// fast_float by Daniel Lemire
// fast_float by João Paulo Magalhaes


// with contributions from Eugene Golushkov
// with contributions from Maksim Kita
// with contributions from Marcin Wojdyr
// with contributions from Neal Richardson
// with contributions from Tim Paine
// with contributions from Fabio Pellacini


// Permission is hereby granted, free of charge, to any
// person obtaining a copy of this software and associated
// documentation files (the "Software"), to deal in the
// Software without restriction, including without
// limitation the rights to use, copy, modify, merge,
// publish, distribute, sublicense, and/or sell copies of
// the Software, and to permit persons to whom the Software
// is furnished to do so, subject to the following
// conditions:
// 
// The above copyright notice and this permission notice
// shall be included in all copies or substantial portions
// of the Software.
// 
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF
// ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED
// TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
// PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT
// SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
// CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION
// OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR
// IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.


#ifndef FASTFLOAT_FAST_FLOAT_H
#define FASTFLOAT_FAST_FLOAT_H

#include <system_error>

namespace fast_float {
enum chars_format {
    scientific = 1<<0,
    fixed = 1<<2,
    hex = 1<<3,
    general = fixed | scientific
};


struct from_chars_result {
  const char *ptr;
  std::errc ec;
};

/**
 * This function parses the character sequence [first,last) for a number. It parses floating-point numbers expecting
 * a locale-indepent format equivalent to what is used by std::strtod in the default ("C") locale.
 * The resulting floating-point value is the closest floating-point values (using either float or double),
 * using the "round to even" convention for values that would otherwise fall right in-between two values.
 * That is, we provide exact parsing according to the IEEE standard.
 *
 * Given a successful parse, the pointer (`ptr`) in the returned value is set to point right after the
 * parsed number, and the `value` referenced is set to the parsed value. In case of error, the returned
 * `ec` contains a representative error, otherwise the default (`std::errc()`) value is stored.
 *
 * The implementation does not throw and does not allocate memory (e.g., with `new` or `malloc`).
 *
 * Like the C++17 standard, the `fast_float::from_chars` functions take an optional last argument of
 * the type `fast_float::chars_format`. It is a bitset value: we check whether
 * `fmt & fast_float::chars_format::fixed` and `fmt & fast_float::chars_format::scientific` are set
 * to determine whether we allowe the fixed point and scientific notation respectively.
 * The default is  `fast_float::chars_format::general` which allows both `fixed` and `scientific`.
 */
template<typename T>
from_chars_result from_chars(const char *first, const char *last,
                             T &value, chars_format fmt = chars_format::general)  noexcept;

}
#endif // FASTFLOAT_FAST_FLOAT_H

#ifndef FASTFLOAT_FLOAT_COMMON_H
#define FASTFLOAT_FLOAT_COMMON_H

#include <cfloat>
#include <cstdint>
#include <cassert>

#if (defined(__x86_64) || defined(__x86_64__) || defined(_M_X64)   \
       || defined(__amd64) || defined(__aarch64__) || defined(_M_ARM64) \
       || defined(__MINGW64__)                                          \
       || defined(__s390x__)                                            \
       || (defined(__ppc64__) || defined(__PPC64__) || defined(__ppc64le__) || defined(__PPC64LE__)) \
       || defined(__EMSCRIPTEN__))
#define FASTFLOAT_64BIT
#elif (defined(__i386) || defined(__i386__) || defined(_M_IX86)   \
     || defined(__arm__) || defined(_M_ARM)                   \
     || defined(__MINGW32__))
#define FASTFLOAT_32BIT
#else
  // Need to check incrementally, since SIZE_MAX is a size_t, avoid overflow.
  // We can never tell the register width, but the SIZE_MAX is a good approximation.
  // UINTPTR_MAX and INTPTR_MAX are optional, so avoid them for max portability.
  #if SIZE_MAX == 0xffff
    #error Unknown platform (16-bit, unsupported)
  #elif SIZE_MAX == 0xffffffff
    #define FASTFLOAT_32BIT
  #elif SIZE_MAX == 0xffffffffffffffff
    #define FASTFLOAT_64BIT
  #else
    #error Unknown platform (not 32-bit, not 64-bit?)
  #endif
#endif

#if ((defined(_WIN32) || defined(_WIN64)) && !defined(__clang__))
#include <intrin.h>
#endif

#if defined(_MSC_VER) && !defined(__clang__)
#define FASTFLOAT_VISUAL_STUDIO 1
#endif

#ifdef _WIN32
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#if defined(__APPLE__) || defined(__FreeBSD__)
#include <machine/endian.h>
#elif defined(sun) || defined(__sun)
#include <sys/byteorder.h>
#else
#include <endian.h>
#endif
#
#ifndef __BYTE_ORDER__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#ifndef __ORDER_LITTLE_ENDIAN__
// safe choice
#define FASTFLOAT_IS_BIG_ENDIAN 0
#endif
#
#if __BYTE_ORDER__ == __ORDER_LITTLE_ENDIAN__
#define FASTFLOAT_IS_BIG_ENDIAN 0
#else
#define FASTFLOAT_IS_BIG_ENDIAN 1
#endif
#endif

#ifdef FASTFLOAT_VISUAL_STUDIO
#define fastfloat_really_inline __forceinline
#else
#define fastfloat_really_inline inline __attribute__((always_inline))
#endif

namespace fast_float {

// Compares two ASCII strings in a case insensitive manner.
inline bool fastfloat_strncasecmp(const char *input1, const char *input2,
                                  size_t length) {
  char running_diff{0};
  for (size_t i = 0; i < length; i++) {
    running_diff |= (input1[i] ^ input2[i]);
  }
  return (running_diff == 0) || (running_diff == 32);
}

#ifndef FLT_EVAL_METHOD
#error "FLT_EVAL_METHOD should be defined, please include cfloat."
#endif

namespace {
constexpr uint32_t max_digits = 768;
constexpr uint32_t max_digit_without_overflow = 19;
constexpr int32_t decimal_point_range = 2047;
} // namespace

struct value128 {
  uint64_t low;
  uint64_t high;
  value128(uint64_t _low, uint64_t _high) : low(_low), high(_high) {}
  value128() : low(0), high(0) {}
};

/* result might be undefined when input_num is zero */
fastfloat_really_inline int leading_zeroes(uint64_t input_num) {
  assert(input_num > 0);
#ifdef FASTFLOAT_VISUAL_STUDIO
  #if defined(_M_X64) || defined(_M_ARM64)
  unsigned long leading_zero = 0;
  // Search the mask data from most significant bit (MSB)
  // to least significant bit (LSB) for a set bit (1).
  _BitScanReverse64(&leading_zero, input_num);
  return (int)(63 - leading_zero);
  #else
  int last_bit = 0;
  if(input_num & uint64_t(0xffffffff00000000)) input_num >>= 32, last_bit |= 32;
  if(input_num & uint64_t(        0xffff0000)) input_num >>= 16, last_bit |= 16;
  if(input_num & uint64_t(            0xff00)) input_num >>=  8, last_bit |=  8;
  if(input_num & uint64_t(              0xf0)) input_num >>=  4, last_bit |=  4;
  if(input_num & uint64_t(               0xc)) input_num >>=  2, last_bit |=  2;
  if(input_num & uint64_t(               0x2)) input_num >>=  1, last_bit |=  1;
  return 63 - last_bit;
  #endif
#else
  return __builtin_clzll(input_num);
#endif
}

#ifdef FASTFLOAT_32BIT

// slow emulation routine for 32-bit
fastfloat_really_inline uint64_t emulu(uint32_t x, uint32_t y) {
    return x * (uint64_t)y;
}

// slow emulation routine for 32-bit
#if !defined(__MINGW64__)
fastfloat_really_inline uint64_t _umul128(uint64_t ab, uint64_t cd,
                                          uint64_t *hi) {
  uint64_t ad = emulu((uint32_t)(ab >> 32), (uint32_t)cd);
  uint64_t bd = emulu((uint32_t)ab, (uint32_t)cd);
  uint64_t adbc = ad + emulu((uint32_t)ab, (uint32_t)(cd >> 32));
  uint64_t adbc_carry = !!(adbc < ad);
  uint64_t lo = bd + (adbc << 32);
  *hi = emulu((uint32_t)(ab >> 32), (uint32_t)(cd >> 32)) + (adbc >> 32) +
        (adbc_carry << 32) + !!(lo < bd);
  return lo;
}
#endif // !__MINGW64__

#endif // FASTFLOAT_32BIT


// compute 64-bit a*b
fastfloat_really_inline value128 full_multiplication(uint64_t a,
                                                     uint64_t b) {
  value128 answer;
#ifdef _M_ARM64
  // ARM64 has native support for 64-bit multiplications, no need to emulate
  answer.high = __umulh(a, b);
  answer.low = a * b;
#elif defined(FASTFLOAT_32BIT) || (defined(_WIN64) && !defined(__clang__))
  answer.low = _umul128(a, b, &answer.high); // _umul128 not available on ARM64
#elif defined(FASTFLOAT_64BIT)
  __uint128_t r = ((__uint128_t)a) * b;
  answer.low = uint64_t(r);
  answer.high = uint64_t(r >> 64);
#else
  #error Not implemented
#endif
  return answer;
}


struct adjusted_mantissa {
  uint64_t mantissa{0};
  int power2{0}; // a negative value indicates an invalid result
  adjusted_mantissa() = default;
  bool operator==(const adjusted_mantissa &o) const {
    return mantissa == o.mantissa && power2 == o.power2;
  }
  bool operator!=(const adjusted_mantissa &o) const {
    return mantissa != o.mantissa || power2 != o.power2;
  }
};

struct decimal {
  uint32_t num_digits{0};
  int32_t decimal_point{0};
  bool negative{false};
  bool truncated{false};
  uint8_t digits[max_digits];
  decimal() = default;
  // Copies are not allowed since this is a fat object.
  decimal(const decimal &) = delete;
  // Copies are not allowed since this is a fat object.
  decimal &operator=(const decimal &) = delete;
  // Moves are allowed:
  decimal(decimal &&) = default;
  decimal &operator=(decimal &&other) = default;
};

constexpr static double powers_of_ten_double[] = {
    1e0,  1e1,  1e2,  1e3,  1e4,  1e5,  1e6,  1e7,  1e8,  1e9,  1e10, 1e11,
    1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22};
constexpr static float powers_of_ten_float[] = {1e0, 1e1, 1e2, 1e3, 1e4, 1e5,
                                                1e6, 1e7, 1e8, 1e9, 1e10};

template <typename T> struct binary_format {
  static inline constexpr int mantissa_explicit_bits();
  static inline constexpr int minimum_exponent();
  static inline constexpr int infinite_power();
  static inline constexpr int sign_index();
  static inline constexpr int min_exponent_fast_path();
  static inline constexpr int max_exponent_fast_path();
  static inline constexpr int max_exponent_round_to_even();
  static inline constexpr int min_exponent_round_to_even();
  static inline constexpr uint64_t max_mantissa_fast_path();
  static inline constexpr int largest_power_of_ten();
  static inline constexpr int smallest_power_of_ten();
  static inline constexpr T exact_power_of_ten(int64_t power);
};

template <> inline constexpr int binary_format<double>::mantissa_explicit_bits() {
  return 52;
}
template <> inline constexpr int binary_format<float>::mantissa_explicit_bits() {
  return 23;
}

template <> inline constexpr int binary_format<double>::max_exponent_round_to_even() {
  return 23;
}

template <> inline constexpr int binary_format<float>::max_exponent_round_to_even() {
  return 10;
}

template <> inline constexpr int binary_format<double>::min_exponent_round_to_even() {
  return -4;
}

template <> inline constexpr int binary_format<float>::min_exponent_round_to_even() {
  return -17;
}

template <> inline constexpr int binary_format<double>::minimum_exponent() {
  return -1023;
}
template <> inline constexpr int binary_format<float>::minimum_exponent() {
  return -127;
}

template <> inline constexpr int binary_format<double>::infinite_power() {
  return 0x7FF;
}
template <> inline constexpr int binary_format<float>::infinite_power() {
  return 0xFF;
}

template <> inline constexpr int binary_format<double>::sign_index() { return 63; }
template <> inline constexpr int binary_format<float>::sign_index() { return 31; }

template <> inline constexpr int binary_format<double>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return 0;
#else
  return -22;
#endif
}
template <> inline constexpr int binary_format<float>::min_exponent_fast_path() {
#if (FLT_EVAL_METHOD != 1) && (FLT_EVAL_METHOD != 0)
  return 0;
#else
  return -10;
#endif
}

template <> inline constexpr int binary_format<double>::max_exponent_fast_path() {
  return 22;
}
template <> inline constexpr int binary_format<float>::max_exponent_fast_path() {
  return 10;
}

template <> inline constexpr uint64_t binary_format<double>::max_mantissa_fast_path() {
  return uint64_t(2) << mantissa_explicit_bits();
}
template <> inline constexpr uint64_t binary_format<float>::max_mantissa_fast_path() {
  return uint64_t(2) << mantissa_explicit_bits();
}

template <>
inline constexpr double binary_format<double>::exact_power_of_ten(int64_t power) {
  return powers_of_ten_double[power];
}
template <>
inline constexpr float binary_format<float>::exact_power_of_ten(int64_t power) {

  return powers_of_ten_float[power];
}


template <>
inline constexpr int binary_format<double>::largest_power_of_ten() {
  return 308;
}
template <>
inline constexpr int binary_format<float>::largest_power_of_ten() {
  return 38;
}

template <>
inline constexpr int binary_format<double>::smallest_power_of_ten() {
  return -342;
}
template <>
inline constexpr int binary_format<float>::smallest_power_of_ten() {
  return -65;
}

} // namespace fast_float

// for convenience:
template<class OStream>
inline OStream& operator<<(OStream &out, const fast_float::decimal &d) {
  out << "0.";
  for (size_t i = 0; i < d.num_digits; i++) {
    out << int32_t(d.digits[i]);
  }
  out << " * 10 ** " << d.decimal_point;
  return out;
}

#endif


#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H

#include <cstdio>
#include <cctype>
#include <cstdint>
#include <cstring>


namespace fast_float {

// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline bool is_integer(char c)  noexcept  { return c >= '0' && c <= '9'; }

fastfloat_really_inline uint64_t byteswap(uint64_t val) {
  return (val & 0xFF00000000000000) >> 56
    | (val & 0x00FF000000000000) >> 40
    | (val & 0x0000FF0000000000) >> 24
    | (val & 0x000000FF00000000) >> 8
    | (val & 0x00000000FF000000) << 8
    | (val & 0x0000000000FF0000) << 24
    | (val & 0x000000000000FF00) << 40
    | (val & 0x00000000000000FF) << 56;
}

fastfloat_really_inline uint64_t read_u64(const char *chars) {
  uint64_t val;
  ::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  return val;
}

fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  ::memcpy(chars, &val, sizeof(uint64_t));
}

// credit  @aqrit
fastfloat_really_inline uint32_t  parse_eight_digits_unrolled(uint64_t val) {
  const uint64_t mask = 0x000000FF000000FF;
  const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
  const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
  val -= 0x3030303030303030;
  val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
  val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
  return uint32_t(val);
}

fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
  return parse_eight_digits_unrolled(read_u64(chars));
}

// credit @aqrit
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val)  noexcept  {
  return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
     0x8080808080808080));
}

fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars)  noexcept  {
  return is_made_of_eight_digits_fast(read_u64(chars));
}

struct parsed_number_string {
  int64_t exponent;
  uint64_t mantissa;
  const char *lastmatch;
  bool negative;
  bool valid;
  bool too_many_digits;
};


// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline
parsed_number_string parse_number_string(const char *p, const char *pend, chars_format fmt) noexcept {
  parsed_number_string answer;
  answer.valid = false;
  answer.too_many_digits = false;
  answer.negative = (*p == '-');
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
    ++p;
    if (p == pend) {
      return answer;
    }
    if (!is_integer(*p) && (*p != '.')) { // a  sign must be followed by an integer or the dot
      return answer;
    }
  }
  const char *const start_digits = p;

  uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)

  while ((p != pend) && is_integer(*p)) {
    // a multiplication by 10 is cheaper than an arbitrary integer
    // multiplication
    i = 10 * i +
        uint64_t(*p - '0'); // might overflow, we will handle the overflow later
    ++p;
  }
  const char *const end_of_integer_part = p;
  int64_t digit_count = int64_t(end_of_integer_part - start_digits);
  int64_t exponent = 0;
  if ((p != pend) && (*p == '.')) {
    ++p;
  // Fast approach only tested under little endian systems
  if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
    i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
    p += 8;
    if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
      i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
      p += 8;
    }
  }
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      ++p;
      i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
    }
    exponent = end_of_integer_part + 1 - p;
    digit_count -= exponent;
  }
  // we must have encountered at least one integer!
  if (digit_count == 0) {
    return answer;
  }
  int64_t exp_number = 0;            // explicit exponential part
  if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
    const char * location_of_e = p;
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    if ((p == pend) || !is_integer(*p)) {
      if(!(fmt & chars_format::fixed)) {
        // We are in error.
        return answer;
      }
      // Otherwise, we will be ignoring the 'e'.
      p = location_of_e;
    } else {
      while ((p != pend) && is_integer(*p)) {
        uint8_t digit = uint8_t(*p - '0');
        if (exp_number < 0x10000) {
          exp_number = 10 * exp_number + digit;
        }
        ++p;
      }
      if(neg_exp) { exp_number = - exp_number; }
      exponent += exp_number;
    }
  } else {
    // If it scientific and not fixed, we have to bail out.
    if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
  }
  answer.lastmatch = p;
  answer.valid = true;

  // If we frequently had to deal with long strings of digits,
  // we could extend our code by using a 128-bit integer instead
  // of a 64-bit integer. However, this is uncommon.
  //
  // We can deal with up to 19 digits.
  if (digit_count > 19) { // this is uncommon
    // It is possible that the integer had an overflow.
    // We have to handle the case where we have 0.0000somenumber.
    // We need to be mindful of the case where we only have zeroes...
    // E.g., 0.000000000...000.
    const char *start = start_digits;
    while ((start != pend) && (*start == '0' || *start == '.')) {
      if(*start == '0') { digit_count --; }
      start++;
    }
    if (digit_count > 19) {
      answer.too_many_digits = true;
      // Let us start again, this time, avoiding overflows.
      i = 0;
      p = start_digits;
      const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
      while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
        i = i * 10 + uint64_t(*p - '0');
        ++p;
      }
      if (i >= minimal_nineteen_digit_integer) { // We have a big integers
        exponent = end_of_integer_part - p + exp_number;
      } else { // We have a value with a fractional component.
          p++; // skip the '.'
          const char *first_after_period = p;
          while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
            i = i * 10 + uint64_t(*p - '0');
            ++p;
          }
          exponent = first_after_period - p + exp_number;
      }
      // We have now corrected both exponent and i, to a truncated value
    }
  }
  answer.exponent = exponent;
  answer.mantissa = i;
  return answer;
}


// This should always succeed since it follows a call to parse_number_string
// This function could be optimized. In particular, we could stop after 19 digits
// and try to bail out. Furthermore, we should be able to recover the computed
// exponent from the pass in parse_number_string.
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend) noexcept {
  decimal answer;
  answer.num_digits = 0;
  answer.decimal_point = 0;
  answer.truncated = false;
  answer.negative = (*p == '-');
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
    ++p;
  }
  // skip leading zeroes
  while ((p != pend) && (*p == '0')) {
    ++p;
  }
  while ((p != pend) && is_integer(*p)) {
    if (answer.num_digits < max_digits) {
      answer.digits[answer.num_digits] = uint8_t(*p - '0');
    }
    answer.num_digits++;
    ++p;
  }
  if ((p != pend) && (*p == '.')) {
    ++p;
    const char *first_after_period = p;
    // if we have not yet encountered a zero, we have to skip it as well
    if(answer.num_digits == 0) {
      // skip zeros
      while ((p != pend) && (*p == '0')) {
       ++p;
      }
    }
    // We expect that this loop will often take the bulk of the running time
    // because when a value has lots of digits, these digits often
    while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
      uint64_t val = read_u64(p);
      if(! is_made_of_eight_digits_fast(val)) { break; }
      // We have eight digits, process them in one go!
      val -= 0x3030303030303030;
      write_u64(answer.digits + answer.num_digits, val);
      answer.num_digits += 8;
      p += 8;
    }
    while ((p != pend) && is_integer(*p)) {
      if (answer.num_digits < max_digits) {
        answer.digits[answer.num_digits] = uint8_t(*p - '0');
      }
      answer.num_digits++;
      ++p;
    }
    answer.decimal_point = int32_t(first_after_period - p);
  }
  // We want num_digits to be the number of significant digits, excluding
  // leading *and* trailing zeros! Otherwise the truncated flag later is
  // going to be misleading.
  if(answer.num_digits > 0) {
    // We potentially need the answer.num_digits > 0 guard because we
    // prune leading zeros. So with answer.num_digits > 0, we know that
    // we have at least one non-zero digit.
    const char *preverse = p - 1;
    int32_t trailing_zeros = 0;
    while ((*preverse == '0') || (*preverse == '.')) {
      if(*preverse == '0') { trailing_zeros++; };
      --preverse;
    }
    answer.decimal_point += int32_t(answer.num_digits);
    answer.num_digits -= uint32_t(trailing_zeros);
  }
  if(answer.num_digits > max_digits) {
    answer.truncated = true;
    answer.num_digits = max_digits;
  }
  if ((p != pend) && (('e' == *p) || ('E' == *p))) {
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    int32_t exp_number = 0; // exponential part
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      if (exp_number < 0x10000) {
        exp_number = 10 * exp_number + digit;
      }
      ++p;
    }
    answer.decimal_point += (neg_exp ? -exp_number : exp_number);
  }
  // In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
  // assume that all digits up to max_digit_without_overflow have been initialized.
  for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }

  return answer;
}
} // namespace fast_float

#endif


#ifndef FASTFLOAT_FAST_TABLE_H
#define FASTFLOAT_FAST_TABLE_H
#include <cstdint>

namespace fast_float {

/**
 * When mapping numbers from decimal to binary,
 * we go from w * 10^q to m * 2^p but we have
 * 10^q = 5^q * 2^q, so effectively
 * we are trying to match
 * w * 2^q * 5^q to m * 2^p. Thus the powers of two
 * are not a concern since they can be represented
 * exactly using the binary notation, only the powers of five
 * affect the binary significand.
 */

/**
 * The smallest non-zero float (binary64) is 2^−1074.
 * We take as input numbers of the form w x 10^q where w < 2^64.
 * We have that w * 10^-343  <  2^(64-344) 5^-343 < 2^-1076.
 * However, we have that
 * (2^64-1) * 10^-342 =  (2^64-1) * 2^-342 * 5^-342 > 2^−1074.
 * Thus it is possible for a number of the form w * 10^-342 where
 * w is a 64-bit value to be a non-zero floating-point number.
 *********
 * Any number of form w * 10^309 where w>= 1 is going to be
 * infinite in binary64 so we never need to worry about powers
 * of 5 greater than 308.
 */
template <class unused = void>
struct powers_template {

constexpr static int smallest_power_of_five = binary_format<double>::smallest_power_of_ten();
constexpr static int largest_power_of_five = binary_format<double>::largest_power_of_ten();
constexpr static int number_of_entries = 2 * (largest_power_of_five - smallest_power_of_five + 1);
// Powers of five from 5^-342 all the way to 5^308 rounded toward one.
static const uint64_t power_of_five_128[number_of_entries];
};

template <class unused>
const uint64_t powers_template<unused>::power_of_five_128[number_of_entries] = {
        0xeef453d6923bd65a,0x113faa2906a13b3f,
        0x9558b4661b6565f8,0x4ac7ca59a424c507,
        0xbaaee17fa23ebf76,0x5d79bcf00d2df649,
        0xe95a99df8ace6f53,0xf4d82c2c107973dc,
        0x91d8a02bb6c10594,0x79071b9b8a4be869,
        0xb64ec836a47146f9,0x9748e2826cdee284,
        0xe3e27a444d8d98b7,0xfd1b1b2308169b25,
        0x8e6d8c6ab0787f72,0xfe30f0f5e50e20f7,
        0xb208ef855c969f4f,0xbdbd2d335e51a935,
        0xde8b2b66b3bc4723,0xad2c788035e61382,
        0x8b16fb203055ac76,0x4c3bcb5021afcc31,
        0xaddcb9e83c6b1793,0xdf4abe242a1bbf3d,
        0xd953e8624b85dd78,0xd71d6dad34a2af0d,
        0x87d4713d6f33aa6b,0x8672648c40e5ad68,
        0xa9c98d8ccb009506,0x680efdaf511f18c2,
        0xd43bf0effdc0ba48,0x212bd1b2566def2,
        0x84a57695fe98746d,0x14bb630f7604b57,
        0xa5ced43b7e3e9188,0x419ea3bd35385e2d,
        0xcf42894a5dce35ea,0x52064cac828675b9,
        0x818995ce7aa0e1b2,0x7343efebd1940993,
        0xa1ebfb4219491a1f,0x1014ebe6c5f90bf8,
        0xca66fa129f9b60a6,0xd41a26e077774ef6,
        0xfd00b897478238d0,0x8920b098955522b4,
        0x9e20735e8cb16382,0x55b46e5f5d5535b0,
        0xc5a890362fddbc62,0xeb2189f734aa831d,
        0xf712b443bbd52b7b,0xa5e9ec7501d523e4,
        0x9a6bb0aa55653b2d,0x47b233c92125366e,
        0xc1069cd4eabe89f8,0x999ec0bb696e840a,
        0xf148440a256e2c76,0xc00670ea43ca250d,
        0x96cd2a865764dbca,0x380406926a5e5728,
        0xbc807527ed3e12bc,0xc605083704f5ecf2,
        0xeba09271e88d976b,0xf7864a44c633682e,
        0x93445b8731587ea3,0x7ab3ee6afbe0211d,
        0xb8157268fdae9e4c,0x5960ea05bad82964,
        0xe61acf033d1a45df,0x6fb92487298e33bd,
        0x8fd0c16206306bab,0xa5d3b6d479f8e056,
        0xb3c4f1ba87bc8696,0x8f48a4899877186c,
        0xe0b62e2929aba83c,0x331acdabfe94de87,
        0x8c71dcd9ba0b4925,0x9ff0c08b7f1d0b14,
        0xaf8e5410288e1b6f,0x7ecf0ae5ee44dd9,
        0xdb71e91432b1a24a,0xc9e82cd9f69d6150,
        0x892731ac9faf056e,0xbe311c083a225cd2,
        0xab70fe17c79ac6ca,0x6dbd630a48aaf406,
        0xd64d3d9db981787d,0x92cbbccdad5b108,
        0x85f0468293f0eb4e,0x25bbf56008c58ea5,
        0xa76c582338ed2621,0xaf2af2b80af6f24e,
        0xd1476e2c07286faa,0x1af5af660db4aee1,
        0x82cca4db847945ca,0x50d98d9fc890ed4d,
        0xa37fce126597973c,0xe50ff107bab528a0,
        0xcc5fc196fefd7d0c,0x1e53ed49a96272c8,
        0xff77b1fcbebcdc4f,0x25e8e89c13bb0f7a,
        0x9faacf3df73609b1,0x77b191618c54e9ac,
        0xc795830d75038c1d,0xd59df5b9ef6a2417,
        0xf97ae3d0d2446f25,0x4b0573286b44ad1d,
        0x9becce62836ac577,0x4ee367f9430aec32,
        0xc2e801fb244576d5,0x229c41f793cda73f,
        0xf3a20279ed56d48a,0x6b43527578c1110f,
        0x9845418c345644d6,0x830a13896b78aaa9,
        0xbe5691ef416bd60c,0x23cc986bc656d553,
        0xedec366b11c6cb8f,0x2cbfbe86b7ec8aa8,
        0x94b3a202eb1c3f39,0x7bf7d71432f3d6a9,
        0xb9e08a83a5e34f07,0xdaf5ccd93fb0cc53,
        0xe858ad248f5c22c9,0xd1b3400f8f9cff68,
        0x91376c36d99995be,0x23100809b9c21fa1,
        0xb58547448ffffb2d,0xabd40a0c2832a78a,
        0xe2e69915b3fff9f9,0x16c90c8f323f516c,
        0x8dd01fad907ffc3b,0xae3da7d97f6792e3,
        0xb1442798f49ffb4a,0x99cd11cfdf41779c,
        0xdd95317f31c7fa1d,0x40405643d711d583,
        0x8a7d3eef7f1cfc52,0x482835ea666b2572,
        0xad1c8eab5ee43b66,0xda3243650005eecf,
        0xd863b256369d4a40,0x90bed43e40076a82,
        0x873e4f75e2224e68,0x5a7744a6e804a291,
        0xa90de3535aaae202,0x711515d0a205cb36,
        0xd3515c2831559a83,0xd5a5b44ca873e03,
        0x8412d9991ed58091,0xe858790afe9486c2,
        0xa5178fff668ae0b6,0x626e974dbe39a872,
        0xce5d73ff402d98e3,0xfb0a3d212dc8128f,
        0x80fa687f881c7f8e,0x7ce66634bc9d0b99,
        0xa139029f6a239f72,0x1c1fffc1ebc44e80,
        0xc987434744ac874e,0xa327ffb266b56220,
        0xfbe9141915d7a922,0x4bf1ff9f0062baa8,
        0x9d71ac8fada6c9b5,0x6f773fc3603db4a9,
        0xc4ce17b399107c22,0xcb550fb4384d21d3,
        0xf6019da07f549b2b,0x7e2a53a146606a48,
        0x99c102844f94e0fb,0x2eda7444cbfc426d,
        0xc0314325637a1939,0xfa911155fefb5308,
        0xf03d93eebc589f88,0x793555ab7eba27ca,
        0x96267c7535b763b5,0x4bc1558b2f3458de,
        0xbbb01b9283253ca2,0x9eb1aaedfb016f16,
        0xea9c227723ee8bcb,0x465e15a979c1cadc,
        0x92a1958a7675175f,0xbfacd89ec191ec9,
        0xb749faed14125d36,0xcef980ec671f667b,
        0xe51c79a85916f484,0x82b7e12780e7401a,
        0x8f31cc0937ae58d2,0xd1b2ecb8b0908810,
        0xb2fe3f0b8599ef07,0x861fa7e6dcb4aa15,
        0xdfbdcece67006ac9,0x67a791e093e1d49a,
        0x8bd6a141006042bd,0xe0c8bb2c5c6d24e0,
        0xaecc49914078536d,0x58fae9f773886e18,
        0xda7f5bf590966848,0xaf39a475506a899e,
        0x888f99797a5e012d,0x6d8406c952429603,
        0xaab37fd7d8f58178,0xc8e5087ba6d33b83,
        0xd5605fcdcf32e1d6,0xfb1e4a9a90880a64,
        0x855c3be0a17fcd26,0x5cf2eea09a55067f,
        0xa6b34ad8c9dfc06f,0xf42faa48c0ea481e,
        0xd0601d8efc57b08b,0xf13b94daf124da26,
        0x823c12795db6ce57,0x76c53d08d6b70858,
        0xa2cb1717b52481ed,0x54768c4b0c64ca6e,
        0xcb7ddcdda26da268,0xa9942f5dcf7dfd09,
        0xfe5d54150b090b02,0xd3f93b35435d7c4c,
        0x9efa548d26e5a6e1,0xc47bc5014a1a6daf,
        0xc6b8e9b0709f109a,0x359ab6419ca1091b,
        0xf867241c8cc6d4c0,0xc30163d203c94b62,
        0x9b407691d7fc44f8,0x79e0de63425dcf1d,
        0xc21094364dfb5636,0x985915fc12f542e4,
        0xf294b943e17a2bc4,0x3e6f5b7b17b2939d,
        0x979cf3ca6cec5b5a,0xa705992ceecf9c42,
        0xbd8430bd08277231,0x50c6ff782a838353,
        0xece53cec4a314ebd,0xa4f8bf5635246428,
        0x940f4613ae5ed136,0x871b7795e136be99,
        0xb913179899f68584,0x28e2557b59846e3f,
        0xe757dd7ec07426e5,0x331aeada2fe589cf,
        0x9096ea6f3848984f,0x3ff0d2c85def7621,
        0xb4bca50b065abe63,0xfed077a756b53a9,
        0xe1ebce4dc7f16dfb,0xd3e8495912c62894,
        0x8d3360f09cf6e4bd,0x64712dd7abbbd95c,
        0xb080392cc4349dec,0xbd8d794d96aacfb3,
        0xdca04777f541c567,0xecf0d7a0fc5583a0,
        0x89e42caaf9491b60,0xf41686c49db57244,
        0xac5d37d5b79b6239,0x311c2875c522ced5,
        0xd77485cb25823ac7,0x7d633293366b828b,
        0x86a8d39ef77164bc,0xae5dff9c02033197,
        0xa8530886b54dbdeb,0xd9f57f830283fdfc,
        0xd267caa862a12d66,0xd072df63c324fd7b,
        0x8380dea93da4bc60,0x4247cb9e59f71e6d,
        0xa46116538d0deb78,0x52d9be85f074e608,
        0xcd795be870516656,0x67902e276c921f8b,
        0x806bd9714632dff6,0xba1cd8a3db53b6,
        0xa086cfcd97bf97f3,0x80e8a40eccd228a4,
        0xc8a883c0fdaf7df0,0x6122cd128006b2cd,
        0xfad2a4b13d1b5d6c,0x796b805720085f81,
        0x9cc3a6eec6311a63,0xcbe3303674053bb0,
        0xc3f490aa77bd60fc,0xbedbfc4411068a9c,
        0xf4f1b4d515acb93b,0xee92fb5515482d44,
        0x991711052d8bf3c5,0x751bdd152d4d1c4a,
        0xbf5cd54678eef0b6,0xd262d45a78a0635d,
        0xef340a98172aace4,0x86fb897116c87c34,
        0x9580869f0e7aac0e,0xd45d35e6ae3d4da0,
        0xbae0a846d2195712,0x8974836059cca109,
        0xe998d258869facd7,0x2bd1a438703fc94b,
        0x91ff83775423cc06,0x7b6306a34627ddcf,
        0xb67f6455292cbf08,0x1a3bc84c17b1d542,
        0xe41f3d6a7377eeca,0x20caba5f1d9e4a93,
        0x8e938662882af53e,0x547eb47b7282ee9c,
        0xb23867fb2a35b28d,0xe99e619a4f23aa43,
        0xdec681f9f4c31f31,0x6405fa00e2ec94d4,
        0x8b3c113c38f9f37e,0xde83bc408dd3dd04,
        0xae0b158b4738705e,0x9624ab50b148d445,
        0xd98ddaee19068c76,0x3badd624dd9b0957,
        0x87f8a8d4cfa417c9,0xe54ca5d70a80e5d6,
        0xa9f6d30a038d1dbc,0x5e9fcf4ccd211f4c,
        0xd47487cc8470652b,0x7647c3200069671f,
        0x84c8d4dfd2c63f3b,0x29ecd9f40041e073,
        0xa5fb0a17c777cf09,0xf468107100525890,
        0xcf79cc9db955c2cc,0x7182148d4066eeb4,
        0x81ac1fe293d599bf,0xc6f14cd848405530,
        0xa21727db38cb002f,0xb8ada00e5a506a7c,
        0xca9cf1d206fdc03b,0xa6d90811f0e4851c,
        0xfd442e4688bd304a,0x908f4a166d1da663,
        0x9e4a9cec15763e2e,0x9a598e4e043287fe,
        0xc5dd44271ad3cdba,0x40eff1e1853f29fd,
        0xf7549530e188c128,0xd12bee59e68ef47c,
        0x9a94dd3e8cf578b9,0x82bb74f8301958ce,
        0xc13a148e3032d6e7,0xe36a52363c1faf01,
        0xf18899b1bc3f8ca1,0xdc44e6c3cb279ac1,
        0x96f5600f15a7b7e5,0x29ab103a5ef8c0b9,
        0xbcb2b812db11a5de,0x7415d448f6b6f0e7,
        0xebdf661791d60f56,0x111b495b3464ad21,
        0x936b9fcebb25c995,0xcab10dd900beec34,
        0xb84687c269ef3bfb,0x3d5d514f40eea742,
        0xe65829b3046b0afa,0xcb4a5a3112a5112,
        0x8ff71a0fe2c2e6dc,0x47f0e785eaba72ab,
        0xb3f4e093db73a093,0x59ed216765690f56,
        0xe0f218b8d25088b8,0x306869c13ec3532c,
        0x8c974f7383725573,0x1e414218c73a13fb,
        0xafbd2350644eeacf,0xe5d1929ef90898fa,
        0xdbac6c247d62a583,0xdf45f746b74abf39,
        0x894bc396ce5da772,0x6b8bba8c328eb783,
        0xab9eb47c81f5114f,0x66ea92f3f326564,
        0xd686619ba27255a2,0xc80a537b0efefebd,
        0x8613fd0145877585,0xbd06742ce95f5f36,
        0xa798fc4196e952e7,0x2c48113823b73704,
        0xd17f3b51fca3a7a0,0xf75a15862ca504c5,
        0x82ef85133de648c4,0x9a984d73dbe722fb,
        0xa3ab66580d5fdaf5,0xc13e60d0d2e0ebba,
        0xcc963fee10b7d1b3,0x318df905079926a8,
        0xffbbcfe994e5c61f,0xfdf17746497f7052,
        0x9fd561f1fd0f9bd3,0xfeb6ea8bedefa633,
        0xc7caba6e7c5382c8,0xfe64a52ee96b8fc0,
        0xf9bd690a1b68637b,0x3dfdce7aa3c673b0,
        0x9c1661a651213e2d,0x6bea10ca65c084e,
        0xc31bfa0fe5698db8,0x486e494fcff30a62,
        0xf3e2f893dec3f126,0x5a89dba3c3efccfa,
        0x986ddb5c6b3a76b7,0xf89629465a75e01c,
        0xbe89523386091465,0xf6bbb397f1135823,
        0xee2ba6c0678b597f,0x746aa07ded582e2c,
        0x94db483840b717ef,0xa8c2a44eb4571cdc,
        0xba121a4650e4ddeb,0x92f34d62616ce413,
        0xe896a0d7e51e1566,0x77b020baf9c81d17,
        0x915e2486ef32cd60,0xace1474dc1d122e,
        0xb5b5ada8aaff80b8,0xd819992132456ba,
        0xe3231912d5bf60e6,0x10e1fff697ed6c69,
        0x8df5efabc5979c8f,0xca8d3ffa1ef463c1,
        0xb1736b96b6fd83b3,0xbd308ff8a6b17cb2,
        0xddd0467c64bce4a0,0xac7cb3f6d05ddbde,
        0x8aa22c0dbef60ee4,0x6bcdf07a423aa96b,
        0xad4ab7112eb3929d,0x86c16c98d2c953c6,
        0xd89d64d57a607744,0xe871c7bf077ba8b7,
        0x87625f056c7c4a8b,0x11471cd764ad4972,
        0xa93af6c6c79b5d2d,0xd598e40d3dd89bcf,
        0xd389b47879823479,0x4aff1d108d4ec2c3,
        0x843610cb4bf160cb,0xcedf722a585139ba,
        0xa54394fe1eedb8fe,0xc2974eb4ee658828,
        0xce947a3da6a9273e,0x733d226229feea32,
        0x811ccc668829b887,0x806357d5a3f525f,
        0xa163ff802a3426a8,0xca07c2dcb0cf26f7,
        0xc9bcff6034c13052,0xfc89b393dd02f0b5,
        0xfc2c3f3841f17c67,0xbbac2078d443ace2,
        0x9d9ba7832936edc0,0xd54b944b84aa4c0d,
        0xc5029163f384a931,0xa9e795e65d4df11,
        0xf64335bcf065d37d,0x4d4617b5ff4a16d5,
        0x99ea0196163fa42e,0x504bced1bf8e4e45,
        0xc06481fb9bcf8d39,0xe45ec2862f71e1d6,
        0xf07da27a82c37088,0x5d767327bb4e5a4c,
        0x964e858c91ba2655,0x3a6a07f8d510f86f,
        0xbbe226efb628afea,0x890489f70a55368b,
        0xeadab0aba3b2dbe5,0x2b45ac74ccea842e,
        0x92c8ae6b464fc96f,0x3b0b8bc90012929d,
        0xb77ada0617e3bbcb,0x9ce6ebb40173744,
        0xe55990879ddcaabd,0xcc420a6a101d0515,
        0x8f57fa54c2a9eab6,0x9fa946824a12232d,
        0xb32df8e9f3546564,0x47939822dc96abf9,
        0xdff9772470297ebd,0x59787e2b93bc56f7,
        0x8bfbea76c619ef36,0x57eb4edb3c55b65a,
        0xaefae51477a06b03,0xede622920b6b23f1,
        0xdab99e59958885c4,0xe95fab368e45eced,
        0x88b402f7fd75539b,0x11dbcb0218ebb414,
        0xaae103b5fcd2a881,0xd652bdc29f26a119,
        0xd59944a37c0752a2,0x4be76d3346f0495f,
        0x857fcae62d8493a5,0x6f70a4400c562ddb,
        0xa6dfbd9fb8e5b88e,0xcb4ccd500f6bb952,
        0xd097ad07a71f26b2,0x7e2000a41346a7a7,
        0x825ecc24c873782f,0x8ed400668c0c28c8,
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        0xb9a74a0637ce2ee1,0x6d953e2bd7173692,
        0xe8111c87c5c1ba99,0xc8fa8db6ccdd0437,
        0x910ab1d4db9914a0,0x1d9c9892400a22a2,
        0xb54d5e4a127f59c8,0x2503beb6d00cab4b,
        0xe2a0b5dc971f303a,0x2e44ae64840fd61d,
        0x8da471a9de737e24,0x5ceaecfed289e5d2,
        0xb10d8e1456105dad,0x7425a83e872c5f47,
        0xdd50f1996b947518,0xd12f124e28f77719,
        0x8a5296ffe33cc92f,0x82bd6b70d99aaa6f,
        0xace73cbfdc0bfb7b,0x636cc64d1001550b,
        0xd8210befd30efa5a,0x3c47f7e05401aa4e,
        0x8714a775e3e95c78,0x65acfaec34810a71,
        0xa8d9d1535ce3b396,0x7f1839a741a14d0d,
        0xd31045a8341ca07c,0x1ede48111209a050,
        0x83ea2b892091e44d,0x934aed0aab460432,
        0xa4e4b66b68b65d60,0xf81da84d5617853f,
        0xce1de40642e3f4b9,0x36251260ab9d668e,
        0x80d2ae83e9ce78f3,0xc1d72b7c6b426019,
        0xa1075a24e4421730,0xb24cf65b8612f81f,
        0xc94930ae1d529cfc,0xdee033f26797b627,
        0xfb9b7cd9a4a7443c,0x169840ef017da3b1,
        0x9d412e0806e88aa5,0x8e1f289560ee864e,
        0xc491798a08a2ad4e,0xf1a6f2bab92a27e2,
        0xf5b5d7ec8acb58a2,0xae10af696774b1db,
        0x9991a6f3d6bf1765,0xacca6da1e0a8ef29,
        0xbff610b0cc6edd3f,0x17fd090a58d32af3,
        0xeff394dcff8a948e,0xddfc4b4cef07f5b0,
        0x95f83d0a1fb69cd9,0x4abdaf101564f98e,
        0xbb764c4ca7a4440f,0x9d6d1ad41abe37f1,
        0xea53df5fd18d5513,0x84c86189216dc5ed,
        0x92746b9be2f8552c,0x32fd3cf5b4e49bb4,
        0xb7118682dbb66a77,0x3fbc8c33221dc2a1,
        0xe4d5e82392a40515,0xfabaf3feaa5334a,
        0x8f05b1163ba6832d,0x29cb4d87f2a7400e,
        0xb2c71d5bca9023f8,0x743e20e9ef511012,
        0xdf78e4b2bd342cf6,0x914da9246b255416,
        0x8bab8eefb6409c1a,0x1ad089b6c2f7548e,
        0xae9672aba3d0c320,0xa184ac2473b529b1,
        0xda3c0f568cc4f3e8,0xc9e5d72d90a2741e,
        0x8865899617fb1871,0x7e2fa67c7a658892,
        0xaa7eebfb9df9de8d,0xddbb901b98feeab7,
        0xd51ea6fa85785631,0x552a74227f3ea565,
        0x8533285c936b35de,0xd53a88958f87275f,
        0xa67ff273b8460356,0x8a892abaf368f137,
        0xd01fef10a657842c,0x2d2b7569b0432d85,
        0x8213f56a67f6b29b,0x9c3b29620e29fc73,
        0xa298f2c501f45f42,0x8349f3ba91b47b8f,
        0xcb3f2f7642717713,0x241c70a936219a73,
        0xfe0efb53d30dd4d7,0xed238cd383aa0110,
        0x9ec95d1463e8a506,0xf4363804324a40aa,
        0xc67bb4597ce2ce48,0xb143c6053edcd0d5,
        0xf81aa16fdc1b81da,0xdd94b7868e94050a,
        0x9b10a4e5e9913128,0xca7cf2b4191c8326,
        0xc1d4ce1f63f57d72,0xfd1c2f611f63a3f0,
        0xf24a01a73cf2dccf,0xbc633b39673c8cec,
        0x976e41088617ca01,0xd5be0503e085d813,
        0xbd49d14aa79dbc82,0x4b2d8644d8a74e18,
        0xec9c459d51852ba2,0xddf8e7d60ed1219e,
        0x93e1ab8252f33b45,0xcabb90e5c942b503,
        0xb8da1662e7b00a17,0x3d6a751f3b936243,
        0xe7109bfba19c0c9d,0xcc512670a783ad4,
        0x906a617d450187e2,0x27fb2b80668b24c5,
        0xb484f9dc9641e9da,0xb1f9f660802dedf6,
        0xe1a63853bbd26451,0x5e7873f8a0396973,
        0x8d07e33455637eb2,0xdb0b487b6423e1e8,
        0xb049dc016abc5e5f,0x91ce1a9a3d2cda62,
        0xdc5c5301c56b75f7,0x7641a140cc7810fb,
        0x89b9b3e11b6329ba,0xa9e904c87fcb0a9d,
        0xac2820d9623bf429,0x546345fa9fbdcd44,
        0xd732290fbacaf133,0xa97c177947ad4095,
        0x867f59a9d4bed6c0,0x49ed8eabcccc485d,
        0xa81f301449ee8c70,0x5c68f256bfff5a74,
        0xd226fc195c6a2f8c,0x73832eec6fff3111,
        0x83585d8fd9c25db7,0xc831fd53c5ff7eab,
        0xa42e74f3d032f525,0xba3e7ca8b77f5e55,
        0xcd3a1230c43fb26f,0x28ce1bd2e55f35eb,
        0x80444b5e7aa7cf85,0x7980d163cf5b81b3,
        0xa0555e361951c366,0xd7e105bcc332621f,
        0xc86ab5c39fa63440,0x8dd9472bf3fefaa7,
        0xfa856334878fc150,0xb14f98f6f0feb951,
        0x9c935e00d4b9d8d2,0x6ed1bf9a569f33d3,
        0xc3b8358109e84f07,0xa862f80ec4700c8,
        0xf4a642e14c6262c8,0xcd27bb612758c0fa,
        0x98e7e9cccfbd7dbd,0x8038d51cb897789c,
        0xbf21e44003acdd2c,0xe0470a63e6bd56c3,
        0xeeea5d5004981478,0x1858ccfce06cac74,
        0x95527a5202df0ccb,0xf37801e0c43ebc8,
        0xbaa718e68396cffd,0xd30560258f54e6ba,
        0xe950df20247c83fd,0x47c6b82ef32a2069,
        0x91d28b7416cdd27e,0x4cdc331d57fa5441,
        0xb6472e511c81471d,0xe0133fe4adf8e952,
        0xe3d8f9e563a198e5,0x58180fddd97723a6,
        0x8e679c2f5e44ff8f,0x570f09eaa7ea7648,};
using powers = powers_template<>;

}

#endif

#ifndef FASTFLOAT_DECIMAL_TO_BINARY_H
#define FASTFLOAT_DECIMAL_TO_BINARY_H

#include <cfloat>
#include <cinttypes>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>

namespace fast_float {

// This will compute or rather approximate w * 5**q and return a pair of 64-bit words approximating
// the result, with the "high" part corresponding to the most significant bits and the
// low part corresponding to the least significant bits.
//
template <int bit_precision>
fastfloat_really_inline
value128 compute_product_approximation(int64_t q, uint64_t w) {
  const int index = 2 * int(q - powers::smallest_power_of_five);
  // For small values of q, e.g., q in [0,27], the answer is always exact because
  // The line value128 firstproduct = full_multiplication(w, power_of_five_128[index]);
  // gives the exact answer.
  value128 firstproduct = full_multiplication(w, powers::power_of_five_128[index]);
  static_assert((bit_precision >= 0) && (bit_precision <= 64), " precision should  be in (0,64]");
  constexpr uint64_t precision_mask = (bit_precision < 64) ?
               (uint64_t(0xFFFFFFFFFFFFFFFF) >> bit_precision)
               : uint64_t(0xFFFFFFFFFFFFFFFF);
  if((firstproduct.high & precision_mask) == precision_mask) { // could further guard with  (lower + w < lower)
    // regarding the second product, we only need secondproduct.high, but our expectation is that the compiler will optimize this extra work away if needed.
    value128 secondproduct = full_multiplication(w, powers::power_of_five_128[index + 1]);
    firstproduct.low += secondproduct.high;
    if(secondproduct.high > firstproduct.low) {
      firstproduct.high++;
    }
  }
  return firstproduct;
}

namespace detail {
/**
 * For q in (0,350), we have that
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to
 *   floor(p) + q
 * where
 *   p = log(5**q)/log(2) = q * log(5)/log(2)
 *
 * For negative values of q in (-400,0), we have that 
 *  f = (((152170 + 65536) * q ) >> 16);
 * is equal to 
 *   -ceil(p) + q
 * where
 *   p = log(5**-q)/log(2) = -q * log(5)/log(2)
 */
  fastfloat_really_inline int power(int q)  noexcept  {
    return (((152170 + 65536) * q) >> 16) + 63;
  }
} // namespace detail


// w * 10 ** q
// The returned value should be a valid ieee64 number that simply need to be packed.
// However, in some very rare cases, the computation will fail. In such cases, we
// return an adjusted_mantissa with a negative power of 2: the caller should recompute
// in such cases.
template <typename binary>
fastfloat_really_inline
adjusted_mantissa compute_float(int64_t q, uint64_t w)  noexcept  {
  adjusted_mantissa answer;
  if ((w == 0) || (q < binary::smallest_power_of_ten())) {
    answer.power2 = 0;
    answer.mantissa = 0;
    // result should be zero
    return answer;
  }
  if (q > binary::largest_power_of_ten()) {
    // we want to get infinity:
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
    return answer;
  }
  // At this point in time q is in [powers::smallest_power_of_five, powers::largest_power_of_five].

  // We want the most significant bit of i to be 1. Shift if needed.
  int lz = leading_zeroes(w);
  w <<= lz;

  // The required precision is binary::mantissa_explicit_bits() + 3 because
  // 1. We need the implicit bit
  // 2. We need an extra bit for rounding purposes
  // 3. We might lose a bit due to the "upperbit" routine (result too small, requiring a shift)

  value128 product = compute_product_approximation<binary::mantissa_explicit_bits() + 3>(q, w);
  if(product.low == 0xFFFFFFFFFFFFFFFF) { //  could guard it further
    // In some very rare cases, this could happen, in which case we might need a more accurate
    // computation that what we can provide cheaply. This is very, very unlikely.
    //
    const bool inside_safe_exponent = (q >= -27) && (q <= 55); // always good because 5**q <2**128 when q>=0, 
    // and otherwise, for q<0, we have 5**-q<2**64 and the 128-bit reciprocal allows for exact computation.
    if(!inside_safe_exponent) {
      answer.power2 = -1; // This (a negative value) indicates an error condition.
      return answer;
    }
  }
  // The "compute_product_approximation" function can be slightly slower than a branchless approach:
  // value128 product = compute_product(q, w);
  // but in practice, we can win big with the compute_product_approximation if its additional branch
  // is easily predicted. Which is best is data specific.
  int upperbit = int(product.high >> 63);

  answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);

  answer.power2 = int(detail::power(int(q)) + upperbit - lz - binary::minimum_exponent());
  if (answer.power2 <= 0) { // we have a subnormal?
    // Here have that answer.power2 <= 0 so -answer.power2 >= 0
    if(-answer.power2 + 1 >= 64) { // if we have more than 64 bits below the minimum exponent, you have a zero for sure.
      answer.power2 = 0;
      answer.mantissa = 0;
      // result should be zero
      return answer;
    }
    // next line is safe because -answer.power2 + 1 < 64
    answer.mantissa >>= -answer.power2 + 1;
    // Thankfully, we can't have both "round-to-even" and subnormals because
    // "round-to-even" only occurs for powers close to 0.
    answer.mantissa += (answer.mantissa & 1); // round up
    answer.mantissa >>= 1;
    // There is a weird scenario where we don't have a subnormal but just.
    // Suppose we start with 2.2250738585072013e-308, we end up
    // with 0x3fffffffffffff x 2^-1023-53 which is technically subnormal
    // whereas 0x40000000000000 x 2^-1023-53  is normal. Now, we need to round
    // up 0x3fffffffffffff x 2^-1023-53  and once we do, we are no longer
    // subnormal, but we can only know this after rounding.
    // So we only declare a subnormal if we are smaller than the threshold.
    answer.power2 = (answer.mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) ? 0 : 1;
    return answer;
  }

  // usually, we round *up*, but if we fall right in between and and we have an
  // even basis, we need to round down
  // We are only concerned with the cases where 5**q fits in single 64-bit word.
  if ((product.low <= 1) &&  (q >= binary::min_exponent_round_to_even()) && (q <= binary::max_exponent_round_to_even()) &&
      ((answer.mantissa & 3) == 1) ) { // we may fall between two floats!
    // To be in-between two floats we need that in doing
    //   answer.mantissa = product.high >> (upperbit + 64 - binary::mantissa_explicit_bits() - 3);
    // ... we dropped out only zeroes. But if this happened, then we can go back!!!
    if((answer.mantissa  << (upperbit + 64 - binary::mantissa_explicit_bits() - 3)) ==  product.high) {
      answer.mantissa &= ~uint64_t(1);          // flip it so that we do not round up
    }
  }

  answer.mantissa += (answer.mantissa & 1); // round up
  answer.mantissa >>= 1;
  if (answer.mantissa >= (uint64_t(2) << binary::mantissa_explicit_bits())) {
    answer.mantissa = (uint64_t(1) << binary::mantissa_explicit_bits());
    answer.power2++; // undo previous addition
  }

  answer.mantissa &= ~(uint64_t(1) << binary::mantissa_explicit_bits());
  if (answer.power2 >= binary::infinite_power()) { // infinity
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
  }
  return answer;
}


} // namespace fast_float

#endif


#ifndef FASTFLOAT_ASCII_NUMBER_H
#define FASTFLOAT_ASCII_NUMBER_H

#include <cstdio>
#include <cctype>
#include <cstdint>
#include <cstring>


namespace fast_float {

// Next function can be micro-optimized, but compilers are entirely
// able to optimize it well.
fastfloat_really_inline bool is_integer(char c)  noexcept  { return c >= '0' && c <= '9'; }

fastfloat_really_inline uint64_t byteswap(uint64_t val) {
  return (val & 0xFF00000000000000) >> 56
    | (val & 0x00FF000000000000) >> 40
    | (val & 0x0000FF0000000000) >> 24
    | (val & 0x000000FF00000000) >> 8
    | (val & 0x00000000FF000000) << 8
    | (val & 0x0000000000FF0000) << 24
    | (val & 0x000000000000FF00) << 40
    | (val & 0x00000000000000FF) << 56;
}

fastfloat_really_inline uint64_t read_u64(const char *chars) {
  uint64_t val;
  ::memcpy(&val, chars, sizeof(uint64_t));
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  return val;
}

fastfloat_really_inline void write_u64(uint8_t *chars, uint64_t val) {
#if FASTFLOAT_IS_BIG_ENDIAN == 1
  // Need to read as-if the number was in little-endian order.
  val = byteswap(val);
#endif
  ::memcpy(chars, &val, sizeof(uint64_t));
}

// credit  @aqrit
fastfloat_really_inline uint32_t  parse_eight_digits_unrolled(uint64_t val) {
  const uint64_t mask = 0x000000FF000000FF;
  const uint64_t mul1 = 0x000F424000000064; // 100 + (1000000ULL << 32)
  const uint64_t mul2 = 0x0000271000000001; // 1 + (10000ULL << 32)
  val -= 0x3030303030303030;
  val = (val * 10) + (val >> 8); // val = (val * 2561) >> 8;
  val = (((val & mask) * mul1) + (((val >> 16) & mask) * mul2)) >> 32;
  return uint32_t(val);
}

fastfloat_really_inline uint32_t parse_eight_digits_unrolled(const char *chars)  noexcept  {
  return parse_eight_digits_unrolled(read_u64(chars));
}

// credit @aqrit
fastfloat_really_inline bool is_made_of_eight_digits_fast(uint64_t val)  noexcept  {
  return !((((val + 0x4646464646464646) | (val - 0x3030303030303030)) &
     0x8080808080808080));
}

fastfloat_really_inline bool is_made_of_eight_digits_fast(const char *chars)  noexcept  {
  return is_made_of_eight_digits_fast(read_u64(chars));
}

struct parsed_number_string {
  int64_t exponent;
  uint64_t mantissa;
  const char *lastmatch;
  bool negative;
  bool valid;
  bool too_many_digits;
};


// Assuming that you use no more than 19 digits, this will
// parse an ASCII string.
fastfloat_really_inline
parsed_number_string parse_number_string(const char *p, const char *pend, chars_format fmt) noexcept {
  parsed_number_string answer;
  answer.valid = false;
  answer.too_many_digits = false;
  answer.negative = (*p == '-');
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
    ++p;
    if (p == pend) {
      return answer;
    }
    if (!is_integer(*p) && (*p != '.')) { // a  sign must be followed by an integer or the dot
      return answer;
    }
  }
  const char *const start_digits = p;

  uint64_t i = 0; // an unsigned int avoids signed overflows (which are bad)

  while ((p != pend) && is_integer(*p)) {
    // a multiplication by 10 is cheaper than an arbitrary integer
    // multiplication
    i = 10 * i +
        uint64_t(*p - '0'); // might overflow, we will handle the overflow later
    ++p;
  }
  const char *const end_of_integer_part = p;
  int64_t digit_count = int64_t(end_of_integer_part - start_digits);
  int64_t exponent = 0;
  if ((p != pend) && (*p == '.')) {
    ++p;
  // Fast approach only tested under little endian systems
  if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
    i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
    p += 8;
    if ((p + 8 <= pend) && is_made_of_eight_digits_fast(p)) {
      i = i * 100000000 + parse_eight_digits_unrolled(p); // in rare cases, this will overflow, but that's ok
      p += 8;
    }
  }
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      ++p;
      i = i * 10 + digit; // in rare cases, this will overflow, but that's ok
    }
    exponent = end_of_integer_part + 1 - p;
    digit_count -= exponent;
  }
  // we must have encountered at least one integer!
  if (digit_count == 0) {
    return answer;
  }
  int64_t exp_number = 0;            // explicit exponential part
  if ((fmt & chars_format::scientific) && (p != pend) && (('e' == *p) || ('E' == *p))) {
    const char * location_of_e = p;
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    if ((p == pend) || !is_integer(*p)) {
      if(!(fmt & chars_format::fixed)) {
        // We are in error.
        return answer;
      }
      // Otherwise, we will be ignoring the 'e'.
      p = location_of_e;
    } else {
      while ((p != pend) && is_integer(*p)) {
        uint8_t digit = uint8_t(*p - '0');
        if (exp_number < 0x10000) {
          exp_number = 10 * exp_number + digit;
        }
        ++p;
      }
      if(neg_exp) { exp_number = - exp_number; }
      exponent += exp_number;
    }
  } else {
    // If it scientific and not fixed, we have to bail out.
    if((fmt & chars_format::scientific) && !(fmt & chars_format::fixed)) { return answer; }
  }
  answer.lastmatch = p;
  answer.valid = true;

  // If we frequently had to deal with long strings of digits,
  // we could extend our code by using a 128-bit integer instead
  // of a 64-bit integer. However, this is uncommon.
  //
  // We can deal with up to 19 digits.
  if (digit_count > 19) { // this is uncommon
    // It is possible that the integer had an overflow.
    // We have to handle the case where we have 0.0000somenumber.
    // We need to be mindful of the case where we only have zeroes...
    // E.g., 0.000000000...000.
    const char *start = start_digits;
    while ((start != pend) && (*start == '0' || *start == '.')) {
      if(*start == '0') { digit_count --; }
      start++;
    }
    if (digit_count > 19) {
      answer.too_many_digits = true;
      // Let us start again, this time, avoiding overflows.
      i = 0;
      p = start_digits;
      const uint64_t minimal_nineteen_digit_integer{1000000000000000000};
      while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
        i = i * 10 + uint64_t(*p - '0');
        ++p;
      }
      if (i >= minimal_nineteen_digit_integer) { // We have a big integers
        exponent = end_of_integer_part - p + exp_number;
      } else { // We have a value with a fractional component.
          p++; // skip the '.'
          const char *first_after_period = p;
          while((i < minimal_nineteen_digit_integer) && (p != pend) && is_integer(*p)) {
            i = i * 10 + uint64_t(*p - '0');
            ++p;
          }
          exponent = first_after_period - p + exp_number;
      }
      // We have now corrected both exponent and i, to a truncated value
    }
  }
  answer.exponent = exponent;
  answer.mantissa = i;
  return answer;
}


// This should always succeed since it follows a call to parse_number_string
// This function could be optimized. In particular, we could stop after 19 digits
// and try to bail out. Furthermore, we should be able to recover the computed
// exponent from the pass in parse_number_string.
fastfloat_really_inline decimal parse_decimal(const char *p, const char *pend) noexcept {
  decimal answer;
  answer.num_digits = 0;
  answer.decimal_point = 0;
  answer.truncated = false;
  answer.negative = (*p == '-');
  if (*p == '-') { // C++17 20.19.3.(7.1) explicitly forbids '+' sign here
    ++p;
  }
  // skip leading zeroes
  while ((p != pend) && (*p == '0')) {
    ++p;
  }
  while ((p != pend) && is_integer(*p)) {
    if (answer.num_digits < max_digits) {
      answer.digits[answer.num_digits] = uint8_t(*p - '0');
    }
    answer.num_digits++;
    ++p;
  }
  if ((p != pend) && (*p == '.')) {
    ++p;
    const char *first_after_period = p;
    // if we have not yet encountered a zero, we have to skip it as well
    if(answer.num_digits == 0) {
      // skip zeros
      while ((p != pend) && (*p == '0')) {
       ++p;
      }
    }
    // We expect that this loop will often take the bulk of the running time
    // because when a value has lots of digits, these digits often
    while ((p + 8 <= pend) && (answer.num_digits + 8 < max_digits)) {
      uint64_t val = read_u64(p);
      if(! is_made_of_eight_digits_fast(val)) { break; }
      // We have eight digits, process them in one go!
      val -= 0x3030303030303030;
      write_u64(answer.digits + answer.num_digits, val);
      answer.num_digits += 8;
      p += 8;
    }
    while ((p != pend) && is_integer(*p)) {
      if (answer.num_digits < max_digits) {
        answer.digits[answer.num_digits] = uint8_t(*p - '0');
      }
      answer.num_digits++;
      ++p;
    }
    answer.decimal_point = int32_t(first_after_period - p);
  }
  // We want num_digits to be the number of significant digits, excluding
  // leading *and* trailing zeros! Otherwise the truncated flag later is
  // going to be misleading.
  if(answer.num_digits > 0) {
    // We potentially need the answer.num_digits > 0 guard because we
    // prune leading zeros. So with answer.num_digits > 0, we know that
    // we have at least one non-zero digit.
    const char *preverse = p - 1;
    int32_t trailing_zeros = 0;
    while ((*preverse == '0') || (*preverse == '.')) {
      if(*preverse == '0') { trailing_zeros++; };
      --preverse;
    }
    answer.decimal_point += int32_t(answer.num_digits);
    answer.num_digits -= uint32_t(trailing_zeros);
  }
  if(answer.num_digits > max_digits) {
    answer.truncated = true;
    answer.num_digits = max_digits;
  }
  if ((p != pend) && (('e' == *p) || ('E' == *p))) {
    ++p;
    bool neg_exp = false;
    if ((p != pend) && ('-' == *p)) {
      neg_exp = true;
      ++p;
    } else if ((p != pend) && ('+' == *p)) { // '+' on exponent is allowed by C++17 20.19.3.(7.1)
      ++p;
    }
    int32_t exp_number = 0; // exponential part
    while ((p != pend) && is_integer(*p)) {
      uint8_t digit = uint8_t(*p - '0');
      if (exp_number < 0x10000) {
        exp_number = 10 * exp_number + digit;
      }
      ++p;
    }
    answer.decimal_point += (neg_exp ? -exp_number : exp_number);
  }
  // In very rare cases, we may have fewer than 19 digits, we want to be able to reliably
  // assume that all digits up to max_digit_without_overflow have been initialized.
  for(uint32_t i = answer.num_digits; i < max_digit_without_overflow; i++) { answer.digits[i] = 0; }

  return answer;
}
} // namespace fast_float

#endif


#ifndef FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H
#define FASTFLOAT_GENERIC_DECIMAL_TO_BINARY_H

/**
 * This code is meant to handle the case where we have more than 19 digits.
 *
 * It is based on work by Nigel Tao (at https://github.com/google/wuffs/)
 * who credits Ken Thompson for the design (via a reference to the Go source
 * code).
 *
 * Rob Pike suggested that this algorithm be called "Simple Decimal Conversion".
 *
 * It is probably not very fast but it is a fallback that should almost never
 * be used in real life. Though it is not fast, it is "easily" understood and debugged.
 **/
#include <cstdint>

namespace fast_float {

namespace detail {

// remove all final zeroes
inline void trim(decimal &h) {
  while ((h.num_digits > 0) && (h.digits[h.num_digits - 1] == 0)) {
    h.num_digits--;
  }
}



inline uint32_t number_of_digits_decimal_left_shift(const decimal &h, uint32_t shift) {
  shift &= 63;
  const static uint16_t number_of_digits_decimal_left_shift_table[65] = {
    0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
    0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
    0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
    0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
    0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
    0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
    0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
    0x051C, 0x051C,
  };
  uint32_t x_a = number_of_digits_decimal_left_shift_table[shift];
  uint32_t x_b = number_of_digits_decimal_left_shift_table[shift + 1];
  uint32_t num_new_digits = x_a >> 11;
  uint32_t pow5_a = 0x7FF & x_a;
  uint32_t pow5_b = 0x7FF & x_b;
  const static uint8_t
    number_of_digits_decimal_left_shift_table_powers_of_5[0x051C] = {
        5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3,
        9, 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8,
        1, 2, 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1,
        0, 3, 5, 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8,
        7, 8, 9, 0, 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6,
        9, 7, 2, 6, 5, 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5,
        3, 6, 7, 4, 3, 1, 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3,
        1, 2, 5, 2, 3, 8, 4, 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0,
        9, 2, 8, 9, 5, 5, 0, 7, 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3,
        9, 0, 6, 2, 5, 2, 9, 8, 0, 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1,
        4, 9, 0, 1, 1, 6, 1, 1, 9, 3, 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8,
        0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1, 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4,
        6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6, 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5,
        7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5, 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5,
        6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0, 7, 7, 3, 9, 2, 5, 7, 8, 1, 2,
        5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6, 9, 6, 2, 8, 9, 0, 6, 2, 5,
        1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8, 1, 4, 4, 5, 3, 1, 2, 5,
        5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7, 2, 2, 6, 5, 6, 2, 5,
        2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6, 1, 3, 2, 8, 1, 2,
        5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8, 0, 6, 6, 4, 0,
        6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9, 0, 3, 3, 2,
        0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2, 9, 5, 1,
        6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8, 5, 6,
        4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7, 2,
        9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
        0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7,
        3, 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5,
        6, 2, 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9,
        3, 7, 9, 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8,
        0, 1, 4, 8, 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0,
        9, 4, 3, 0, 4, 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2,
        5, 1, 4, 2, 1, 0, 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2,
        4, 8, 5, 3, 5, 1, 5, 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0,
        0, 1, 8, 5, 8, 7, 1, 1, 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7,
        1, 3, 6, 7, 8, 8, 0, 0, 5, 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8,
        9, 0, 6, 2, 5, 1, 7, 7, 6, 3, 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4,
        6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4, 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1,
        9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3, 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5,
        6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8, 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9,
        4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2, 5, 2, 2, 2, 0, 4, 4, 6, 0, 4,
        9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6, 3, 3, 3, 6, 1, 8, 1, 6, 4,
        0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2, 5, 1, 5, 6, 5, 4, 0, 4,
        2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2, 5, 5, 5, 5, 1, 1, 1,
        5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5, 8, 3, 4, 0, 4, 5,
        4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5, 6, 2, 8, 9, 1,
        3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8, 1, 2, 5, 1,
        3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9, 5, 3, 9,
        5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3, 9, 0,
        3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6, 2,
        6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
        8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5,
        1, 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2,
        4, 4, 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1,
        7, 3, 7, 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5,
        9, 5, 3, 3, 6, 9, 1, 4, 0, 6, 2, 5,
  };
  const uint8_t *pow5 =
      &number_of_digits_decimal_left_shift_table_powers_of_5[pow5_a];
  uint32_t i = 0;
  uint32_t n = pow5_b - pow5_a;
  for (; i < n; i++) {
    if (i >= h.num_digits) {
      return num_new_digits - 1;
    } else if (h.digits[i] == pow5[i]) {
      continue;
    } else if (h.digits[i] < pow5[i]) {
      return num_new_digits - 1;
    } else {
      return num_new_digits;
    }
  }
  return num_new_digits;
}

inline uint64_t round(decimal &h) {
  if ((h.num_digits == 0) || (h.decimal_point < 0)) {
    return 0;
  } else if (h.decimal_point > 18) {
    return UINT64_MAX;
  }
  // at this point, we know that h.decimal_point >= 0
  uint32_t dp = uint32_t(h.decimal_point);
  uint64_t n = 0;
  for (uint32_t i = 0; i < dp; i++) {
    n = (10 * n) + ((i < h.num_digits) ? h.digits[i] : 0);
  }
  bool round_up = false;
  if (dp < h.num_digits) {
    round_up = h.digits[dp] >= 5; // normally, we round up  
    // but we may need to round to even!
    if ((h.digits[dp] == 5) && (dp + 1 == h.num_digits)) {
      round_up = h.truncated || ((dp > 0) && (1 & h.digits[dp - 1]));
    }
  }
  if (round_up) {
    n++;
  }
  return n;
}

// computes h * 2^-shift
inline void decimal_left_shift(decimal &h, uint32_t shift) {
  if (h.num_digits == 0) {
    return;
  }
  uint32_t num_new_digits = number_of_digits_decimal_left_shift(h, shift);
  int32_t read_index = int32_t(h.num_digits - 1);
  uint32_t write_index = h.num_digits - 1 + num_new_digits;
  uint64_t n = 0;

  while (read_index >= 0) {
    n += uint64_t(h.digits[read_index]) << shift;
    uint64_t quotient = n / 10;
    uint64_t remainder = n - (10 * quotient);
    if (write_index < max_digits) {
      h.digits[write_index] = uint8_t(remainder);
    } else if (remainder > 0) {
      h.truncated = true;
    }
    n = quotient;
    write_index--;
    read_index--;
  }
  while (n > 0) {
    uint64_t quotient = n / 10;
    uint64_t remainder = n - (10 * quotient);
    if (write_index < max_digits) {
      h.digits[write_index] = uint8_t(remainder);
    } else if (remainder > 0) {
      h.truncated = true;
    }
    n = quotient;
    write_index--;
  }
  h.num_digits += num_new_digits;
  if (h.num_digits > max_digits) {
    h.num_digits = max_digits;
  }
  h.decimal_point += int32_t(num_new_digits);
  trim(h);
}

// computes h * 2^shift
inline void decimal_right_shift(decimal &h, uint32_t shift) {
  uint32_t read_index = 0;
  uint32_t write_index = 0;

  uint64_t n = 0;

  while ((n >> shift) == 0) {
    if (read_index < h.num_digits) {
      n = (10 * n) + h.digits[read_index++];
    } else if (n == 0) {
      return;
    } else {
      while ((n >> shift) == 0) {
        n = 10 * n;
        read_index++;
      }
      break;
    }
  }
  h.decimal_point -= int32_t(read_index - 1);
  if (h.decimal_point < -decimal_point_range) { // it is zero
    h.num_digits = 0;
    h.decimal_point = 0;
    h.negative = false;
    h.truncated = false;
    return;
  }
  uint64_t mask = (uint64_t(1) << shift) - 1;
  while (read_index < h.num_digits) {
    uint8_t new_digit = uint8_t(n >> shift);
    n = (10 * (n & mask)) + h.digits[read_index++];
    h.digits[write_index++] = new_digit;
  }
  while (n > 0) {
    uint8_t new_digit = uint8_t(n >> shift);
    n = 10 * (n & mask);
    if (write_index < max_digits) {
      h.digits[write_index++] = new_digit;
    } else if (new_digit > 0) {
      h.truncated = true;
    }
  }
  h.num_digits = write_index;
  trim(h);
}

} // namespace detail

template <typename binary>
adjusted_mantissa compute_float(decimal &d) {
  adjusted_mantissa answer;
  if (d.num_digits == 0) {
    // should be zero
    answer.power2 = 0;
    answer.mantissa = 0;
    return answer;
  }
  // At this point, going further, we can assume that d.num_digits > 0.
  //
  // We want to guard against excessive decimal point values because
  // they can result in long running times. Indeed, we do
  // shifts by at most 60 bits. We have that log(10**400)/log(2**60) ~= 22
  // which is fine, but log(10**299995)/log(2**60) ~= 16609 which is not
  // fine (runs for a long time).
  //
  if(d.decimal_point < -324) {
    // We have something smaller than 1e-324 which is always zero
    // in binary64 and binary32.
    // It should be zero.
    answer.power2 = 0;
    answer.mantissa = 0;
    return answer;
  } else if(d.decimal_point >= 310) {
    // We have something at least as large as 0.1e310 which is
    // always infinite.  
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
    return answer;
  }
  static const uint32_t max_shift = 60;
  static const uint32_t num_powers = 19;
  static const uint8_t decimal_powers[19] = {
      0,  3,  6,  9,  13, 16, 19, 23, 26, 29, //
      33, 36, 39, 43, 46, 49, 53, 56, 59,     //
  };
  int32_t exp2 = 0;
  while (d.decimal_point > 0) {
    uint32_t n = uint32_t(d.decimal_point);
    uint32_t shift = (n < num_powers) ? decimal_powers[n] : max_shift;
    detail::decimal_right_shift(d, shift);
    if (d.decimal_point < -decimal_point_range) {
      // should be zero
      answer.power2 = 0;
      answer.mantissa = 0;
      return answer;
    }
    exp2 += int32_t(shift);
  }
  // We shift left toward [1/2 ... 1].
  while (d.decimal_point <= 0) {
    uint32_t shift;
    if (d.decimal_point == 0) {
      if (d.digits[0] >= 5) {
        break;
      }
      shift = (d.digits[0] < 2) ? 2 : 1;
    } else {
      uint32_t n = uint32_t(-d.decimal_point);
      shift = (n < num_powers) ? decimal_powers[n] : max_shift;
    }
    detail::decimal_left_shift(d, shift);
    if (d.decimal_point > decimal_point_range) {
      // we want to get infinity:
      answer.power2 = binary::infinite_power();
      answer.mantissa = 0;
      return answer;
    }
    exp2 -= int32_t(shift);
  }
  // We are now in the range [1/2 ... 1] but the binary format uses [1 ... 2].
  exp2--;
  constexpr int32_t minimum_exponent = binary::minimum_exponent();
  while ((minimum_exponent + 1) > exp2) {
    uint32_t n = uint32_t((minimum_exponent + 1) - exp2);
    if (n > max_shift) {
      n = max_shift;
    }
    detail::decimal_right_shift(d, n);
    exp2 += int32_t(n);
  }
  if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
    answer.power2 = binary::infinite_power();
    answer.mantissa = 0;
    return answer;
  }

  const int mantissa_size_in_bits = binary::mantissa_explicit_bits() + 1;
  detail::decimal_left_shift(d, mantissa_size_in_bits);

  uint64_t mantissa = detail::round(d);
  // It is possible that we have an overflow, in which case we need
  // to shift back.
  if(mantissa >= (uint64_t(1) << mantissa_size_in_bits)) {
    detail::decimal_right_shift(d, 1);
    exp2 += 1;
    mantissa = detail::round(d);
    if ((exp2 - minimum_exponent) >= binary::infinite_power()) {
      answer.power2 = binary::infinite_power();
      answer.mantissa = 0;
      return answer;
    }
  }
  answer.power2 = exp2  - binary::minimum_exponent();
  if(mantissa < (uint64_t(1) << binary::mantissa_explicit_bits())) { answer.power2--; }
  answer.mantissa = mantissa & ((uint64_t(1) << binary::mantissa_explicit_bits()) - 1);
  return answer;
}

template <typename binary>
adjusted_mantissa parse_long_mantissa(const char *first, const char* last) {
    decimal d = parse_decimal(first, last);
    return compute_float<binary>(d);
}

} // namespace fast_float
#endif


#ifndef FASTFLOAT_PARSE_NUMBER_H
#define FASTFLOAT_PARSE_NUMBER_H

#include <cassert>
#include <cmath>
#include <cstring>
#include <limits>
#include <system_error>

namespace fast_float {


namespace detail {
/**
 * Special case +inf, -inf, nan, infinity, -infinity.
 * The case comparisons could be made much faster given that we know that the
 * strings a null-free and fixed.
 **/
template <typename T>
from_chars_result parse_infnan(const char *first, const char *last, T &value)  noexcept  {
  from_chars_result answer;
  answer.ptr = first;
  answer.ec = std::errc(); // be optimistic
  bool minusSign = false;
  if (*first == '-') { // assume first < last, so dereference without checks; C++17 20.19.3.(7.1) explicitly forbids '+' here
      minusSign = true;
      ++first;
  }
  if (last - first >= 3) {
    if (fastfloat_strncasecmp(first, "nan", 3)) {
      answer.ptr = (first += 3);
      value = minusSign ? -std::numeric_limits<T>::quiet_NaN() : std::numeric_limits<T>::quiet_NaN();
      // Check for possible nan(n-char-seq-opt), C++17 20.19.3.7, C11 7.20.1.3.3. At least MSVC produces nan(ind) and nan(snan).
      if(first != last && *first == '(') {
        for(const char* ptr = first + 1; ptr != last; ++ptr) {
          if (*ptr == ')') {
            answer.ptr = ptr + 1; // valid nan(n-char-seq-opt)
            break;
          }
          else if(!(('a' <= *ptr && *ptr <= 'z') || ('A' <= *ptr && *ptr <= 'Z') || ('0' <= *ptr && *ptr <= '9') || *ptr == '_'))
            break; // forbidden char, not nan(n-char-seq-opt)
        }
      }
      return answer;
    }
    if (fastfloat_strncasecmp(first, "inf", 3)) {
      if ((last - first >= 8) && fastfloat_strncasecmp(first + 3, "inity", 5)) {
        answer.ptr = first + 8;
      } else {
        answer.ptr = first + 3;
      }
      value = minusSign ? -std::numeric_limits<T>::infinity() : std::numeric_limits<T>::infinity();
      return answer;
    }
  }
  answer.ec = std::errc::invalid_argument;
  return answer;
}

template<typename T>
fastfloat_really_inline void to_float(bool negative, adjusted_mantissa am, T &value) {
  uint64_t word = am.mantissa;
  word |= uint64_t(am.power2) << binary_format<T>::mantissa_explicit_bits();
  word = negative
  ? word | (uint64_t(1) << binary_format<T>::sign_index()) : word;
#if FASTFLOAT_IS_BIG_ENDIAN == 1
   if (std::is_same<T, float>::value) {
     ::memcpy(&value, (char *)&word + 4, sizeof(T)); // extract value at offset 4-7 if float on big-endian
   } else {
     ::memcpy(&value, &word, sizeof(T));
   }
#else
   // For little-endian systems:
   ::memcpy(&value, &word, sizeof(T));
#endif
}

} // namespace detail



template<typename T>
from_chars_result from_chars(const char *first, const char *last,
                             T &value, chars_format fmt /*= chars_format::general*/)  noexcept  {
  static_assert (std::is_same<T, double>::value || std::is_same<T, float>::value, "only float and double are supported");


  from_chars_result answer;
  if (first == last) {
    answer.ec = std::errc::invalid_argument;
    answer.ptr = first;
    return answer;
  }
  parsed_number_string pns = parse_number_string(first, last, fmt);
  if (!pns.valid) {
    return detail::parse_infnan(first, last, value);
  }
  answer.ec = std::errc(); // be optimistic
  answer.ptr = pns.lastmatch;
  // Next is Clinger's fast path.
  if (binary_format<T>::min_exponent_fast_path() <= pns.exponent && pns.exponent <= binary_format<T>::max_exponent_fast_path() && pns.mantissa <=binary_format<T>::max_mantissa_fast_path() && !pns.too_many_digits) {
    value = T(pns.mantissa);
    if (pns.exponent < 0) { value = value / binary_format<T>::exact_power_of_ten(-pns.exponent); }
    else { value = value * binary_format<T>::exact_power_of_ten(pns.exponent); }
    if (pns.negative) { value = -value; }
    return answer;
  }
  adjusted_mantissa am = compute_float<binary_format<T>>(pns.exponent, pns.mantissa);
  if(pns.too_many_digits) {
    if(am != compute_float<binary_format<T>>(pns.exponent, pns.mantissa + 1)) {
      am.power2 = -1; // value is invalid.
    }
  }
  // If we called compute_float<binary_format<T>>(pns.exponent, pns.mantissa) and we have an invalid power (am.power2 < 0),
  // then we need to go the long way around again. This is very uncommon.
  if(am.power2 < 0) { am = parse_long_mantissa<binary_format<T>>(first,last); }
  detail::to_float(pns.negative, am, value);
  return answer;
}

} // namespace fast_float

#endif