#include <limits>
namespace std
{
const bool __numeric_limits_base::is_specialized;
const int __numeric_limits_base::digits;
const int __numeric_limits_base::digits10;
const bool __numeric_limits_base::is_signed;
const bool __numeric_limits_base::is_integer;
const bool __numeric_limits_base::is_exact;
const int __numeric_limits_base::radix;
const int __numeric_limits_base::min_exponent;
const int __numeric_limits_base::min_exponent10;
const int __numeric_limits_base::max_exponent;
const int __numeric_limits_base::max_exponent10;
const bool __numeric_limits_base::has_infinity;
const bool __numeric_limits_base::has_quiet_NaN;
const bool __numeric_limits_base::has_signaling_NaN;
const float_denorm_style __numeric_limits_base::has_denorm;
const bool __numeric_limits_base::has_denorm_loss;
const bool __numeric_limits_base::is_iec559;
const bool __numeric_limits_base::is_bounded;
const bool __numeric_limits_base::is_modulo;
const bool __numeric_limits_base::traps;
const bool __numeric_limits_base::tinyness_before;
const float_round_style __numeric_limits_base::round_style;
const bool numeric_limits<bool>::is_specialized;
const int numeric_limits<bool>::digits;
const int numeric_limits<bool>::digits10;
const bool numeric_limits<bool>::is_signed;
const bool numeric_limits<bool>::is_integer;
const bool numeric_limits<bool>::is_exact;
const int numeric_limits<bool>::radix;
const int numeric_limits<bool>::min_exponent;
const int numeric_limits<bool>::min_exponent10;
const int numeric_limits<bool>::max_exponent;
const int numeric_limits<bool>::max_exponent10;
const bool numeric_limits<bool>::has_infinity;
const bool numeric_limits<bool>::has_quiet_NaN;
const bool numeric_limits<bool>::has_signaling_NaN;
const float_denorm_style numeric_limits<bool>::has_denorm;
const bool numeric_limits<bool>::has_denorm_loss;
const bool numeric_limits<bool>::is_iec559;
const bool numeric_limits<bool>::is_bounded;
const bool numeric_limits<bool>::is_modulo;
const bool numeric_limits<bool>::traps;
const bool numeric_limits<bool>::tinyness_before;
const float_round_style numeric_limits<bool>::round_style;
const bool numeric_limits<char>::is_specialized;
const int numeric_limits<char>::digits;
const int numeric_limits<char>::digits10;
const bool numeric_limits<char>::is_signed;
const bool numeric_limits<char>::is_integer;
const bool numeric_limits<char>::is_exact;
const int numeric_limits<char>::radix;
const int numeric_limits<char>::min_exponent;
const int numeric_limits<char>::min_exponent10;
const int numeric_limits<char>::max_exponent;
const int numeric_limits<char>::max_exponent10;
const bool numeric_limits<char>::has_infinity;
const bool numeric_limits<char>::has_quiet_NaN;
const bool numeric_limits<char>::has_signaling_NaN;
const float_denorm_style numeric_limits<char>::has_denorm;
const bool numeric_limits<char>::has_denorm_loss;
const bool numeric_limits<char>::is_iec559;
const bool numeric_limits<char>::is_bounded;
const bool numeric_limits<char>::is_modulo;
const bool numeric_limits<char>::traps;
const bool numeric_limits<char>::tinyness_before;
const float_round_style numeric_limits<char>::round_style;
const bool numeric_limits<signed char>::is_specialized;
const int numeric_limits<signed char>::digits;
const int numeric_limits<signed char>::digits10;
const bool numeric_limits<signed char>::is_signed;
const bool numeric_limits<signed char>::is_integer;
const bool numeric_limits<signed char>::is_exact;
const int numeric_limits<signed char>::radix;
const int numeric_limits<signed char>::min_exponent;
const int numeric_limits<signed char>::min_exponent10;
const int numeric_limits<signed char>::max_exponent;
const int numeric_limits<signed char>::max_exponent10;
const bool numeric_limits<signed char>::has_infinity;
const bool numeric_limits<signed char>::has_quiet_NaN;
const bool numeric_limits<signed char>::has_signaling_NaN;
const float_denorm_style numeric_limits<signed char>::has_denorm;
const bool numeric_limits<signed char>::has_denorm_loss;
const bool numeric_limits<signed char>::is_iec559;
const bool numeric_limits<signed char>::is_bounded;
const bool numeric_limits<signed char>::is_modulo;
const bool numeric_limits<signed char>::traps;
const bool numeric_limits<signed char>::tinyness_before;
const float_round_style numeric_limits<signed char>::round_style;
const bool numeric_limits<unsigned char>::is_specialized;
const int numeric_limits<unsigned char>::digits;
const int numeric_limits<unsigned char>::digits10;
const bool numeric_limits<unsigned char>::is_signed;
const bool numeric_limits<unsigned char>::is_integer;
const bool numeric_limits<unsigned char>::is_exact;
const int numeric_limits<unsigned char>::radix;
const int numeric_limits<unsigned char>::min_exponent;
const int numeric_limits<unsigned char>::min_exponent10;
const int numeric_limits<unsigned char>::max_exponent;
const int numeric_limits<unsigned char>::max_exponent10;
const bool numeric_limits<unsigned char>::has_infinity;
const bool numeric_limits<unsigned char>::has_quiet_NaN;
const bool numeric_limits<unsigned char>::has_signaling_NaN;
const float_denorm_style numeric_limits<unsigned char>::has_denorm;
const bool numeric_limits<unsigned char>::has_denorm_loss;
const bool numeric_limits<unsigned char>::is_iec559;
const bool numeric_limits<unsigned char>::is_bounded;
const bool numeric_limits<unsigned char>::is_modulo;
const bool numeric_limits<unsigned char>::traps;
const bool numeric_limits<unsigned char>::tinyness_before;
const float_round_style numeric_limits<unsigned char>::round_style;
#ifdef _GLIBCXX_USE_WCHAR_T
const bool numeric_limits<wchar_t>::is_specialized;
const int numeric_limits<wchar_t>::digits;
const int numeric_limits<wchar_t>::digits10;
const bool numeric_limits<wchar_t>::is_signed;
const bool numeric_limits<wchar_t>::is_integer;
const bool numeric_limits<wchar_t>::is_exact;
const int numeric_limits<wchar_t>::radix;
const int numeric_limits<wchar_t>::min_exponent;
const int numeric_limits<wchar_t>::min_exponent10;
const int numeric_limits<wchar_t>::max_exponent;
const int numeric_limits<wchar_t>::max_exponent10;
const bool numeric_limits<wchar_t>::has_infinity;
const bool numeric_limits<wchar_t>::has_quiet_NaN;
const bool numeric_limits<wchar_t>::has_signaling_NaN;
const float_denorm_style numeric_limits<wchar_t>::has_denorm;
const bool numeric_limits<wchar_t>::has_denorm_loss;
const bool numeric_limits<wchar_t>::is_iec559;
const bool numeric_limits<wchar_t>::is_bounded;
const bool numeric_limits<wchar_t>::is_modulo;
const bool numeric_limits<wchar_t>::traps;
const bool numeric_limits<wchar_t>::tinyness_before;
const float_round_style numeric_limits<wchar_t>::round_style;
#endif // _GLIBCXX_USE_WCHAR_T
const bool numeric_limits<short>::is_specialized;
const int numeric_limits<short>::digits;
const int numeric_limits<short>::digits10;
const bool numeric_limits<short>::is_signed;
const bool numeric_limits<short>::is_integer;
const bool numeric_limits<short>::is_exact;
const int numeric_limits<short>::radix;
const int numeric_limits<short>::min_exponent;
const int numeric_limits<short>::min_exponent10;
const int numeric_limits<short>::max_exponent;
const int numeric_limits<short>::max_exponent10;
const bool numeric_limits<short>::has_infinity;
const bool numeric_limits<short>::has_quiet_NaN;
const bool numeric_limits<short>::has_signaling_NaN;
const float_denorm_style numeric_limits<short>::has_denorm;
const bool numeric_limits<short>::has_denorm_loss;
const bool numeric_limits<short>::is_iec559;
const bool numeric_limits<short>::is_bounded;
const bool numeric_limits<short>::is_modulo;
const bool numeric_limits<short>::traps;
const bool numeric_limits<short>::tinyness_before;
const float_round_style numeric_limits<short>::round_style;
const bool numeric_limits<unsigned short>::is_specialized;
const int numeric_limits<unsigned short>::digits;
const int numeric_limits<unsigned short>::digits10;
const bool numeric_limits<unsigned short>::is_signed;
const bool numeric_limits<unsigned short>::is_integer;
const bool numeric_limits<unsigned short>::is_exact;
const int numeric_limits<unsigned short>::radix;
const int numeric_limits<unsigned short>::min_exponent;
const int numeric_limits<unsigned short>::min_exponent10;
const int numeric_limits<unsigned short>::max_exponent;
const int numeric_limits<unsigned short>::max_exponent10;
const bool numeric_limits<unsigned short>::has_infinity;
const bool numeric_limits<unsigned short>::has_quiet_NaN;
const bool numeric_limits<unsigned short>::has_signaling_NaN;
const float_denorm_style numeric_limits<unsigned short>::has_denorm;
const bool numeric_limits<unsigned short>::has_denorm_loss;
const bool numeric_limits<unsigned short>::is_iec559;
const bool numeric_limits<unsigned short>::is_bounded;
const bool numeric_limits<unsigned short>::is_modulo;
const bool numeric_limits<unsigned short>::traps;
const bool numeric_limits<unsigned short>::tinyness_before;
const float_round_style numeric_limits<unsigned short>::round_style;
const bool numeric_limits<int>::is_specialized;
const int numeric_limits<int>::digits;
const int numeric_limits<int>::digits10;
const bool numeric_limits<int>::is_signed;
const bool numeric_limits<int>::is_integer;
const bool numeric_limits<int>::is_exact;
const int numeric_limits<int>::radix;
const int numeric_limits<int>::min_exponent;
const int numeric_limits<int>::min_exponent10;
const int numeric_limits<int>::max_exponent;
const int numeric_limits<int>::max_exponent10;
const bool numeric_limits<int>::has_infinity;
const bool numeric_limits<int>::has_quiet_NaN;
const bool numeric_limits<int>::has_signaling_NaN;
const float_denorm_style numeric_limits<int>::has_denorm;
const bool numeric_limits<int>::has_denorm_loss;
const bool numeric_limits<int>::is_iec559;
const bool numeric_limits<int>::is_bounded;
const bool numeric_limits<int>::is_modulo;
const bool numeric_limits<int>::traps;
const bool numeric_limits<int>::tinyness_before;
const float_round_style numeric_limits<int>::round_style;
const bool numeric_limits<unsigned int>::is_specialized;
const int numeric_limits<unsigned int>::digits;
const int numeric_limits<unsigned int>::digits10;
const bool numeric_limits<unsigned int>::is_signed;
const bool numeric_limits<unsigned int>::is_integer;
const bool numeric_limits<unsigned int>::is_exact;
const int numeric_limits<unsigned int>::radix;
const int numeric_limits<unsigned int>::min_exponent;
const int numeric_limits<unsigned int>::min_exponent10;
const int numeric_limits<unsigned int>::max_exponent;
const int numeric_limits<unsigned int>::max_exponent10;
const bool numeric_limits<unsigned int>::has_infinity;
const bool numeric_limits<unsigned int>::has_quiet_NaN;
const bool numeric_limits<unsigned int>::has_signaling_NaN;
const float_denorm_style numeric_limits<unsigned int>::has_denorm;
const bool numeric_limits<unsigned int>::has_denorm_loss;
const bool numeric_limits<unsigned int>::is_iec559;
const bool numeric_limits<unsigned int>::is_bounded;
const bool numeric_limits<unsigned int>::is_modulo;
const bool numeric_limits<unsigned int>::traps;
const bool numeric_limits<unsigned int>::tinyness_before;
const float_round_style numeric_limits<unsigned int>::round_style;
const bool numeric_limits<long>::is_specialized;
const int numeric_limits<long>::digits;
const int numeric_limits<long>::digits10;
const bool numeric_limits<long>::is_signed;
const bool numeric_limits<long>::is_integer;
const bool numeric_limits<long>::is_exact;
const int numeric_limits<long>::radix;
const int numeric_limits<long>::min_exponent;
const int numeric_limits<long>::min_exponent10;
const int numeric_limits<long>::max_exponent;
const int numeric_limits<long>::max_exponent10;
const bool numeric_limits<long>::has_infinity;
const bool numeric_limits<long>::has_quiet_NaN;
const bool numeric_limits<long>::has_signaling_NaN;
const float_denorm_style numeric_limits<long>::has_denorm;
const bool numeric_limits<long>::has_denorm_loss;
const bool numeric_limits<long>::is_iec559;
const bool numeric_limits<long>::is_bounded;
const bool numeric_limits<long>::is_modulo;
const bool numeric_limits<long>::traps;
const bool numeric_limits<long>::tinyness_before;
const float_round_style numeric_limits<long>::round_style;
const bool numeric_limits<unsigned long>::is_specialized;
const int numeric_limits<unsigned long>::digits;
const int numeric_limits<unsigned long>::digits10;
const bool numeric_limits<unsigned long>::is_signed;
const bool numeric_limits<unsigned long>::is_integer;
const bool numeric_limits<unsigned long>::is_exact;
const int numeric_limits<unsigned long>::radix;
const int numeric_limits<unsigned long>::min_exponent;
const int numeric_limits<unsigned long>::min_exponent10;
const int numeric_limits<unsigned long>::max_exponent;
const int numeric_limits<unsigned long>::max_exponent10;
const bool numeric_limits<unsigned long>::has_infinity;
const bool numeric_limits<unsigned long>::has_quiet_NaN;
const bool numeric_limits<unsigned long>::has_signaling_NaN;
const float_denorm_style numeric_limits<unsigned long>::has_denorm;
const bool numeric_limits<unsigned long>::has_denorm_loss;
const bool numeric_limits<unsigned long>::is_iec559;
const bool numeric_limits<unsigned long>::is_bounded;
const bool numeric_limits<unsigned long>::is_modulo;
const bool numeric_limits<unsigned long>::traps;
const bool numeric_limits<unsigned long>::tinyness_before;
const float_round_style numeric_limits<unsigned long>::round_style;
const bool numeric_limits<long long>::is_specialized;
const int numeric_limits<long long>::digits;
const int numeric_limits<long long>::digits10;
const bool numeric_limits<long long>::is_signed;
const bool numeric_limits<long long>::is_integer;
const bool numeric_limits<long long>::is_exact;
const int numeric_limits<long long>::radix;
const int numeric_limits<long long>::min_exponent;
const int numeric_limits<long long>::min_exponent10;
const int numeric_limits<long long>::max_exponent;
const int numeric_limits<long long>::max_exponent10;
const bool numeric_limits<long long>::has_infinity;
const bool numeric_limits<long long>::has_quiet_NaN;
const bool numeric_limits<long long>::has_signaling_NaN;
const float_denorm_style numeric_limits<long long>::has_denorm;
const bool numeric_limits<long long>::has_denorm_loss;
const bool numeric_limits<long long>::is_iec559;
const bool numeric_limits<long long>::is_bounded;
const bool numeric_limits<long long>::is_modulo;
const bool numeric_limits<long long>::traps;
const bool numeric_limits<long long>::tinyness_before;
const float_round_style numeric_limits<long long>::round_style;
const bool numeric_limits<unsigned long long>::is_specialized;
const int numeric_limits<unsigned long long>::digits;
const int numeric_limits<unsigned long long>::digits10;
const bool numeric_limits<unsigned long long>::is_signed;
const bool numeric_limits<unsigned long long>::is_integer;
const bool numeric_limits<unsigned long long>::is_exact;
const int numeric_limits<unsigned long long>::radix;
const int numeric_limits<unsigned long long>::min_exponent;
const int numeric_limits<unsigned long long>::min_exponent10;
const int numeric_limits<unsigned long long>::max_exponent;
const int numeric_limits<unsigned long long>::max_exponent10;
const bool numeric_limits<unsigned long long>::has_infinity;
const bool numeric_limits<unsigned long long>::has_quiet_NaN;
const bool numeric_limits<unsigned long long>::has_signaling_NaN;
const float_denorm_style numeric_limits<unsigned long long>::has_denorm;
const bool numeric_limits<unsigned long long>::has_denorm_loss;
const bool numeric_limits<unsigned long long>::is_iec559;
const bool numeric_limits<unsigned long long>::is_bounded;
const bool numeric_limits<unsigned long long>::is_modulo;
const bool numeric_limits<unsigned long long>::traps;
const bool numeric_limits<unsigned long long>::tinyness_before;
const float_round_style numeric_limits<unsigned long long>::round_style;
const bool numeric_limits<float>::is_specialized;
const int numeric_limits<float>::digits;
const int numeric_limits<float>::digits10;
const bool numeric_limits<float>::is_signed;
const bool numeric_limits<float>::is_integer;
const bool numeric_limits<float>::is_exact;
const int numeric_limits<float>::radix;
const int numeric_limits<float>::min_exponent;
const int numeric_limits<float>::min_exponent10;
const int numeric_limits<float>::max_exponent;
const int numeric_limits<float>::max_exponent10;
const bool numeric_limits<float>::has_infinity;
const bool numeric_limits<float>::has_quiet_NaN;
const bool numeric_limits<float>::has_signaling_NaN;
const float_denorm_style numeric_limits<float>::has_denorm;
const bool numeric_limits<float>::has_denorm_loss;
const bool numeric_limits<float>::is_iec559;
const bool numeric_limits<float>::is_bounded;
const bool numeric_limits<float>::is_modulo;
const bool numeric_limits<float>::traps;
const bool numeric_limits<float>::tinyness_before;
const float_round_style numeric_limits<float>::round_style;
const bool numeric_limits<double>::is_specialized;
const int numeric_limits<double>::digits;
const int numeric_limits<double>::digits10;
const bool numeric_limits<double>::is_signed;
const bool numeric_limits<double>::is_integer;
const bool numeric_limits<double>::is_exact;
const int numeric_limits<double>::radix;
const int numeric_limits<double>::min_exponent;
const int numeric_limits<double>::min_exponent10;
const int numeric_limits<double>::max_exponent;
const int numeric_limits<double>::max_exponent10;
const bool numeric_limits<double>::has_infinity;
const bool numeric_limits<double>::has_quiet_NaN;
const bool numeric_limits<double>::has_signaling_NaN;
const float_denorm_style numeric_limits<double>::has_denorm;
const bool numeric_limits<double>::has_denorm_loss;
const bool numeric_limits<double>::is_iec559;
const bool numeric_limits<double>::is_bounded;
const bool numeric_limits<double>::is_modulo;
const bool numeric_limits<double>::traps;
const bool numeric_limits<double>::tinyness_before;
const float_round_style numeric_limits<double>::round_style;
const bool numeric_limits<long double>::is_specialized;
const int numeric_limits<long double>::digits;
const int numeric_limits<long double>::digits10;
const bool numeric_limits<long double>::is_signed;
const bool numeric_limits<long double>::is_integer;
const bool numeric_limits<long double>::is_exact;
const int numeric_limits<long double>::radix;
const int numeric_limits<long double>::min_exponent;
const int numeric_limits<long double>::min_exponent10;
const int numeric_limits<long double>::max_exponent;
const int numeric_limits<long double>::max_exponent10;
const bool numeric_limits<long double>::has_infinity;
const bool numeric_limits<long double>::has_quiet_NaN;
const bool numeric_limits<long double>::has_signaling_NaN;
const float_denorm_style numeric_limits<long double>::has_denorm;
const bool numeric_limits<long double>::has_denorm_loss;
const bool numeric_limits<long double>::is_iec559;
const bool numeric_limits<long double>::is_bounded;
const bool numeric_limits<long double>::is_modulo;
const bool numeric_limits<long double>::traps;
const bool numeric_limits<long double>::tinyness_before;
const float_round_style numeric_limits<long double>::round_style;
}