






'''simple docstring'''
import re
import time
from typing import Optional

import IPython.display as disp

from ..trainer_callback import TrainerCallback
from ..trainer_utils import IntervalStrategy, has_length





def  _a(  UpperCamelCase__				:						List[Any]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=int(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				List[str]									=t // 3_6_0_0, (t // 6_0) % 6_0, t % 6_0
      return f"{h}:{m:02d}:{s:02d}" if h != 0 else f"{m:02d}:{s:02d}"





def  _a(  UpperCamelCase__				:						Optional[Any],	UpperCamelCase__				:						Dict,	UpperCamelCase__				:						int,	UpperCamelCase__				:						Union[str, Any],	UpperCamelCase__				:						Dict=3_0_0							):




      '''simple docstring'''






      return f"\n    <div>\n      {prefix}\n      <progress value='{value}' max='{total}' style='width:{width}px; height:20px; vertical-align: middle;'></progress>\n      {label}\n    </div>\n    "





def  _a(  UpperCamelCase__				:						Any							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				List[str]									='''<table border="1" class="dataframe">\n'''
      html_code += """  <thead>\n <tr style="text-align: left;">\n"""
      for i in items[0]:
            html_code += f"      <th>{i}</th>\n"
      html_code += "    </tr>\n  </thead>\n  <tbody>\n"
      for line in items[1:]:
            html_code += "    <tr>\n"
            for elt in line:
                  SCREAMING_SNAKE_CASE__     :				List[Any]									=f"{elt:.6f}" if isinstance(UpperCamelCase__,	UpperCamelCase__							) else str(UpperCamelCase__							)
                  html_code += f"      <td>{elt}</td>\n"
            html_code += "    </tr>\n"
      html_code += "  </tbody>\n</table><p>"
      return html_code






class      __SCREAMING_SNAKE_CASE      :
 snake_case_  							=							5
 snake_case_  							=							0.2




 def __init__(      self	:							str					,      __lowercase	:							int					,      __lowercase	:							Optional[str] = None					,      __lowercase	:							bool = True					,      __lowercase	:							Optional["NotebookTrainingTracker"] = None					,      __lowercase	:							int = 3_00					,      )	->						Optional[Any]:
       SCREAMING_SNAKE_CASE__     :				List[Any]									=total
       SCREAMING_SNAKE_CASE__     :				List[str]									='''''' if prefix is None else prefix
       SCREAMING_SNAKE_CASE__     :				Tuple									=leave
       SCREAMING_SNAKE_CASE__     :				Optional[Any]									=parent
       SCREAMING_SNAKE_CASE__     :				List[Any]									=width
       SCREAMING_SNAKE_CASE__     :				List[Any]									=None
       SCREAMING_SNAKE_CASE__     :				List[str]									=None
       SCREAMING_SNAKE_CASE__     :				str									=None




 def      __magic_name__	(      self	:							int					,      __lowercase	:							int					,      __lowercase	:							bool = False					,      __lowercase	:							str = None      )	->						Union[str, Any]:
       SCREAMING_SNAKE_CASE__     :				Tuple									=value
       if comment is not None:
             SCREAMING_SNAKE_CASE__     :				Tuple									=comment
       if self.last_value is None:
             SCREAMING_SNAKE_CASE__     :				str									=time.time()
             SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=value
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=None
             SCREAMING_SNAKE_CASE__     :				Any									=self.warmup
             SCREAMING_SNAKE_CASE__     :				Any									=1
             self.update_bar(__lowercase      )
       elif value <= self.last_value and not force_update:
             return
       elif force_update or self.first_calls > 0 or value >= min(self.last_value + self.wait_for					,      self.total      ):
             if self.first_calls > 0:
                   self.first_calls -= 1
             SCREAMING_SNAKE_CASE__     :				Optional[int]									=time.time()
             SCREAMING_SNAKE_CASE__     :				Any									=current_time - self.start_time
             # We could have value = self.start_value if the update is called twixe with the same start value.
             if value > self.start_value:
                   SCREAMING_SNAKE_CASE__     :				Any									=self.elapsed_time / (value - self.start_value)
             else:
                   SCREAMING_SNAKE_CASE__     :				Dict									=None
             if value >= self.total:
                   SCREAMING_SNAKE_CASE__     :				int									=self.total
                   SCREAMING_SNAKE_CASE__     :				Optional[int]									=None
                   if not self.leave:
                         self.close()
             elif self.average_time_per_item is not None:
                   SCREAMING_SNAKE_CASE__     :				List[Any]									=self.average_time_per_item * (self.total - value)
             self.update_bar(__lowercase      )
             SCREAMING_SNAKE_CASE__     :				int									=value
             SCREAMING_SNAKE_CASE__     :				Optional[int]									=current_time
             if self.average_time_per_item is None:
                   SCREAMING_SNAKE_CASE__     :				List[str]									=1
             else:
                   SCREAMING_SNAKE_CASE__     :				int									=max(int(self.update_every / self.average_time_per_item      )					,      1      )




 def      __magic_name__	(      self	:							str					,      __lowercase	:							List[str]					,      __lowercase	:							Union[str, Any]=None      )	->						List[str]:
       SCREAMING_SNAKE_CASE__     :				Tuple									=''' ''' * (len(str(self.total      )      ) - len(str(__lowercase      )      )) + str(__lowercase      )
       if self.elapsed_time is None:
             SCREAMING_SNAKE_CASE__     :				str									=F"[{spaced_value}/{self.total} : < :"
       elif self.predicted_remaining is None:
             SCREAMING_SNAKE_CASE__     :				Any									=F"[{spaced_value}/{self.total} {format_time(self.elapsed_time      )}"
       else:
             SCREAMING_SNAKE_CASE__     :				List[str]									=(
                 F"[{spaced_value}/{self.total} {format_time(self.elapsed_time      )} <"
                 F" {format_time(self.predicted_remaining      )}"
             )
             self.label += F", {1/self.average_time_per_item:.2f} it/s"
       self.label += "]" if self.comment is None or len(self.comment      ) == 0 else F", {self.comment}]"
       self.display()




 def      __magic_name__	(      self	:							Dict      )	->						Optional[Any]:
       SCREAMING_SNAKE_CASE__     :				int									=html_progress_bar(self.value					,      self.total					,      self.prefix					,      self.label					,      self.width      )
       if self.parent is not None:
             # If this is a child bar, the parent will take care of the display.
             self.parent.display()
             return
       if self.output is None:
             SCREAMING_SNAKE_CASE__     :				Optional[int]									=disp.display(disp.HTML(self.html_code      )					,      display_id=__lowercase      )
       else:
             self.output.update(disp.HTML(self.html_code      )      )




 def      __magic_name__	(      self	:							Dict      )	->						str:
       if self.parent is None and self.output is not None:
             self.output.update(disp.HTML(''''''      )      )






class      __SCREAMING_SNAKE_CASE      (			lowerCamelCase				):




 def __init__(      self	:							Union[str, Any]					,      __lowercase	:							Dict					,      __lowercase	:							Union[str, Any]=None      )	->						Optional[int]:
       super().__init__(__lowercase      )
       SCREAMING_SNAKE_CASE__     :				Any									=None if column_names is None else [column_names]
       SCREAMING_SNAKE_CASE__     :				Dict									=None




 def      __magic_name__	(      self	:							Optional[int]      )	->						Union[str, Any]:
       SCREAMING_SNAKE_CASE__     :				str									=html_progress_bar(self.value					,      self.total					,      self.prefix					,      self.label					,      self.width      )
       if self.inner_table is not None:
             self.html_code += text_to_html_table(self.inner_table      )
       if self.child_bar is not None:
             self.html_code += self.child_bar.html_code
       if self.output is None:
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=disp.display(disp.HTML(self.html_code      )					,      display_id=__lowercase      )
       else:
             self.output.update(disp.HTML(self.html_code      )      )




 def      __magic_name__	(      self	:							int					,      __lowercase	:							str      )	->						List[str]:
       if self.inner_table is None:
             SCREAMING_SNAKE_CASE__     :				List[str]									=[list(values.keys()      ), list(values.values()      )]
       else:
             SCREAMING_SNAKE_CASE__     :				Dict									=self.inner_table[0]
             if len(self.inner_table      ) == 1:
                   # We give a chance to update the column names at the first iteration
                   for key in values.keys():
                         if key not in columns:
                               columns.append(__lowercase      )
                   SCREAMING_SNAKE_CASE__     :				List[str]									=columns
             self.inner_table.append([values[c] for c in columns]      )




 def      __magic_name__	(      self	:							Optional[Any]					,      __lowercase	:							str					,      __lowercase	:							Dict=None					,      __lowercase	:							List[Any]=3_00      )	->						Union[str, Any]:
       SCREAMING_SNAKE_CASE__     :				int									=NotebookProgressBar(__lowercase					,      prefix=__lowercase					,      parent=self					,      width=__lowercase      )
       return self.child_bar




 def      __magic_name__	(      self	:							Union[str, Any]      )	->						int:
       SCREAMING_SNAKE_CASE__     :				Any									=None
       self.display()






class      __SCREAMING_SNAKE_CASE      (			lowerCamelCase				):




 def __init__(      self	:							Tuple      )	->						Optional[int]:
       SCREAMING_SNAKE_CASE__     :				int									=None
       SCREAMING_SNAKE_CASE__     :				Optional[int]									=None
       SCREAMING_SNAKE_CASE__     :				Any									=False




 def      __magic_name__	(      self	:							Dict					,      __lowercase	:							Optional[int]					,      __lowercase	:							Dict					,      __lowercase	:							List[Any]					,      **__lowercase	:							Any      )	->						List[Any]:
       SCREAMING_SNAKE_CASE__     :				Optional[int]									='''Epoch''' if args.evaluation_strategy == IntervalStrategy.EPOCH else '''Step'''
       SCREAMING_SNAKE_CASE__     :				Any									=0
       SCREAMING_SNAKE_CASE__     :				List[Any]									=0
       SCREAMING_SNAKE_CASE__     :				Tuple									=[self.first_column] + ['''Training Loss''']
       if args.evaluation_strategy != IntervalStrategy.NO:
             column_names.append('''Validation Loss'''      )
       SCREAMING_SNAKE_CASE__     :				Dict									=NotebookTrainingTracker(state.max_steps					,      __lowercase      )




 def      __magic_name__	(      self	:							Optional[int]					,      __lowercase	:							List[str]					,      __lowercase	:							str					,      __lowercase	:							int					,      **__lowercase	:							Optional[int]      )	->						str:
       SCREAMING_SNAKE_CASE__     :				Dict									=int(state.epoch      ) if int(state.epoch      ) == state.epoch else F"{state.epoch:.2f}"
       self.training_tracker.update(
           state.global_step + 1					,      comment=F"Epoch {epoch}/{state.num_train_epochs}"					,      force_update=self._force_next_update					,      )
       SCREAMING_SNAKE_CASE__     :				List[str]									=False




 def      __magic_name__	(      self	:							Union[str, Any]					,      __lowercase	:							Dict					,      __lowercase	:							int					,      __lowercase	:							Optional[int]					,      __lowercase	:							str=None					,      **__lowercase	:							int      )	->						List[str]:
       if not has_length(__lowercase      ):
             return
       if self.prediction_bar is None:
             if self.training_tracker is not None:
                   SCREAMING_SNAKE_CASE__     :				List[str]									=self.training_tracker.add_child(len(__lowercase      )      )
             else:
                   SCREAMING_SNAKE_CASE__     :				Optional[Any]									=NotebookProgressBar(len(__lowercase      )      )
             self.prediction_bar.update(1      )
       else:
             self.prediction_bar.update(self.prediction_bar.value + 1      )




 def      __magic_name__	(      self	:							Dict					,      __lowercase	:							List[Any]					,      __lowercase	:							Any					,      __lowercase	:							Dict					,      **__lowercase	:							Dict      )	->						Optional[int]:
       if self.prediction_bar is not None:
             self.prediction_bar.close()
       SCREAMING_SNAKE_CASE__     :				int									=None




 def      __magic_name__	(      self	:							Optional[Any]					,      __lowercase	:							Optional[Any]					,      __lowercase	:							Dict					,      __lowercase	:							List[str]					,      __lowercase	:							Tuple=None					,      **__lowercase	:							List[str]      )	->						int:
       # Only for when there is no evaluation
       if args.evaluation_strategy == IntervalStrategy.NO and "loss" in logs:
             SCREAMING_SNAKE_CASE__     :				List[Any]									={'''Training Loss''': logs['''loss''']}
             # First column is necessarily Step sine we're not in epoch eval strategy
             SCREAMING_SNAKE_CASE__     :				List[Any]									=state.global_step
             self.training_tracker.write_line(__lowercase      )




 def      __magic_name__	(      self	:							Optional[Any]					,      __lowercase	:							List[str]					,      __lowercase	:							List[str]					,      __lowercase	:							str					,      __lowercase	:							List[str]=None					,      **__lowercase	:							List[str]      )	->						Tuple:
       if self.training_tracker is not None:
             SCREAMING_SNAKE_CASE__     :				Tuple									={'''Training Loss''': '''No log''', '''Validation Loss''': '''No log'''}
             for log in reversed(state.log_history      ):
                   if "loss" in log:
                         SCREAMING_SNAKE_CASE__     :				Optional[Any]									=log['''loss''']
                         break

             if self.first_column == "Epoch":
                   SCREAMING_SNAKE_CASE__     :				Optional[Any]									=int(state.epoch      )
             else:
                   SCREAMING_SNAKE_CASE__     :				int									=state.global_step
             SCREAMING_SNAKE_CASE__     :				Tuple									='''eval'''
             for k in metrics:
                   if k.endswith('''_loss'''      ):
                         SCREAMING_SNAKE_CASE__     :				Optional[Any]									=re.sub(r'''\_loss$'''					,      ''''''					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				List[str]									=metrics.pop('''total_flos'''					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				List[Any]									=metrics.pop('''epoch'''					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				int									=metrics.pop(F"{metric_key_prefix}_runtime"					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				Any									=metrics.pop(F"{metric_key_prefix}_samples_per_second"					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				Tuple									=metrics.pop(F"{metric_key_prefix}_steps_per_second"					,      __lowercase      )
             SCREAMING_SNAKE_CASE__     :				int									=metrics.pop(F"{metric_key_prefix}_jit_compilation_time"					,      __lowercase      )
             for k, v in metrics.items():
                   if k == F"{metric_key_prefix}_loss":
                         SCREAMING_SNAKE_CASE__     :				int									=v
                   else:
                         SCREAMING_SNAKE_CASE__     :				Tuple									=k.split('''_'''      )
                         SCREAMING_SNAKE_CASE__     :				Dict									=''' '''.join([part.capitalize() for part in splits[1:]]      )
                         SCREAMING_SNAKE_CASE__     :				str									=v
             self.training_tracker.write_line(__lowercase      )
             self.training_tracker.remove_child()
             SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=None
             # Evaluation takes a long time so we should force the next update.
             SCREAMING_SNAKE_CASE__     :				Optional[Any]									=True




 def      __magic_name__	(      self	:							Union[str, Any]					,      __lowercase	:							Union[str, Any]					,      __lowercase	:							Tuple					,      __lowercase	:							int					,      **__lowercase	:							Optional[int]      )	->						Tuple:
       self.training_tracker.update(
           state.global_step					,      comment=F"Epoch {int(state.epoch      )}/{state.num_train_epochs}"					,      force_update=__lowercase      )
       SCREAMING_SNAKE_CASE__     :				Dict									=None







'''simple docstring'''
from __future__ import annotations

from collections.abc import Callable

a_					= list[list[float | int]]





def  _a(  UpperCamelCase__				:						Matrix,	UpperCamelCase__				:						Matrix							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(size + 1							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				float

      for row in range(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Tuple									=matrix[row][col]

            SCREAMING_SNAKE_CASE__     :				Optional[int]									=vector[row][0]

      SCREAMING_SNAKE_CASE__     :				Any									=0
      SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=0
      while row < size and col < size:
            # pivoting
            SCREAMING_SNAKE_CASE__     :				Any									=max((abs(augmented[rowa][col]							), rowa) for rowa in range(UpperCamelCase__,	UpperCamelCase__							)							)[
                1
            ]
            if augmented[pivot_row][col] == 0:
                  col += 1
                  continue
            else:
                  SCREAMING_SNAKE_CASE__		,	SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[pivot_row], augmented[row]

            for rowa in range(row + 1,	UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Union[str, Any]									=augmented[rowa][col] / augmented[row][col]
                  SCREAMING_SNAKE_CASE__     :				Tuple									=0
                  for cola in range(col + 1,	size + 1							):
                        augmented[rowa][cola] -= augmented[row][cola] * ratio

            row += 1
            col += 1

      # back substitution
      for col in range(1,	UpperCamelCase__							):
            for row in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[Any]									=augmented[row][col] / augmented[col][col]
                  for cola in range(UpperCamelCase__,	size + 1							):
                        augmented[row][cola] -= augmented[col][cola] * ratio

    # round to get rid of numbers like 2.000000000000004
      return [
          [round(augmented[row][size] / augmented[row][row],	1_0							)] for row in range(UpperCamelCase__							)
      ]





def  _a(  UpperCamelCase__				:						list[int]							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				int									=len(UpperCamelCase__							)
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0 for _ in range(UpperCamelCase__							)] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix									=[[0] for _ in range(UpperCamelCase__							)]
      SCREAMING_SNAKE_CASE__     :				Matrix
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int
      SCREAMING_SNAKE_CASE__     :				int

      for x_val, y_val in enumerate(UpperCamelCase__							):
            for col in range(UpperCamelCase__							):
                  SCREAMING_SNAKE_CASE__     :				Optional[int]									=(x_val + 1) ** (size - col - 1)
            SCREAMING_SNAKE_CASE__     :				Dict									=y_val

      SCREAMING_SNAKE_CASE__     :				Optional[int]									=solve(UpperCamelCase__,	UpperCamelCase__							)

      def interpolated_func(UpperCamelCase__				:						int							) -> int:
            return sum(
                round(coeffs[x_val][0]							) * (var ** (size - x_val - 1))
                for x_val in range(UpperCamelCase__							)							)

      return interpolated_func





def  _a(  UpperCamelCase__				:						int							):




      '''simple docstring'''






      return (
          1
          - variable
          + variable**2
          - variable**3
          + variable**4
          - variable**5
          + variable**6
          - variable**7
          + variable**8
          - variable**9
          + variable**1_0
      )





def  _a(  UpperCamelCase__				:						Callable[[int], int] = question_function,	UpperCamelCase__				:						int = 1_0							):




      '''simple docstring'''






      SCREAMING_SNAKE_CASE__     :				list[int]									=[func(UpperCamelCase__							) for x_val in range(1,	order + 1							)]

      SCREAMING_SNAKE_CASE__     :				list[Callable[[int], int]]									=[
          interpolate(data_points[:max_coeff]							) for max_coeff in range(1,	order + 1							)
      ]

      SCREAMING_SNAKE_CASE__     :				int									=0
      SCREAMING_SNAKE_CASE__     :				Callable[[int], int]
      SCREAMING_SNAKE_CASE__     :				int

      for poly in polynomials:
            SCREAMING_SNAKE_CASE__     :				Any									=1
            while func(UpperCamelCase__							) == poly(UpperCamelCase__							):
                  x_val += 1

            ret += poly(UpperCamelCase__							)

      return ret


if __name__ == "__main__":
  print(F'''{solution() = }''')