| 
| double _Complex  | cacos (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __cacos (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | casin (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __casin (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | catan (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __catan (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | ccos (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __ccos (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | csin (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __csin (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | ctan (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __ctan (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | cacosh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __cacosh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | casinh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __casinh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | catanh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __catanh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | ccosh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __ccosh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | csinh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __csinh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | ctanh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __ctanh (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | cexp (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __cexp (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | clog (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __clog (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | cpow (double _Complex __x, double _Complex __y) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __cpow (double _Complex __x, double _Complex __y) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | csqrt (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __csqrt (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | cabs (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | __cabs (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | carg (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | __carg (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | conj (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __conj (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | cproj (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double _Complex  | __cproj (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | cimag (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | __cimag (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | creal (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| double  | __creal (double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | cacosf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __cacosf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | casinf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __casinf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | catanf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __catanf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | ccosf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __ccosf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | csinf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __csinf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | ctanf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __ctanf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | cacoshf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __cacoshf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | casinhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __casinhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | catanhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __catanhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | ccoshf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __ccoshf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | csinhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __csinhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | ctanhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __ctanhf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | cexpf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __cexpf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | clogf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __clogf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | cpowf (float _Complex __x, float _Complex __y) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __cpowf (float _Complex __x, float _Complex __y) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | csqrtf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __csqrtf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | cabsf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | __cabsf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | cargf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | __cargf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | conjf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __conjf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | cprojf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float _Complex  | __cprojf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | cimagf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | __cimagf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | crealf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| float  | __crealf (float _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | cacosl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __cacosl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | casinl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __casinl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | catanl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __catanl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | ccosl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __ccosl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | csinl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __csinl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | ctanl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __ctanl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | cacoshl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __cacoshl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | casinhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __casinhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | catanhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __catanhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | ccoshl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __ccoshl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | csinhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __csinhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | ctanhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __ctanhl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | cexpl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __cexpl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | clogl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __clogl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | cpowl (long double _Complex __x, long double _Complex __y) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __cpowl (long double _Complex __x, long double _Complex __y) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | csqrtl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __csqrtl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | cabsl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | __cabsl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | cargl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | __cargl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | conjl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __conjl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | cprojl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double _Complex  | __cprojl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | cimagl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | __cimagl (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | creall (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| long double  | __creall (long double _Complex __z) __attribute__((__nothrow__ | 
|   | 
| int  | __fpclassify (double __value) __attribute__((__nothrow__ | 
|   | 
| int __leaf__  | __attribute__ ((__const__)) | 
|   | 
| int  | __signbit (double __value) __attribute__((__nothrow__ | 
|   | 
| int  | __isinf (double __value) __attribute__((__nothrow__ | 
|   | 
| int  | __finite (double __value) __attribute__((__nothrow__ | 
|   | 
| int  | __isnan (double __value) __attribute__((__nothrow__ | 
|   | 
| int  | __iseqsig (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| int  | __issignaling (double __value) __attribute__((__nothrow__ | 
|   | 
| double  | acos (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __acos (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | asin (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __asin (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | atan (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __atan (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | atan2 (double __y, double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __atan2 (double __y, double __x) __attribute__((__nothrow__ | 
|   | 
| double  | cos (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __cos (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | sin (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __sin (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | tan (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __tan (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | cosh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __cosh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | sinh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __sinh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | tanh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __tanh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | acosh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __acosh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | asinh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __asinh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | atanh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __atanh (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | exp (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __exp (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | frexp (double __x, int *__exponent) __attribute__((__nothrow__ | 
|   | 
| double  | __frexp (double __x, int *__exponent) __attribute__((__nothrow__ | 
|   | 
| double  | ldexp (double __x, int __exponent) __attribute__((__nothrow__ | 
|   | 
| double  | __ldexp (double __x, int __exponent) __attribute__((__nothrow__ | 
|   | 
| double  | log (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __log (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | log10 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __log10 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | modf (double __x, double *__iptr) __attribute__((__nothrow__ | 
|   | 
| double  | __modf (double __x, double *__iptr) __attribute__((__nothrow__ | 
|   | 
| double __leaf__  | __attribute__ ((__nonnull__(2))) | 
|   | 
| double  | expm1 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __expm1 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | log1p (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __log1p (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | logb (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __logb (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | exp2 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __exp2 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | log2 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __log2 (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | pow (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | __pow (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | sqrt (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __sqrt (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | hypot (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | __hypot (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | cbrt (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __cbrt (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | ceil (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __ceil (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | fabs (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __fabs (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | floor (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __floor (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | fmod (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | __fmod (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| int  | isinf (double __value) __attribute__((__nothrow__ | 
|   | 
| int  | finite (double __value) __attribute__((__nothrow__ | 
|   | 
| double  | drem (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | __drem (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | significand (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | __significand (double __x) __attribute__((__nothrow__ | 
|   | 
| double  | copysign (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | __copysign (double __x, double __y) __attribute__((__nothrow__ | 
|   | 
| double  | nan (const char *__tagb) __attribute__((__nothrow__ | 
|   | 
| double  | __nan (const char *__tagb) __attribute__((__nothrow__ | 
|   | 
| int  | isnan (double __value) __attribute__((__nothrow__ | 
|   | 
| double  | j0 (extern double lgamma_r(double) | 
|   | 
| int  | remove (const char *__filename) __attribute__((__nothrow__ | 
|   | 
| int  | rename (const char *__old, const char *__new) __attribute__((__nothrow__ | 
|   | 
| int  | renameat (int __oldfd, const char *__old, int __newfd, const char *__new) __attribute__((__nothrow__ | 
|   | 
| int  | fclose (FILE *__stream) | 
|   | 
| FILE *  | tmpfile (void) | 
|   | 
| size_t  | __ctype_get_mb_cur_max (void) | 
|   | 
| static __inline __uint32_t  | __bswap_32 (__uint32_t __bsx) | 
|   | 
| static __extension__ __inline __uint64_t  | __bswap_64 (__uint64_t __bsx) | 
|   | 
| static __inline __uint16_t  | __uint16_identity (__uint16_t __x) | 
|   | 
| static __inline __uint32_t  | __uint32_identity (__uint32_t __x) | 
|   | 
| static __inline __uint64_t  | __uint64_identity (__uint64_t __x) | 
|   | 
| int  | select (int __nfds, fd_set *__restrict __readfds, fd_set *__restrict __writefds, fd_set *__restrict __exceptfds, struct timeval *__restrict __timeout) | 
|   | 
| 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) | 
|   | 
| long int  | random (void) | 
|   | 
| int  | random_r (struct random_data *__restrict __buf, int32_t *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int __leaf__  | __attribute__ ((__nonnull__(1, 2))) | 
|   | 
| int  | srandom_r (unsigned int __seed, struct random_data *__buf) __attribute__((__nothrow__ | 
|   | 
| int  | initstate_r (unsigned int __seed, char *__restrict __statebuf, size_t __statelen, struct random_data *__restrict __buf) __attribute__((__nothrow__ | 
|   | 
| int __leaf__  | __attribute__ ((__nonnull__(2, 4))) | 
|   | 
| int  | setstate_r (char *__restrict __statebuf, struct random_data *__restrict __buf) __attribute__((__nothrow__ | 
|   | 
| int  | rand (void) | 
|   | 
| int  | drand48_r (struct drand48_data *__restrict __buffer, double *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | erand48_r (unsigned short int __xsubi[3], struct drand48_data *__restrict __buffer, double *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | lrand48_r (struct drand48_data *__restrict __buffer, long int *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | nrand48_r (unsigned short int __xsubi[3], struct drand48_data *__restrict __buffer, long int *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | mrand48_r (struct drand48_data *__restrict __buffer, long int *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | jrand48_r (unsigned short int __xsubi[3], struct drand48_data *__restrict __buffer, long int *__restrict __result) __attribute__((__nothrow__ | 
|   | 
| int  | srand48_r (long int __seedval, struct drand48_data *__buffer) __attribute__((__nothrow__ | 
|   | 
| int  | seed48_r (unsigned short int __seed16v[3], struct drand48_data *__buffer) __attribute__((__nothrow__ | 
|   | 
| int  | lcong48_r (unsigned short int __param[7], struct drand48_data *__buffer) __attribute__((__nothrow__ | 
|   | 
| __uint32_t  | arc4random (void) | 
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| int  | strcoll_l (const char *__s1, const char *__s2, locale_t __l) __attribute__((__nothrow__ | 
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