enum
  {
    FE_INVALID =

      0x01,
    __FE_DENORM = 0x02,
    FE_DIVBYZERO =

      0x04,
    FE_OVERFLOW =

      0x08,
    FE_UNDERFLOW =

      0x10,
    FE_INEXACT =

      0x20
  };







enum
  {
    FE_TONEAREST =

      0,
    FE_DOWNWARD =

      0x400,
    FE_UPWARD =

      0x800,
    FE_TOWARDZERO =

      0xc00
  };



typedef unsigned short int fexcept_t;






typedef struct
  {
    unsigned short int __control_word;
    unsigned short int __glibc_reserved1;
    unsigned short int __status_word;
    unsigned short int __glibc_reserved2;
    unsigned short int __tags;
    unsigned short int __glibc_reserved3;
    unsigned int __eip;
    unsigned short int __cs_selector;
    unsigned int __opcode:11;
    unsigned int __glibc_reserved4:5;
    unsigned int __data_offset;
    unsigned short int __data_selector;
    unsigned short int __glibc_reserved5;



  }
fenv_t;






extern int feclearexcept (int __excepts) __attribute__ ((__nothrow__ ));



extern int fegetexceptflag (fexcept_t *__flagp, int __excepts) __attribute__ ((__nothrow__ ));


extern int feraiseexcept (int __excepts) __attribute__ ((__nothrow__ ));



extern int fesetexceptflag (const fexcept_t *__flagp, int __excepts) __attribute__ ((__nothrow__ ));



extern int fetestexcept (int __excepts) __attribute__ ((__nothrow__ ));





extern int fegetround (void) __attribute__ ((__nothrow__ ));


extern int fesetround (int __rounding_direction) __attribute__ ((__nothrow__ ));






extern int fegetenv (fenv_t *__envp) __attribute__ ((__nothrow__ ));




extern int feholdexcept (fenv_t *__envp) __attribute__ ((__nothrow__ ));



extern int fesetenv (const fenv_t *__envp) __attribute__ ((__nothrow__ ));




extern int feupdateenv (const fenv_t *__envp) __attribute__ ((__nothrow__ ));











typedef float float_t;
typedef double double_t;
extern double acos (double __x) __attribute__ ((__nothrow__ )); extern double __acos (double __x) __attribute__ ((__nothrow__ ));

extern double asin (double __x) __attribute__ ((__nothrow__ )); extern double __asin (double __x) __attribute__ ((__nothrow__ ));

extern double atan (double __x) __attribute__ ((__nothrow__ )); extern double __atan (double __x) __attribute__ ((__nothrow__ ));

extern double atan2 (double __y, double __x) __attribute__ ((__nothrow__ )); extern double __atan2 (double __y, double __x) __attribute__ ((__nothrow__ ));


 extern double cos (double __x) __attribute__ ((__nothrow__ )); extern double __cos (double __x) __attribute__ ((__nothrow__ ));

 extern double sin (double __x) __attribute__ ((__nothrow__ )); extern double __sin (double __x) __attribute__ ((__nothrow__ ));

extern double tan (double __x) __attribute__ ((__nothrow__ )); extern double __tan (double __x) __attribute__ ((__nothrow__ ));




extern double cosh (double __x) __attribute__ ((__nothrow__ )); extern double __cosh (double __x) __attribute__ ((__nothrow__ ));

extern double sinh (double __x) __attribute__ ((__nothrow__ )); extern double __sinh (double __x) __attribute__ ((__nothrow__ ));

extern double tanh (double __x) __attribute__ ((__nothrow__ )); extern double __tanh (double __x) __attribute__ ((__nothrow__ ));
extern double acosh (double __x) __attribute__ ((__nothrow__ )); extern double __acosh (double __x) __attribute__ ((__nothrow__ ));

extern double asinh (double __x) __attribute__ ((__nothrow__ )); extern double __asinh (double __x) __attribute__ ((__nothrow__ ));

extern double atanh (double __x) __attribute__ ((__nothrow__ )); extern double __atanh (double __x) __attribute__ ((__nothrow__ ));







 extern double exp (double __x) __attribute__ ((__nothrow__ )); extern double __exp (double __x) __attribute__ ((__nothrow__ ));


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


extern double ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ )); extern double __ldexp (double __x, int __exponent) __attribute__ ((__nothrow__ ));


 extern double log (double __x) __attribute__ ((__nothrow__ )); extern double __log (double __x) __attribute__ ((__nothrow__ ));


extern double log10 (double __x) __attribute__ ((__nothrow__ )); extern double __log10 (double __x) __attribute__ ((__nothrow__ ));


extern double modf (double __x, double *__iptr) __attribute__ ((__nothrow__ )); extern double __modf (double __x, double *__iptr) __attribute__ ((__nothrow__ )) __attribute__ ((__nonnull__ (2)));
extern double expm1 (double __x) __attribute__ ((__nothrow__ )); extern double __expm1 (double __x) __attribute__ ((__nothrow__ ));


extern double log1p (double __x) __attribute__ ((__nothrow__ )); extern double __log1p (double __x) __attribute__ ((__nothrow__ ));


extern double logb (double __x) __attribute__ ((__nothrow__ )); extern double __logb (double __x) __attribute__ ((__nothrow__ ));






extern double exp2 (double __x) __attribute__ ((__nothrow__ )); extern double __exp2 (double __x) __attribute__ ((__nothrow__ ));


extern double log2 (double __x) __attribute__ ((__nothrow__ )); extern double __log2 (double __x) __attribute__ ((__nothrow__ ));
 extern double pow (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __pow (double __x, double __y) __attribute__ ((__nothrow__ ));


extern double sqrt (double __x) __attribute__ ((__nothrow__ )); extern double __sqrt (double __x) __attribute__ ((__nothrow__ ));





extern double hypot (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __hypot (double __x, double __y) __attribute__ ((__nothrow__ ));






extern double cbrt (double __x) __attribute__ ((__nothrow__ )); extern double __cbrt (double __x) __attribute__ ((__nothrow__ ));
extern double ceil (double __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern double __ceil (double __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


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


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


extern double fmod (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __fmod (double __x, double __y) __attribute__ ((__nothrow__ ));




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


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





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


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


extern double drem (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __drem (double __x, double __y) __attribute__ ((__nothrow__ ));



extern double significand (double __x) __attribute__ ((__nothrow__ )); extern double __significand (double __x) __attribute__ ((__nothrow__ ));





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






extern double nan (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern double __nan (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));





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



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


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






extern double erf (double) __attribute__ ((__nothrow__ )); extern double __erf (double) __attribute__ ((__nothrow__ ));
extern double erfc (double) __attribute__ ((__nothrow__ )); extern double __erfc (double) __attribute__ ((__nothrow__ ));
extern double lgamma (double) __attribute__ ((__nothrow__ )); extern double __lgamma (double) __attribute__ ((__nothrow__ ));






extern double tgamma (double) __attribute__ ((__nothrow__ )); extern double __tgamma (double) __attribute__ ((__nothrow__ ));





extern double gamma (double) __attribute__ ((__nothrow__ )); extern double __gamma (double) __attribute__ ((__nothrow__ ));






extern double lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ )); extern double __lgamma_r (double, int *__signgamp) __attribute__ ((__nothrow__ ));







extern double rint (double __x) __attribute__ ((__nothrow__ )); extern double __rint (double __x) __attribute__ ((__nothrow__ ));


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

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



extern double remainder (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __remainder (double __x, double __y) __attribute__ ((__nothrow__ ));



extern double scalbn (double __x, int __n) __attribute__ ((__nothrow__ )); extern double __scalbn (double __x, int __n) __attribute__ ((__nothrow__ ));



extern int ilogb (double __x) __attribute__ ((__nothrow__ )); extern int __ilogb (double __x) __attribute__ ((__nothrow__ ));




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



extern double nearbyint (double __x) __attribute__ ((__nothrow__ )); extern double __nearbyint (double __x) __attribute__ ((__nothrow__ ));



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



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




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






extern long int lrint (double __x) __attribute__ ((__nothrow__ )); extern long int __lrint (double __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llrint (double __x) __attribute__ ((__nothrow__ )); extern long long int __llrint (double __x) __attribute__ ((__nothrow__ ));



extern long int lround (double __x) __attribute__ ((__nothrow__ )); extern long int __lround (double __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llround (double __x) __attribute__ ((__nothrow__ )); extern long long int __llround (double __x) __attribute__ ((__nothrow__ ));



extern double fdim (double __x, double __y) __attribute__ ((__nothrow__ )); extern double __fdim (double __x, double __y) __attribute__ ((__nothrow__ ));


extern double fmax (double __x, double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern double __fmax (double __x, double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


extern double fmin (double __x, double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern double __fmin (double __x, double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));



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


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



extern double fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ )); extern double __fma (double __x, double __y, double __z) __attribute__ ((__nothrow__ ));
extern double scalb (double __x, double __n) __attribute__ ((__nothrow__ )); extern double __scalb (double __x, double __n) __attribute__ ((__nothrow__ ));
extern float acosf (float __x) __attribute__ ((__nothrow__ )); extern float __acosf (float __x) __attribute__ ((__nothrow__ ));

extern float asinf (float __x) __attribute__ ((__nothrow__ )); extern float __asinf (float __x) __attribute__ ((__nothrow__ ));

extern float atanf (float __x) __attribute__ ((__nothrow__ )); extern float __atanf (float __x) __attribute__ ((__nothrow__ ));

extern float atan2f (float __y, float __x) __attribute__ ((__nothrow__ )); extern float __atan2f (float __y, float __x) __attribute__ ((__nothrow__ ));


 extern float cosf (float __x) __attribute__ ((__nothrow__ )); extern float __cosf (float __x) __attribute__ ((__nothrow__ ));

 extern float sinf (float __x) __attribute__ ((__nothrow__ )); extern float __sinf (float __x) __attribute__ ((__nothrow__ ));

extern float tanf (float __x) __attribute__ ((__nothrow__ )); extern float __tanf (float __x) __attribute__ ((__nothrow__ ));




extern float coshf (float __x) __attribute__ ((__nothrow__ )); extern float __coshf (float __x) __attribute__ ((__nothrow__ ));

extern float sinhf (float __x) __attribute__ ((__nothrow__ )); extern float __sinhf (float __x) __attribute__ ((__nothrow__ ));

extern float tanhf (float __x) __attribute__ ((__nothrow__ )); extern float __tanhf (float __x) __attribute__ ((__nothrow__ ));
extern float acoshf (float __x) __attribute__ ((__nothrow__ )); extern float __acoshf (float __x) __attribute__ ((__nothrow__ ));

extern float asinhf (float __x) __attribute__ ((__nothrow__ )); extern float __asinhf (float __x) __attribute__ ((__nothrow__ ));

extern float atanhf (float __x) __attribute__ ((__nothrow__ )); extern float __atanhf (float __x) __attribute__ ((__nothrow__ ));







 extern float expf (float __x) __attribute__ ((__nothrow__ )); extern float __expf (float __x) __attribute__ ((__nothrow__ ));


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


extern float ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ )); extern float __ldexpf (float __x, int __exponent) __attribute__ ((__nothrow__ ));


 extern float logf (float __x) __attribute__ ((__nothrow__ )); extern float __logf (float __x) __attribute__ ((__nothrow__ ));


extern float log10f (float __x) __attribute__ ((__nothrow__ )); extern float __log10f (float __x) __attribute__ ((__nothrow__ ));


extern float modff (float __x, float *__iptr) __attribute__ ((__nothrow__ )); extern float __modff (float __x, float *__iptr) __attribute__ ((__nothrow__ )) __attribute__ ((__nonnull__ (2)));
extern float expm1f (float __x) __attribute__ ((__nothrow__ )); extern float __expm1f (float __x) __attribute__ ((__nothrow__ ));


extern float log1pf (float __x) __attribute__ ((__nothrow__ )); extern float __log1pf (float __x) __attribute__ ((__nothrow__ ));


extern float logbf (float __x) __attribute__ ((__nothrow__ )); extern float __logbf (float __x) __attribute__ ((__nothrow__ ));






extern float exp2f (float __x) __attribute__ ((__nothrow__ )); extern float __exp2f (float __x) __attribute__ ((__nothrow__ ));


extern float log2f (float __x) __attribute__ ((__nothrow__ )); extern float __log2f (float __x) __attribute__ ((__nothrow__ ));
 extern float powf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __powf (float __x, float __y) __attribute__ ((__nothrow__ ));


extern float sqrtf (float __x) __attribute__ ((__nothrow__ )); extern float __sqrtf (float __x) __attribute__ ((__nothrow__ ));





extern float hypotf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __hypotf (float __x, float __y) __attribute__ ((__nothrow__ ));






extern float cbrtf (float __x) __attribute__ ((__nothrow__ )); extern float __cbrtf (float __x) __attribute__ ((__nothrow__ ));
extern float ceilf (float __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern float __ceilf (float __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


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


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


extern float fmodf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __fmodf (float __x, float __y) __attribute__ ((__nothrow__ ));




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


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





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


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


extern float dremf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __dremf (float __x, float __y) __attribute__ ((__nothrow__ ));



extern float significandf (float __x) __attribute__ ((__nothrow__ )); extern float __significandf (float __x) __attribute__ ((__nothrow__ ));





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






extern float nanf (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern float __nanf (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));





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



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


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






extern float erff (float) __attribute__ ((__nothrow__ )); extern float __erff (float) __attribute__ ((__nothrow__ ));
extern float erfcf (float) __attribute__ ((__nothrow__ )); extern float __erfcf (float) __attribute__ ((__nothrow__ ));
extern float lgammaf (float) __attribute__ ((__nothrow__ )); extern float __lgammaf (float) __attribute__ ((__nothrow__ ));






extern float tgammaf (float) __attribute__ ((__nothrow__ )); extern float __tgammaf (float) __attribute__ ((__nothrow__ ));





extern float gammaf (float) __attribute__ ((__nothrow__ )); extern float __gammaf (float) __attribute__ ((__nothrow__ ));






extern float lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ )); extern float __lgammaf_r (float, int *__signgamp) __attribute__ ((__nothrow__ ));







extern float rintf (float __x) __attribute__ ((__nothrow__ )); extern float __rintf (float __x) __attribute__ ((__nothrow__ ));


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

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



extern float remainderf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __remainderf (float __x, float __y) __attribute__ ((__nothrow__ ));



extern float scalbnf (float __x, int __n) __attribute__ ((__nothrow__ )); extern float __scalbnf (float __x, int __n) __attribute__ ((__nothrow__ ));



extern int ilogbf (float __x) __attribute__ ((__nothrow__ )); extern int __ilogbf (float __x) __attribute__ ((__nothrow__ ));




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



extern float nearbyintf (float __x) __attribute__ ((__nothrow__ )); extern float __nearbyintf (float __x) __attribute__ ((__nothrow__ ));



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



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




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






extern long int lrintf (float __x) __attribute__ ((__nothrow__ )); extern long int __lrintf (float __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llrintf (float __x) __attribute__ ((__nothrow__ )); extern long long int __llrintf (float __x) __attribute__ ((__nothrow__ ));



extern long int lroundf (float __x) __attribute__ ((__nothrow__ )); extern long int __lroundf (float __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llroundf (float __x) __attribute__ ((__nothrow__ )); extern long long int __llroundf (float __x) __attribute__ ((__nothrow__ ));



extern float fdimf (float __x, float __y) __attribute__ ((__nothrow__ )); extern float __fdimf (float __x, float __y) __attribute__ ((__nothrow__ ));


extern float fmaxf (float __x, float __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern float __fmaxf (float __x, float __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


extern float fminf (float __x, float __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern float __fminf (float __x, float __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));



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


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



extern float fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ )); extern float __fmaf (float __x, float __y, float __z) __attribute__ ((__nothrow__ ));
extern float scalbf (float __x, float __n) __attribute__ ((__nothrow__ )); extern float __scalbf (float __x, float __n) __attribute__ ((__nothrow__ ));
extern long double acosl (long double __x) __attribute__ ((__nothrow__ )); extern long double __acosl (long double __x) __attribute__ ((__nothrow__ ));

extern long double asinl (long double __x) __attribute__ ((__nothrow__ )); extern long double __asinl (long double __x) __attribute__ ((__nothrow__ ));

extern long double atanl (long double __x) __attribute__ ((__nothrow__ )); extern long double __atanl (long double __x) __attribute__ ((__nothrow__ ));

extern long double atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ )); extern long double __atan2l (long double __y, long double __x) __attribute__ ((__nothrow__ ));


 extern long double cosl (long double __x) __attribute__ ((__nothrow__ )); extern long double __cosl (long double __x) __attribute__ ((__nothrow__ ));

 extern long double sinl (long double __x) __attribute__ ((__nothrow__ )); extern long double __sinl (long double __x) __attribute__ ((__nothrow__ ));

extern long double tanl (long double __x) __attribute__ ((__nothrow__ )); extern long double __tanl (long double __x) __attribute__ ((__nothrow__ ));




extern long double coshl (long double __x) __attribute__ ((__nothrow__ )); extern long double __coshl (long double __x) __attribute__ ((__nothrow__ ));

extern long double sinhl (long double __x) __attribute__ ((__nothrow__ )); extern long double __sinhl (long double __x) __attribute__ ((__nothrow__ ));

extern long double tanhl (long double __x) __attribute__ ((__nothrow__ )); extern long double __tanhl (long double __x) __attribute__ ((__nothrow__ ));
extern long double acoshl (long double __x) __attribute__ ((__nothrow__ )); extern long double __acoshl (long double __x) __attribute__ ((__nothrow__ ));

extern long double asinhl (long double __x) __attribute__ ((__nothrow__ )); extern long double __asinhl (long double __x) __attribute__ ((__nothrow__ ));

extern long double atanhl (long double __x) __attribute__ ((__nothrow__ )); extern long double __atanhl (long double __x) __attribute__ ((__nothrow__ ));







 extern long double expl (long double __x) __attribute__ ((__nothrow__ )); extern long double __expl (long double __x) __attribute__ ((__nothrow__ ));


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


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


 extern long double logl (long double __x) __attribute__ ((__nothrow__ )); extern long double __logl (long double __x) __attribute__ ((__nothrow__ ));


extern long double log10l (long double __x) __attribute__ ((__nothrow__ )); extern long double __log10l (long double __x) __attribute__ ((__nothrow__ ));


extern long double modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ )); extern long double __modfl (long double __x, long double *__iptr) __attribute__ ((__nothrow__ )) __attribute__ ((__nonnull__ (2)));
extern long double expm1l (long double __x) __attribute__ ((__nothrow__ )); extern long double __expm1l (long double __x) __attribute__ ((__nothrow__ ));


extern long double log1pl (long double __x) __attribute__ ((__nothrow__ )); extern long double __log1pl (long double __x) __attribute__ ((__nothrow__ ));


extern long double logbl (long double __x) __attribute__ ((__nothrow__ )); extern long double __logbl (long double __x) __attribute__ ((__nothrow__ ));






extern long double exp2l (long double __x) __attribute__ ((__nothrow__ )); extern long double __exp2l (long double __x) __attribute__ ((__nothrow__ ));


extern long double log2l (long double __x) __attribute__ ((__nothrow__ )); extern long double __log2l (long double __x) __attribute__ ((__nothrow__ ));
 extern long double powl (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __powl (long double __x, long double __y) __attribute__ ((__nothrow__ ));


extern long double sqrtl (long double __x) __attribute__ ((__nothrow__ )); extern long double __sqrtl (long double __x) __attribute__ ((__nothrow__ ));





extern long double hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __hypotl (long double __x, long double __y) __attribute__ ((__nothrow__ ));






extern long double cbrtl (long double __x) __attribute__ ((__nothrow__ )); extern long double __cbrtl (long double __x) __attribute__ ((__nothrow__ ));
extern long double ceill (long double __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern long double __ceill (long double __x) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


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


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


extern long double fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __fmodl (long double __x, long double __y) __attribute__ ((__nothrow__ ));




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


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





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


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


extern long double dreml (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __dreml (long double __x, long double __y) __attribute__ ((__nothrow__ ));



extern long double significandl (long double __x) __attribute__ ((__nothrow__ )); extern long double __significandl (long double __x) __attribute__ ((__nothrow__ ));





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






extern long double nanl (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern long double __nanl (const char *__tagb) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));





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



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


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






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






extern long double tgammal (long double) __attribute__ ((__nothrow__ )); extern long double __tgammal (long double) __attribute__ ((__nothrow__ ));





extern long double gammal (long double) __attribute__ ((__nothrow__ )); extern long double __gammal (long double) __attribute__ ((__nothrow__ ));






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







extern long double rintl (long double __x) __attribute__ ((__nothrow__ )); extern long double __rintl (long double __x) __attribute__ ((__nothrow__ ));


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

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



extern long double remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __remainderl (long double __x, long double __y) __attribute__ ((__nothrow__ ));



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



extern int ilogbl (long double __x) __attribute__ ((__nothrow__ )); extern int __ilogbl (long double __x) __attribute__ ((__nothrow__ ));




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



extern long double nearbyintl (long double __x) __attribute__ ((__nothrow__ )); extern long double __nearbyintl (long double __x) __attribute__ ((__nothrow__ ));



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



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




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






extern long int lrintl (long double __x) __attribute__ ((__nothrow__ )); extern long int __lrintl (long double __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llrintl (long double __x) __attribute__ ((__nothrow__ )); extern long long int __llrintl (long double __x) __attribute__ ((__nothrow__ ));



extern long int lroundl (long double __x) __attribute__ ((__nothrow__ )); extern long int __lroundl (long double __x) __attribute__ ((__nothrow__ ));
__extension__
extern long long int llroundl (long double __x) __attribute__ ((__nothrow__ )); extern long long int __llroundl (long double __x) __attribute__ ((__nothrow__ ));



extern long double fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ )); extern long double __fdiml (long double __x, long double __y) __attribute__ ((__nothrow__ ));


extern long double fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern long double __fmaxl (long double __x, long double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));


extern long double fminl (long double __x, long double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__)); extern long double __fminl (long double __x, long double __y) __attribute__ ((__nothrow__ )) __attribute__ ((__const__));



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


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



extern long double fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ )); extern long double __fmal (long double __x, long double __y, long double __z) __attribute__ ((__nothrow__ ));
extern long double scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ )); extern long double __scalbl (long double __x, long double __n) __attribute__ ((__nothrow__ ));
extern int signgam;
enum
  {
    FP_NAN =

      0,
    FP_INFINITE =

      1,
    FP_ZERO =

      2,
    FP_SUBNORMAL =

      3,
    FP_NORMAL =

      4
  };
typedef enum
{
  _IEEE_ = -1,
  _SVID_,
  _XOPEN_,
  _POSIX_,
  _ISOC_
} _LIB_VERSION_TYPE;




extern _LIB_VERSION_TYPE _LIB_VERSION;
struct exception

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




extern int matherr (struct exception *__exc);

extern void __VERIFIER_error() __attribute__ ((__noreturn__));
void __VERIFIER_assert(int cond) { if (!(cond)) { ERROR: __VERIFIER_error(); } return; }

int main(void)
{
  fesetround(0);
  __VERIFIER_assert(rint(2.3) == 2.0);
  __VERIFIER_assert(rint(2.5) == 2.0);
  __VERIFIER_assert(rint(3.5) == 4.0);
  __VERIFIER_assert(rint(-2.3) == -2.0);
  __VERIFIER_assert(rint(-2.5) == -2.0);
  __VERIFIER_assert(rint(-3.5) == -4.0);

  fesetround(0x400);
  __VERIFIER_assert(rint(2.3) == 2.0);
  __VERIFIER_assert(rint(2.5) == 2.0);
  __VERIFIER_assert(rint(3.5) == 3.0);
  __VERIFIER_assert(rint(-2.3) == -3.0);
  __VERIFIER_assert(rint(-2.5) == -3.0);
  __VERIFIER_assert(rint(-3.5) == -4.0);

  __VERIFIER_assert((sizeof (rint(-0.0)) == sizeof (float) ? __signbitf (rint(-0.0)) : sizeof (rint(-0.0)) == sizeof (double) ? __signbit (rint(-0.0)) : __signbitl (rint(-0.0))));
  __VERIFIER_assert(rint(-(__builtin_inff())) == -(__builtin_inff()));
}