typedef long double __long_double_t;



 




 





 











 








 





 


 



 



 



 





 

 



 

 
























typedef unsigned int size_t;















 




 






















 
typedef long int wchar_t;













 





 


















































































































































 









extern int sys_nerr;
extern char *sys_errlist[];


extern int _sys_nerr;
extern char *_sys_errlist[];


extern int	errno;

 

extern void	perror  (__const char* __s) 	;
extern char*	strerror  (int __errno) 	;

 




 

 


 

    


    


    


    


    


    


    


    


    


    


    



    


    


    


    


    


    


    


    


    



    


    


    



union __convert_long_double {
  unsigned __convert_long_double_i[4];
  long double __convert_long_double_d;
};


    


    


    


    


    


    








 

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

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


 





 





 




 
extern double atof  (__const char *__nptr) 	;
 
extern int atoi  (__const char *__nptr) 	;
 
extern long int atol  (__const char *__nptr) 	;

 
extern double strtod  (__const char *__nptr, char **__endptr) 	;
 
extern long int strtol  (__const char *__nptr, char **__endptr,
			       int __base) 	;
 
extern unsigned long int strtoul  (__const char *__nptr,
					 char **__endptr, int __base) 	;




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

 



 
extern long int __random  (void) 	;
 
extern void __srandom  (unsigned int __seed) 	;

 



extern void * __initstate  (unsigned int __seed, void * __statebuf,
			       size_t __statelen) 	;
 

extern void * __setstate  (void * __statebuf) 	;


extern long int random  (void) 	;
extern void srandom  (unsigned int __seed) 	;
extern void * initstate  (unsigned int __seed, void * __statebuf,
			     size_t __statelen) 	;
extern void * setstate  (void * __statebuf) 	;







 
extern void * malloc  (size_t __size) 	;
 

extern void * realloc  (void * __ptr, size_t __size) 	;
 
extern void * calloc  (size_t __nmemb, size_t __size) 	;
 
extern void free  (void * __ptr) 	;	


 
extern void cfree  (void * __ptr) 	;




 




 



static __inline void* __gnu_calloc (size_t __nmemb, size_t __n)
{
  return calloc (__nmemb ? __nmemb : 1, __n ? __n : 1);
}

static __inline void* __gnu_malloc (size_t __n)
{
  return malloc (__n ? __n : 1);
}









 



























 





 


 



 



 



 





 

 



 

 







 




 



 





 












 

 



 
extern void *  __alloca  (size_t __size) 	;

 

extern void *  alloca  (size_t __size) 	;








 






 
extern void * valloc(size_t __size);



 
extern   void abort  (void) 	 __attribute__ ((noreturn)) ;


 
extern int atexit  (void (*__func)(void)) 	;


 

extern int on_exit  (void (*__func)(int __status, void * __arg),
			   void * __arg) 	;


 


extern   void exit  (int __status) 	 __attribute__ ((noreturn)) ;


 
extern char *getenv  (__const char *__name) 	;


 
 

extern int putenv  (__const char *__string) 	;


 
extern int system  (__const char *__command) 	;


 


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) 	;

 

extern void qsort  (void * __base, size_t __nmemb, size_t __size,
			  __compar_fn_t __compar) 	;

 
extern   int abs  (int __x) 	 __attribute__ ((const)) ;
extern   long int labs  (long int __x) 	 __attribute__ ((const)) ;




 

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


 

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

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

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




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


 


extern char **environ;
extern char **__environ;

extern void*	memalign  (size_t __alignment, size_t __size) 	;
extern void*	valloc  (size_t __size) 	;

extern char*	ecvt  (double __value, size_t __ndigit, int *__decpt,
			int *__sign) 	;
extern char*	fcvt  (double __value, size_t __ndigit, int *__decpt,
			int *__sign) 	;
extern char*	gcvt  (double __value, size_t __ndigit, char *__buf) 	;


 
extern char*	dtoa  (double __d, int __mode, int __ndigits,
			int *__decpt, int *__sign, char **__rve) 	;


extern double	drand48  (void) 	;
extern double	erand48  (unsigned short int __xsubi[3]) 	;
extern long int	lrand48  (void) 	;
extern long int	nrand48  (unsigned short int __xsubi[3]) 	;
extern long int	mrand48  (void) 	;
extern long int	jrand48  (unsigned short int __xsubi[3]) 	;
extern void	srand48  (long int __seedval) 	;
extern unsigned short int
			*seed48  (unsigned short int __seed16v[3]) 	;
extern void	lcong48  (unsigned short int __param[7]) 	;

extern int	setenv  (__const char *__name, __const char *__value,
			int __overwrite) 	;
extern void	unsetenv  (__const char *__name) 	;

struct qelem {
  struct qelem *q_forw;
  struct qelem *q_back;
  char q_data[1];
};

extern void insque  (struct qelem *__elem, struct qelem *__prev) 	;
extern void remque  (struct qelem *__elem) 	;