock (pthread_condattr_t *__attr,
          __clockid_t __clock_id)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_spin_init (pthread_spinlock_t *__lock, int __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_spin_destroy (pthread_spinlock_t *__lock)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_spin_lock (pthread_spinlock_t *__lock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_spin_trylock (pthread_spinlock_t *__lock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_spin_unlock (pthread_spinlock_t *__lock)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrier_init (pthread_barrier_t *__restrict __barrier,
     const pthread_barrierattr_t *__restrict
     __attr, unsigned int __count)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrier_destroy (pthread_barrier_t *__barrier)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrier_wait (pthread_barrier_t *__barrier)
     __attribute__ ((__nothrow__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrierattr_init (pthread_barrierattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrierattr_destroy (pthread_barrierattr_t *__attr)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_barrierattr_getpshared (const pthread_barrierattr_t *
        __restrict __attr,
        int *__restrict __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1, 2)));
extern int pthread_barrierattr_setpshared (pthread_barrierattr_t *__attr,
        int __pshared)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_key_create (pthread_key_t *__key,
          void (*__destr_function) (void *))
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (1)));
extern int pthread_key_delete (pthread_key_t __key) __attribute__ ((__nothrow__ , __leaf__));
extern void *pthread_getspecific (pthread_key_t __key) __attribute__ ((__nothrow__ , __leaf__));
extern int pthread_setspecific (pthread_key_t __key,
    const void *__pointer) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int pthread_getcpuclockid (pthread_t __thread_id,
      __clockid_t *__clock_id)
     __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern int pthread_atfork (void (*__prepare) (void),
      void (*__parent) (void),
      void (*__child) (void)) __attribute__ ((__nothrow__ , __leaf__));

typedef struct bounded_buf_tag
{
    int valid;
    pthread_mutex_t mutex;
    pthread_cond_t not_full;
    pthread_cond_t not_empty;
    size_t item_num;
    size_t max_size;
    size_t head, rear;
    size_t p_wait;
    size_t c_wait;
    void ** buf;
}bounded_buf_t;
int bounded_buf_init(bounded_buf_t * bbuf, size_t sz)
{
    int status = 0;
    if (bbuf == ((void *)0)) return 22;
    bbuf->valid = 0xACDEFA;
    status = pthread_mutex_init(&bbuf->mutex, ((void *)0));
    if (status != 0) return status;
    status = pthread_cond_init(&bbuf->not_full, ((void *)0));
    if (status != 0)
    {
        pthread_mutex_destroy(&bbuf->mutex);
        return status;
    }
    status = pthread_cond_init(&bbuf->not_empty, ((void *)0));
    if (status != 0)
    {
        pthread_cond_destroy(&bbuf->not_full);
        pthread_mutex_destroy(&bbuf->mutex);
        return status;
    }
    bbuf->item_num = 0;
    bbuf->max_size = sz;
    bbuf->head = 0;
    bbuf->rear = 0;
    bbuf->buf = calloc( sz, sizeof(void*) );
    if (bbuf->buf == ((void *)0))
    {
        pthread_mutex_destroy(&bbuf->mutex);
        pthread_cond_destroy(&bbuf->not_full);
        pthread_cond_destroy(&bbuf->not_empty);
        return 12;
    }
    bbuf->head = 0;
    bbuf->rear = 0;
    bbuf->p_wait = 0;
    bbuf->c_wait = 0;
    return 0;
}
int bounded_buf_destroy(bounded_buf_t * bbuf)
{
    int status = 0, status1 = 0, status2 = 0;
    if (bbuf == ((void *)0) || bbuf->valid != 0xACDEFA)
        return 22;
    status = pthread_mutex_lock(&bbuf->mutex);
    if (status != 0) return status;
    bbuf->valid = 0;
    status = pthread_mutex_unlock(&bbuf->mutex);
    if (status != 0) return status;
    status = pthread_mutex_destroy(&bbuf->mutex);
    status1= pthread_cond_destroy(&bbuf->not_full);
    status2= pthread_cond_destroy(&bbuf->not_empty);
    int i;
    if (bbuf->rear >= bbuf->head ) {
        for (i = bbuf->head; i < bbuf->rear; i++) free(bbuf->buf[i]);
    }
    else{
        for (i = bbuf->head; i < bbuf->max_size; i++) free(bbuf->buf[i]);
        for (i = 0; i < bbuf->rear; i++) free(bbuf->buf[i]);
    }
    free(bbuf->buf);
    return (status != 0)? status:((status1 != 0)? status1 : status2);
}
void bounded_buf_putcleanup(void * arg)
{
    bounded_buf_t * bbuf = (bounded_buf_t*) arg;
    bbuf->p_wait--;
    pthread_mutex_unlock(&bbuf->mutex);
}
void bounded_buf_getcleanup(void *arg)
{
    bounded_buf_t * bbuf = (bounded_buf_t*) arg;
    bbuf->c_wait--;
    pthread_mutex_unlock(&bbuf->mutex);
}
int bounded_buf_put(bounded_buf_t * bbuf, void *item)
{
    int status = 0, status1 = 0, status2 = 0;
    if (bbuf == ((void *)0) || bbuf->valid != 0xACDEFA)
        return 22;
    status = pthread_mutex_lock(&bbuf->mutex);
    ;
    if (status != 0) return status;
    if ( (bbuf->rear + 1)% bbuf->max_size == bbuf->head )
    {
        bbuf->p_wait++;
        while ( (bbuf->rear + 1)% bbuf->max_size == bbuf->head ){
            ;
            status = pthread_cond_wait(&bbuf->not_full, &bbuf->mutex);
            if (status != 0) break;
        }
        bbuf->p_wait--;
    }
    if (status == 0){
        bbuf->buf[bbuf->rear]= item;
        bbuf->rear = (bbuf->rear+1)% (bbuf->max_size);
        if (bbuf->c_wait > 0){
            ;
            status1 = pthread_cond_signal(&bbuf->not_empty);
        }
    }
    ;
    status2 = pthread_mutex_unlock(&bbuf->mutex);
    return (status == 0)? status2 : status;
}
int bounded_buf_get(bounded_buf_t *bbuf, void **item)
{
    int status = 0,status1 = 0, status2 = 0;
    if (bbuf == ((void *)0) || item == ((void *)0) || bbuf->valid != 0xACDEFA)
        return 22;
    status = pthread_mutex_lock(&bbuf->mutex);
    ;
    if (status != 0) return status;
    if (bbuf->head == bbuf->rear)
    {
        bbuf->c_wait++;
        while (bbuf->head == bbuf->rear)
        {
            ;
            status = pthread_cond_wait(&bbuf->not_empty, &bbuf->mutex);
            if (status != 0) break;
        }
        bbuf->c_wait--;
    }
    ;
    status = pthread_mutex_unlock(&bbuf->mutex);
    status = pthread_mutex_lock(&bbuf->mutex);
    ;
    if (status == 0)
    {
        if(bbuf->head == bbuf->rear)
        {
            ERROR: __VERIFIER_error();
        }
        *item = bbuf->buf[bbuf->head];
        bbuf->head = (bbuf->head+1) % bbuf->max_size;
        if (bbuf->p_wait > 0){
            ;
            status1 = pthread_cond_signal(&bbuf->not_full);
        }
    }
    ;
    status2 = pthread_mutex_unlock(&bbuf->mutex);
    return (status != 0)? status : (status1 != 0)? status1 : status2;
}
int bounded_buf_is_empty(bounded_buf_t* bbuf)
{
    int status = 0, retval;
    if (bbuf == ((void *)0) || bbuf->valid != 0xACDEFA)
        return -1;
    status = pthread_mutex_lock(&bbuf->mutex);
    if (status != 0) return status;
    retval = (bbuf->rear == bbuf->head )? 1 : 0;
    status = pthread_mutex_unlock(&bbuf->mutex);
    return (status == 0)? retval : -1;
}
int bounded_buf_is_full(bounded_buf_t* bbuf)
{
    int status = 0, retval;
    if (bbuf == ((void *)0) || bbuf->valid != 0xACDEFA) return -1;
    status = pthread_mutex_lock(&bbuf->mutex);
    if (status != 0) return status;
    retval = ( (bbuf->rear + 1) % bbuf->max_size == bbuf->head )? 1 : 0;
    status = pthread_mutex_unlock(&bbuf->mutex);
    return (status == 0)? retval : -1;
}
typedef struct thread_tag
{
    pthread_t pid;
    int id;
    bounded_buf_t * bbuf;
}thread_t;
void * producer_routine(void *arg)
{
    thread_t * thread = (thread_t*) arg;
    int i, temp;
    int ch;
    int status = 0;
    for (i = 0; i < 4; i++)
    {
        ch = __VERIFIER_nondet_int();
        temp = ch;
        status = bounded_buf_put(thread->bbuf, (void*)((int)temp));
        if (status != 0)
            ;
        else
            ;
        fflush(stdout);
    }
    return ((void *)0);
}
void * consumer_routine(void * arg)
{
    thread_t * thread = (thread_t*) arg;
    int i;
    int ch;
    int status = 0;
    void* temp;
    for (i = 0; i < 4; i++)
    {
        status = bounded_buf_get(thread->bbuf, &temp);
        if (status != 0)
            ;
        else
        {
            ch = (char)( (int)temp );
            ;
        }
        fflush(stdout);
    }
    return ((void *)0);
}
int main(void)
{
    thread_t producers[2];
    thread_t consumers[2];
    int i;
    bounded_buf_t buffer;
    bounded_buf_init(&buffer, 3);
    for (i = 0; i < 2; i++)
    {
        producers[i].id = i;
        producers[i].bbuf = &buffer;
        pthread_create(&producers[i].pid, ((void *)0), producer_routine, (void*)&producers[i]);
    }
    for (i = 0; i < 2; i++)
    {
        consumers[i].id = i;
        consumers[i].bbuf = &buffer;
        pthread_create(&consumers[i].pid, ((void *)0), consumer_routine, (void*)&consumers[i]);
    }
    for (i = 0; i < 2; i++)
        pthread_join(producers[i].pid, ((void *)0));
    for (i = 0; i < 2; i++)
        pthread_join(consumers[i].pid, ((void *)0));
    bounded_buf_destroy(&buffer);
    return 0;
}