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namespace std{enum float_round_style;enum float_denorm_style; template<class T>class numeric_limits; template<class T>class numeric_limits<const T>;template<class T>class numeric_limits<volatile T>;template<class T>class numeric_limits<constvolatile T>; template<>class numeric_limits<bool>; template<>class numeric_limits<char>;template<>class numeric_limits<signedchar>;template<>class numeric_limits<unsignedchar>;template<>class numeric_limits<char8_t>;template<>class numeric_limits<char16_t>;template<>class numeric_limits<char32_t>;template<>class numeric_limits<wchar_t>; template<>class numeric_limits<short>;template<>class numeric_limits<int>;template<>class numeric_limits<long>;template<>class numeric_limits<longlong>;template<>class numeric_limits<unsignedshort>;template<>class numeric_limits<unsignedint>;template<>class numeric_limits<unsignedlong>;template<>class numeric_limits<unsignedlonglong>; template<>class numeric_limits<float>;template<>class numeric_limits<double>;template<>class numeric_limits<longdouble>;}

namespace std{enum float_round_style{        round_indeterminate=-1,        round_toward_zero=0,        round_to_nearest=1,        round_toward_infinity=2,        round_toward_neg_infinity=3,};}

namespace std{enum float_denorm_style{        denorm_indeterminate=-1,        denorm_absent=0,        denorm_present=1};}

template<class T>class numeric_limits{public:staticconstexprbool is_specialized=false; staticconstexpr T min()noexcept{return T();}staticconstexpr T max()noexcept{return T();}staticconstexpr T lowest()noexcept{return T();} staticconstexprint digits=0;staticconstexprint digits10=0;staticconstexprint max_digits10=0; staticconstexprbool is_signed=false;staticconstexprbool is_integer=false;staticconstexprbool is_exact=false;staticconstexprint radix=0;staticconstexpr T epsilon()noexcept{return T();}staticconstexpr T round_error()noexcept{return T();} staticconstexprint min_exponent=0;staticconstexprint min_exponent10=0;staticconstexprint max_exponent=0;staticconstexprint max_exponent10=0; staticconstexprbool has_infinity=false;staticconstexprbool has_quiet_NaN=false;staticconstexprbool has_signaling_NaN=false;staticconstexpr float_denorm_style has_denorm= denorm_absent;staticconstexprbool has_denorm_loss=false;staticconstexpr T infinity()noexcept{return T();}staticconstexpr T quiet_NaN()noexcept{return T();}staticconstexpr T signaling_NaN()noexcept{return T();}staticconstexpr T denorm_min()noexcept{return T();} staticconstexprbool is_iec559=false;staticconstexprbool is_bounded=false;staticconstexprbool is_modulo=false; staticconstexprbool traps=false;staticconstexprbool tinyness_before=false;staticconstexpr float_round_style round_style= round_toward_zero;};

template<>class numeric_limits<bool>{public:staticconstexprbool is_specialized=true; staticconstexprbool min()noexcept{returnfalse;}staticconstexprbool max()noexcept{returntrue;}staticconstexprbool lowest()noexcept{returnfalse;} staticconstexprint digits=1;staticconstexprint digits10=0;staticconstexprint max_digits10=0; staticconstexprbool is_signed=false;staticconstexprbool is_integer=true;staticconstexprbool is_exact=true;staticconstexprint radix=2;staticconstexprbool epsilon()noexcept{return0;}staticconstexprbool round_error()noexcept{return0;} staticconstexprint min_exponent=0;staticconstexprint min_exponent10=0;staticconstexprint max_exponent=0;staticconstexprint max_exponent10=0; staticconstexprbool has_infinity=false;staticconstexprbool has_quiet_NaN=false;staticconstexprbool has_signaling_NaN=false;staticconstexpr float_denorm_style has_denorm= denorm_absent;staticconstexprbool has_denorm_loss=false;staticconstexprbool infinity()noexcept{return0;}staticconstexprbool quiet_NaN()noexcept{return0;}staticconstexprbool signaling_NaN()noexcept{return0;}staticconstexprbool denorm_min()noexcept{return0;} staticconstexprbool is_iec559=false;staticconstexprbool is_bounded=true;staticconstexprbool is_modulo=false; staticconstexprbool traps=false;staticconstexprbool tinyness_before=false;staticconstexpr float_round_style round_style= round_toward_zero;};