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preprocessed_oracle.c
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preprocessed_oracle.c
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void DCEMarker0_(void);
void DCEMarker1_(void);
void DCEMarker2_(void);
void DCEMarker3_(void);
void DCEMarker4_(void);
void DCEMarker5_(void);
void DCEMarker6_(void);
void DCEMarker7_(void);
void DCEMarker8_(void);
void DCEMarker9_(void);
void DCEMarker10_(void);
void DCEMarker11_(void);
void DCEMarker12_(void);
void DCEMarker13_(void);
void DCEMarker14_(void);
void DCEMarker15_(void);
void DCEMarker16_(void);
void DCEMarker17_(void);
void DCEMarker18_(void);
void DCEMarker19_(void);
void DCEMarker20_(void);
void DCEMarker21_(void);
void DCEMarker22_(void);
void DCEMarker23_(void);
void DCEMarker24_(void);
void DCEMarker25_(void);
void DCEMarker26_(void);
void DCEMarker27_(void);
void DCEMarker28_(void);
void DCEMarker29_(void);
void DCEMarker30_(void);
typedef long unsigned int size_t;
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 *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 int __memcmpeq (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)));
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];
};
typedef struct __locale_struct *__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 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 char *strerror_l (int __errnum, locale_t __l) __attribute__ ((__nothrow__ , __leaf__));
extern int bcmp (const void *__s1, const void *__s2, size_t __n)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2)));
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 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 ffsl (long int __l) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
__extension__ extern int ffsll (long long int __ll)
__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 int strcasecmp_l (const char *__s1, const char *__s2, locale_t __loc)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 3)));
extern int strncasecmp_l (const char *__s1, const char *__s2,
size_t __n, locale_t __loc)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__pure__)) __attribute__ ((__nonnull__ (1, 2, 4)));
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)));
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 __int8_t __int_least8_t;
typedef __uint8_t __uint_least8_t;
typedef __int16_t __int_least16_t;
typedef __uint16_t __uint_least16_t;
typedef __int32_t __int_least32_t;
typedef __uint32_t __uint_least32_t;
typedef __int64_t __int_least64_t;
typedef __uint64_t __uint_least64_t;
typedef long int __quad_t;
typedef unsigned long int __u_quad_t;
typedef long int __intmax_t;
typedef unsigned long int __uintmax_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 long int __suseconds64_t;
typedef int __daddr_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 __fsword_t;
typedef long int __ssize_t;
typedef long int __syscall_slong_t;
typedef unsigned long int __syscall_ulong_t;
typedef __off64_t __loff_t;
typedef char *__caddr_t;
typedef long int __intptr_t;
typedef unsigned int __socklen_t;
typedef int __sig_atomic_t;
typedef float float_t;
typedef double double_t;
extern int __fpclassify (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __signbit (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isinf (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __finite (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isnan (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __iseqsig (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern int __issignaling (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern double acos (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __acos (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double asin (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __asin (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double atan (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atan (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double atan2 (double __y, double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atan2 (double __y, double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double cos (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cos (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double sin (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sin (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double tan (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __tan (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double cosh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cosh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double sinh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sinh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double tanh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __tanh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double acosh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __acosh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double asinh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __asinh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double atanh (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __atanh (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double exp (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double frexp (double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern double __frexp (double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));
extern double ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern double __ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));
extern double log (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double log10 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log10 (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double modf (double __x, double *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern double __modf (double __x, double *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern double expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __expm1 (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double log1p (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log1p (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double logb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __logb (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __exp2 (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double log2 (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __log2 (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __pow (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __sqrt (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __hypot (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __cbrt (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __ceil (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fabs (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __floor (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fmod (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern int isinf (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int finite (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern double drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __drem (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double significand (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __significand (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __copysign (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern double __nan (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
extern int isnan (double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern double j0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j0 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double j1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __j1 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double jn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __jn (int, double) __attribute__ ((__nothrow__ , __leaf__));
extern double y0 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y0 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double y1 (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __y1 (double) __attribute__ ((__nothrow__ , __leaf__));
extern double yn (int, double) __attribute__ ((__nothrow__ , __leaf__)); extern double __yn (int, double) __attribute__ ((__nothrow__ , __leaf__));
extern double erf (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erf (double) __attribute__ ((__nothrow__ , __leaf__));
extern double erfc (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __erfc (double) __attribute__ ((__nothrow__ , __leaf__));
extern double lgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma (double) __attribute__ ((__nothrow__ , __leaf__));
extern double tgamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __tgamma (double) __attribute__ ((__nothrow__ , __leaf__));
extern double gamma (double) __attribute__ ((__nothrow__ , __leaf__)); extern double __gamma (double) __attribute__ ((__nothrow__ , __leaf__));
extern double lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern double __lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));
extern double rint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __rint (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __nextafter (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __nexttoward (double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __remainder (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbn (double __x, int __n) __attribute__ ((__nothrow__ , __leaf__));
extern int ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogb (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalbln (double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));
extern double nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern double __nearbyint (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __round (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __trunc (double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern double __remquo (double __x, double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));
extern long int lrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrint (double __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrint (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrint (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long int lround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lround (double __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llround (double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llround (double __x) __attribute__ ((__nothrow__ , __leaf__));
extern double fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)); extern double __fdim (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__));
extern double fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern double fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__)); extern double __fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ , __leaf__));
extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__)); extern double __scalb (double __x, double __n) __attribute__ ((__nothrow__ , __leaf__));
extern int __fpclassifyf (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __signbitf (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isinff (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __finitef (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isnanf (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __iseqsigf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern int __issignalingf (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern float acosf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __acosf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float asinf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __asinf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float atanf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atanf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float atan2f (float __y, float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atan2f (float __y, float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float cosf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __cosf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float sinf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sinf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float tanf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __tanf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float coshf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __coshf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float sinhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sinhf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float tanhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __tanhf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float acoshf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __acoshf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float asinhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __asinhf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float atanhf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __atanhf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float expf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __expf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float frexpf (float __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern float __frexpf (float __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));
extern float ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern float __ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));
extern float logf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __logf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float log10f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log10f (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float modff (float __x, float *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern float __modff (float __x, float *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern float expm1f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __expm1f (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float log1pf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log1pf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float logbf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __logbf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float exp2f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __exp2f (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float log2f (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __log2f (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float powf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __powf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float sqrtf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __sqrtf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float hypotf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __hypotf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float cbrtf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __cbrtf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float ceilf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __ceilf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float fabsf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fabsf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float floorf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __floorf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float fmodf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __fmodf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern int isinff (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int finitef (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern float dremf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __dremf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float significandf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __significandf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float copysignf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __copysignf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float nanf (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern float __nanf (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
extern int isnanf (float __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern float j0f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __j0f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float j1f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __j1f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float jnf (int, float) __attribute__ ((__nothrow__ , __leaf__)); extern float __jnf (int, float) __attribute__ ((__nothrow__ , __leaf__));
extern float y0f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __y0f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float y1f (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __y1f (float) __attribute__ ((__nothrow__ , __leaf__));
extern float ynf (int, float) __attribute__ ((__nothrow__ , __leaf__)); extern float __ynf (int, float) __attribute__ ((__nothrow__ , __leaf__));
extern float erff (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __erff (float) __attribute__ ((__nothrow__ , __leaf__));
extern float erfcf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __erfcf (float) __attribute__ ((__nothrow__ , __leaf__));
extern float lgammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __lgammaf (float) __attribute__ ((__nothrow__ , __leaf__));
extern float tgammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __tgammaf (float) __attribute__ ((__nothrow__ , __leaf__));
extern float gammaf (float) __attribute__ ((__nothrow__ , __leaf__)); extern float __gammaf (float) __attribute__ ((__nothrow__ , __leaf__));
extern float lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern float __lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));
extern float rintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __rintf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float nextafterf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __nextafterf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float nexttowardf (float __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __nexttowardf (float __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern float remainderf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __remainderf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float scalbnf (float __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalbnf (float __x, int __n) __attribute__ ((__nothrow__ , __leaf__));
extern int ilogbf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float scalblnf (float __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalblnf (float __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));
extern float nearbyintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern float __nearbyintf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float roundf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __roundf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float truncf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __truncf (float __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float remquof (float __x, float __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern float __remquof (float __x, float __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));
extern long int lrintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintf (float __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern long int lroundf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundf (float __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundf (float __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundf (float __x) __attribute__ ((__nothrow__ , __leaf__));
extern float fdimf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)); extern float __fdimf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__));
extern float fmaxf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fmaxf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float fminf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern float __fminf (float __x, float __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern float fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ , __leaf__)); extern float __fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ , __leaf__));
extern float scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__)); extern float __scalbf (float __x, float __n) __attribute__ ((__nothrow__ , __leaf__));
extern int __fpclassifyl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __signbitl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isinfl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __finitel (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __isnanl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int __iseqsigl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern int __issignalingl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern long double acosl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __acosl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double asinl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __asinl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double atanl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atanl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double cosl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __cosl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double sinl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sinl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double tanl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tanl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double coshl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __coshl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double sinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double tanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double acoshl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __acoshl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double asinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __asinhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double atanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __atanhl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double expl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __expl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double frexpl (long double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__)); extern long double __frexpl (long double __x, int *__exponent) __attribute__ ((__nothrow__ , __leaf__));
extern long double ldexpl (long double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__)); extern long double __ldexpl (long double __x, int __exponent) __attribute__ ((__nothrow__ , __leaf__));
extern long double logl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __logl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double log10l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log10l (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ , __leaf__)); extern long double __modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__nonnull__ (2)));
extern long double expm1l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __expm1l (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double log1pl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log1pl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double logbl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __logbl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double exp2l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __exp2l (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double log2l (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __log2l (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double powl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __powl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double sqrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __sqrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double cbrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __cbrtl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double ceill (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __ceill (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double fabsl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fabsl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double floorl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __floorl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern int isinfl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern int finitel (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern long double dreml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __dreml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double significandl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __significandl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double copysignl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __copysignl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double nanl (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nanl (const char *__tagb) __attribute__ ((__nothrow__ , __leaf__));
extern int isnanl (long double __value) __attribute__ ((__nothrow__ , __leaf__))
__attribute__ ((__const__));
extern long double j0l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __j0l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double j1l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __j1l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double jnl (int, long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __jnl (int, long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double y0l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __y0l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double y1l (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __y1l (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double ynl (int, long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __ynl (int, long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double erfl (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __erfl (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double erfcl (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __erfcl (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double lgammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __lgammal (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double tgammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __tgammal (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double gammal (long double) __attribute__ ((__nothrow__ , __leaf__)); extern long double __gammal (long double) __attribute__ ((__nothrow__ , __leaf__));
extern long double lgammal_r (long double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__)); extern long double __lgammal_r (long double, int *__signgamp) __attribute__ ((__nothrow__ , __leaf__));
extern long double rintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __rintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double nextafterl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nextafterl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double nexttowardl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nexttowardl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double scalbnl (long double __x, int __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalbnl (long double __x, int __n) __attribute__ ((__nothrow__ , __leaf__));
extern int ilogbl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern int __ilogbl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double scalblnl (long double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalblnl (long double __x, long int __n) __attribute__ ((__nothrow__ , __leaf__));
extern long double nearbyintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long double __nearbyintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double roundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __roundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double truncl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __truncl (long double __x) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double remquol (long double __x, long double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__)); extern long double __remquol (long double __x, long double __y, int *__quo) __attribute__ ((__nothrow__ , __leaf__));
extern long int lrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llrintl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long int lroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long int __lroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
__extension__
extern long long int llroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__)); extern long long int __llroundl (long double __x) __attribute__ ((__nothrow__ , __leaf__));
extern long double fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__));
extern long double fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double fminl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__)); extern long double __fminl (long double __x, long double __y) __attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__const__));
extern long double fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ , __leaf__)); extern long double __fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ , __leaf__));
extern long double scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ , __leaf__)); extern long double __scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ , __leaf__));
extern int signgam;
enum
{
FP_NAN =
0,
FP_INFINITE =
1,
FP_ZERO =
2,
FP_SUBNORMAL =
3,
FP_NORMAL =
4
};
typedef __int8_t int8_t;
typedef __int16_t int16_t;
typedef __int32_t int32_t;
typedef __int64_t int64_t;
typedef __uint8_t uint8_t;
typedef __uint16_t uint16_t;
typedef __uint32_t uint32_t;
typedef __uint64_t uint64_t;
typedef __int_least8_t int_least8_t;
typedef __int_least16_t int_least16_t;
typedef __int_least32_t int_least32_t;
typedef __int_least64_t int_least64_t;
typedef __uint_least8_t uint_least8_t;
typedef __uint_least16_t uint_least16_t;
typedef __uint_least32_t uint_least32_t;
typedef __uint_least64_t 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 __intmax_t intmax_t;
typedef __uintmax_t uintmax_t;
extern void __assert_fail (const char *__assertion, const char *__file,
unsigned int __line, const char *__function)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));
extern void __assert_perror_fail (int __errnum, const char *__file,
unsigned int __line, const char *__function)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));
extern void __assert (const char *__assertion, const char *__file, int __line)
__attribute__ ((__nothrow__ , __leaf__)) __attribute__ ((__noreturn__));
typedef __builtin_va_list __gnuc_va_list;
typedef struct
{
int __count;
union
{
unsigned int __wch;
char __wchb[4];
} __value;
} __mbstate_t;
typedef struct _G_fpos_t
{
__off_t __pos;
__mbstate_t __state;
} __fpos_t;
typedef struct _G_fpos64_t
{
__off64_t __pos;
__mbstate_t __state;
} __fpos64_t;
struct _IO_FILE;
typedef struct _IO_FILE __FILE;
struct _IO_FILE;
typedef struct _IO_FILE FILE;
struct _IO_FILE;
struct _IO_marker;
struct _IO_codecvt;
struct _IO_wide_data;
typedef void _IO_lock_t;
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;
struct _IO_codecvt *_codecvt;
struct _IO_wide_data *_wide_data;
struct _IO_FILE *_freeres_list;
void *_freeres_buf;
size_t __pad5;
int _mode;
char _unused2[15 * sizeof (int) - 4 * sizeof (void *) - sizeof (size_t)];
};
typedef __gnuc_va_list va_list;
typedef __off_t off_t;
typedef __ssize_t ssize_t;
typedef __fpos_t fpos_t;
extern FILE *stdin;
extern FILE *stdout;
extern 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 int fclose (FILE *__stream);
extern char *tmpnam (char[20]) __attribute__ ((__nothrow__ , __leaf__)) ;
extern char *tmpnam_r (char __s[20]) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int fflush (FILE *__stream);
extern int fflush_unlocked (FILE *__stream);
extern FILE *freopen (const char *__restrict __filename,
const char *__restrict __modes,
FILE *__restrict __stream) ;
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 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 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 __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 fileno (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int fileno_unlocked (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern int pclose (FILE *__stream);
extern void flockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int ftrylockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__)) ;
extern void funlockfile (FILE *__stream) __attribute__ ((__nothrow__ , __leaf__));
extern int __uflow (FILE *);
extern int __overflow (FILE *, int);
static void
platform_main_begin(void)
{
}
static void
platform_main_end(uint32_t crc, int flag)
{
printf ("checksum = %X\n", crc);
}
static int8_t
(safe_unary_minus_func_int8_t_s)(int8_t si )
{
return
-si;
}
static int8_t
(safe_add_func_int8_t_s_s)(int8_t si1, int8_t si2 )
{
return
(si1 + si2);
}
static int8_t
(safe_sub_func_int8_t_s_s)(int8_t si1, int8_t si2 )
{
return
(si1 - si2);
}
static int8_t
(safe_mul_func_int8_t_s_s)(int8_t si1, int8_t si2 )
{
return
si1 * si2;
}
static int8_t
(safe_mod_func_int8_t_s_s)(int8_t si1, int8_t si2 )
{
return
((si2 == 0) || ((si1 == (-128)) && (si2 == (-1)))) ?
((si1)) :
(si1 % si2);
}
static int8_t
(safe_div_func_int8_t_s_s)(int8_t si1, int8_t si2 )
{
return
((si2 == 0) || ((si1 == (-128)) && (si2 == (-1)))) ?
((si1)) :
(si1 / si2);
}
static int8_t
(safe_lshift_func_int8_t_s_s)(int8_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32) || (left > ((127) >> ((int)right)))) ?
((left)) :
(left << ((int)right));
}
static int8_t
(safe_lshift_func_int8_t_s_u)(int8_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32) || (left > ((127) >> ((unsigned int)right)))) ?
((left)) :
(left << ((unsigned int)right));
}
static int8_t
(safe_rshift_func_int8_t_s_s)(int8_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32))?
((left)) :
(left >> ((int)right));
}
static int8_t
(safe_rshift_func_int8_t_s_u)(int8_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32)) ?
((left)) :
(left >> ((unsigned int)right));
}
static int16_t
(safe_unary_minus_func_int16_t_s)(int16_t si )
{
return
-si;
}
static int16_t
(safe_add_func_int16_t_s_s)(int16_t si1, int16_t si2 )
{
return
(si1 + si2);
}
static int16_t
(safe_sub_func_int16_t_s_s)(int16_t si1, int16_t si2 )
{
return
(si1 - si2);
}
static int16_t
(safe_mul_func_int16_t_s_s)(int16_t si1, int16_t si2 )
{
return
si1 * si2;
}
static int16_t
(safe_mod_func_int16_t_s_s)(int16_t si1, int16_t si2 )
{
return
((si2 == 0) || ((si1 == (-32767-1)) && (si2 == (-1)))) ?
((si1)) :
(si1 % si2);
}
static int16_t
(safe_div_func_int16_t_s_s)(int16_t si1, int16_t si2 )
{
return
((si2 == 0) || ((si1 == (-32767-1)) && (si2 == (-1)))) ?
((si1)) :
(si1 / si2);
}
static int16_t
(safe_lshift_func_int16_t_s_s)(int16_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32) || (left > ((32767) >> ((int)right)))) ?
((left)) :
(left << ((int)right));
}
static int16_t
(safe_lshift_func_int16_t_s_u)(int16_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32) || (left > ((32767) >> ((unsigned int)right)))) ?
((left)) :
(left << ((unsigned int)right));
}
static int16_t
(safe_rshift_func_int16_t_s_s)(int16_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32))?
((left)) :
(left >> ((int)right));
}
static int16_t
(safe_rshift_func_int16_t_s_u)(int16_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32)) ?
((left)) :
(left >> ((unsigned int)right));
}
static int32_t
(safe_unary_minus_func_int32_t_s)(int32_t si )
{
return
(si==(-2147483647-1)) ?
((si)) :
-si;
}
static int32_t
(safe_add_func_int32_t_s_s)(int32_t si1, int32_t si2 )
{
return
(((si1>0) && (si2>0) && (si1 > ((2147483647)-si2))) || ((si1<0) && (si2<0) && (si1 < ((-2147483647-1)-si2)))) ?
((si1)) :
(si1 + si2);
}
static int32_t
(safe_sub_func_int32_t_s_s)(int32_t si1, int32_t si2 )
{
return
(((si1^si2) & (((si1 ^ ((si1^si2) & (~(2147483647))))-si2)^si2)) < 0) ?
((si1)) :
(si1 - si2);
}
static int32_t
(safe_mul_func_int32_t_s_s)(int32_t si1, int32_t si2 )
{
return
(((si1 > 0) && (si2 > 0) && (si1 > ((2147483647) / si2))) || ((si1 > 0) && (si2 <= 0) && (si2 < ((-2147483647-1) / si1))) || ((si1 <= 0) && (si2 > 0) && (si1 < ((-2147483647-1) / si2))) || ((si1 <= 0) && (si2 <= 0) && (si1 != 0) && (si2 < ((2147483647) / si1)))) ?
((si1)) :
si1 * si2;
}
static int32_t
(safe_mod_func_int32_t_s_s)(int32_t si1, int32_t si2 )
{
return
((si2 == 0) || ((si1 == (-2147483647-1)) && (si2 == (-1)))) ?
((si1)) :
(si1 % si2);
}
static int32_t
(safe_div_func_int32_t_s_s)(int32_t si1, int32_t si2 )
{
return
((si2 == 0) || ((si1 == (-2147483647-1)) && (si2 == (-1)))) ?
((si1)) :
(si1 / si2);
}
static int32_t
(safe_lshift_func_int32_t_s_s)(int32_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32) || (left > ((2147483647) >> ((int)right)))) ?
((left)) :
(left << ((int)right));
}
static int32_t
(safe_lshift_func_int32_t_s_u)(int32_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32) || (left > ((2147483647) >> ((unsigned int)right)))) ?
((left)) :
(left << ((unsigned int)right));
}
static int32_t
(safe_rshift_func_int32_t_s_s)(int32_t left, int right )
{
return
((left < 0) || (((int)right) < 0) || (((int)right) >= 32))?
((left)) :
(left >> ((int)right));
}
static int32_t
(safe_rshift_func_int32_t_s_u)(int32_t left, unsigned int right )
{
return
((left < 0) || (((unsigned int)right) >= 32)) ?
((left)) :
(left >> ((unsigned int)right));
}
static uint8_t
(safe_unary_minus_func_uint8_t_u)(uint8_t ui )
{
return -ui;
}
static uint8_t
(safe_add_func_uint8_t_u_u)(uint8_t ui1, uint8_t ui2 )
{
return ui1 + ui2;
}
static uint8_t
(safe_sub_func_uint8_t_u_u)(uint8_t ui1, uint8_t ui2 )
{
return ui1 - ui2;
}
static uint8_t
(safe_mul_func_uint8_t_u_u)(uint8_t ui1, uint8_t ui2 )
{
return ((unsigned int)ui1) * ((unsigned int)ui2);
}
static uint8_t
(safe_mod_func_uint8_t_u_u)(uint8_t ui1, uint8_t ui2 )
{
return
(ui2 == 0) ?
((ui1)) :
(ui1 % ui2);
}
static uint8_t
(safe_div_func_uint8_t_u_u)(uint8_t ui1, uint8_t ui2 )
{