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

import math
import random
from collections.abc import Collection
from typing import overload







class lowerCamelCase							:




  '''simple docstring'''



  def __init__(      self			:       Any  ,							UpperCAmelCase__			:       List[Any] = None  )				->Any:
        if components is None:
              UpperCAmelCase_            =  []
        UpperCAmelCase_            =  list(lowercase__  )






  def __len__(      self			:       Tuple  )				->Optional[int]:
        return len(self.__components  )






  def __str__(      self			:       Optional[int]  )				->Tuple:
        return "(" + ",".join(map(lowercase__  ,							self.__components  )  ) + ")"






  def __add__(      self			:       List[Any]  ,							UpperCAmelCase__			:       Optional[Any]  )				->str:
        UpperCAmelCase_            =  len(self  )
        if size == len(lowercase__  ):
              UpperCAmelCase_            =  [self.__components[i] + other.component(lowercase__  ) for i in range(lowercase__  )]
              return Vector(lowercase__  )
        else:
              raise Exception('''must have the same size'''  )






  def __sub__(      self			:       Dict  ,							UpperCAmelCase__			:       Optional[Any]  )				->List[str]:
        UpperCAmelCase_            =  len(self  )
        if size == len(lowercase__  ):
              UpperCAmelCase_            =  [self.__components[i] - other.component(lowercase__  ) for i in range(lowercase__  )]
              return Vector(lowercase__  )
        else:  # error case
              raise Exception('''must have the same size'''  )






  @overload
  def __mul__(      self			:       Optional[int]  ,							UpperCAmelCase__			:       int  )				->Dict:
        ...






  @overload
  def __mul__(      self			:       Optional[int]  ,							UpperCAmelCase__			:       List[str]  )				->str:
        ...






  def __mul__(      self			:       List[Any]  ,							UpperCAmelCase__			:       Tuple  )				->str:
        if isinstance(lowercase__  ,							(float, int)  ):
              UpperCAmelCase_            =  [c * other for c in self.__components]
              return Vector(lowercase__  )
        elif isinstance(lowercase__  ,							lowercase__  ) and len(self  ) == len(lowercase__  ):
              UpperCAmelCase_            =  len(self  )
              UpperCAmelCase_            =  [self.__components[i] * other.component(lowercase__  ) for i in range(lowercase__  )]
              return sum(lowercase__  )
        else:  # error case
              raise Exception('''invalid operand!'''  )






  def  lowerCAmelCase__ (      self			:       Union[str, Any]  )				->Optional[Any]:
        return Vector(self.__components  )






  def  lowerCAmelCase__ (      self			:       Optional[int]  ,							UpperCAmelCase__			:       Dict  )				->List[str]:
        if isinstance(lowercase__  ,							lowercase__  ) and -len(self.__components  ) <= i < len(self.__components  ):
              return self.__components[i]
        else:
              raise Exception('''index out of range'''  )






  def  lowerCAmelCase__ (      self			:       Any  ,							UpperCAmelCase__			:       Optional[int]  ,							UpperCAmelCase__			:       Optional[int]  )				->Dict:
        assert -len(self.__components  ) <= pos < len(self.__components  )
        UpperCAmelCase_            =  value






  def  lowerCAmelCase__ (      self			:       str  )				->Optional[Any]:
        if len(self.__components  ) == 0:
              raise Exception('''Vector is empty'''  )
        UpperCAmelCase_            =  [c**2 for c in self.__components]
        return math.sqrt(sum(lowercase__  )  )






  def  lowerCAmelCase__ (      self			:       Optional[Any]  ,							UpperCAmelCase__			:       List[Any]  ,							UpperCAmelCase__			:       Tuple = False  )				->Dict:
        UpperCAmelCase_            =  self * other
        UpperCAmelCase_            =  self.euclidean_length() * other.euclidean_length()
        if deg:
              return math.degrees(math.acos(num / den  )  )
        else:
              return math.acos(num / den  )






def  __lowerCamelCase       (      _UpperCamelCase  :  int					):


      '''simple docstring'''


      assert isinstance(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					)
      return Vector([0] * dimension					)



def  __lowerCamelCase       (      _UpperCamelCase  :  int							,    _UpperCamelCase  :  int					):


      '''simple docstring'''


      assert isinstance(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					) and (isinstance(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					))
      UpperCAmelCase_            =  [0] * dimension
      UpperCAmelCase_            =  1
      return Vector(SCREAMING_SNAKE_CASE__					)



def  __lowerCamelCase       (      _UpperCamelCase  :  float							,    _UpperCamelCase  :  Vector							,    _UpperCamelCase  :  Vector					):


      '''simple docstring'''


      assert (
          isinstance(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					)
          and isinstance(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					)
          and (isinstance(SCREAMING_SNAKE_CASE__							,    (int, float)					))
      )
      return x * scalar + y



def  __lowerCamelCase       (      _UpperCamelCase  :  int							,    _UpperCamelCase  :  int							,    _UpperCamelCase  :  int					):


      '''simple docstring'''


      random.seed(SCREAMING_SNAKE_CASE__					)
      UpperCAmelCase_            =  [random.randint(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					) for _ in range(SCREAMING_SNAKE_CASE__					)]
      return Vector(SCREAMING_SNAKE_CASE__					)







class lowerCamelCase							:




  '''simple docstring'''



  def __init__(      self			:       Dict  ,							UpperCAmelCase__			:       Optional[Any]  ,							UpperCAmelCase__			:       Any  ,							UpperCAmelCase__			:       List[Any]  )				->int:
        UpperCAmelCase_            =  matrix
        UpperCAmelCase_            =  w
        UpperCAmelCase_            =  h






  def __str__(      self			:       Tuple  )				->Dict:
        UpperCAmelCase_            =  """"""
        for i in range(self.__height  ):
              ans += "|"
              for j in range(self.__width  ):
                    if j < self.__width - 1:
                          ans += str(self.__matrix[i][j]  ) + ","
                    else:
                          ans += str(self.__matrix[i][j]  ) + "|\n"
        return ans






  def __add__(      self			:       Optional[Any]  ,							UpperCAmelCase__			:       Dict  )				->Union[str, Any]:
        if self.__width == other.width() and self.__height == other.height():
              UpperCAmelCase_            =  []
              for i in range(self.__height  ):
                    UpperCAmelCase_            =  [
                        self.__matrix[i][j] + other.component(lowercase__  ,							lowercase__  )
                        for j in range(self.__width  )
                    ]
                    matrix.append(lowercase__  )
              return Matrix(lowercase__  ,							self.__width  ,							self.__height  )
        else:
              raise Exception('''matrix must have the same dimension!'''  )






  def __sub__(      self			:       Dict  ,							UpperCAmelCase__			:       int  )				->str:
        if self.__width == other.width() and self.__height == other.height():
              UpperCAmelCase_            =  []
              for i in range(self.__height  ):
                    UpperCAmelCase_            =  [
                        self.__matrix[i][j] - other.component(lowercase__  ,							lowercase__  )
                        for j in range(self.__width  )
                    ]
                    matrix.append(lowercase__  )
              return Matrix(lowercase__  ,							self.__width  ,							self.__height  )
        else:
              raise Exception('''matrices must have the same dimension!'''  )






  @overload
  def __mul__(      self			:       Any  ,							UpperCAmelCase__			:       Optional[Any]  )				->str:
        ...






  @overload
  def __mul__(      self			:       Tuple  ,							UpperCAmelCase__			:       List[str]  )				->Any:
        ...






  def __mul__(      self			:       Tuple  ,							UpperCAmelCase__			:       Tuple  )				->Optional[Any]:
        if isinstance(lowercase__  ,							lowercase__  ):  # matrix-vector
              if len(lowercase__  ) == self.__width:
                    UpperCAmelCase_            =  zero_vector(self.__height  )
                    for i in range(self.__height  ):
                          UpperCAmelCase_            =  [
                              self.__matrix[i][j] * other.component(lowercase__  )
                              for j in range(self.__width  )
                          ]
                          ans.change_component(lowercase__  ,							sum(lowercase__  )  )
                    return ans
              else:
                    raise Exception(
                        '''vector must have the same size as the '''
                        '''number of columns of the matrix!'''  )
        elif isinstance(lowercase__  ,							(int, float)  ):  # matrix-scalar
              UpperCAmelCase_            =  [
                  [self.__matrix[i][j] * other for j in range(self.__width  )]
                  for i in range(self.__height  )
              ]
              return Matrix(lowercase__  ,							self.__width  ,							self.__height  )
        return None






  def  lowerCAmelCase__ (      self			:       Optional[int]  )				->Dict:
        return self.__height






  def  lowerCAmelCase__ (      self			:       Optional[int]  )				->str:
        return self.__width






  def  lowerCAmelCase__ (      self			:       str  ,							UpperCAmelCase__			:       List[Any]  ,							UpperCAmelCase__			:       Union[str, Any]  )				->Union[str, Any]:
        if 0 <= x < self.__height and 0 <= y < self.__width:
              return self.__matrix[x][y]
        else:
              raise Exception('''change_component: indices out of bounds'''  )






  def  lowerCAmelCase__ (      self			:       Dict  ,							UpperCAmelCase__			:       Optional[Any]  ,							UpperCAmelCase__			:       Optional[int]  ,							UpperCAmelCase__			:       Union[str, Any]  )				->int:
        if 0 <= x < self.__height and 0 <= y < self.__width:
              UpperCAmelCase_            =  value
        else:
              raise Exception('''change_component: indices out of bounds'''  )






  def  lowerCAmelCase__ (      self			:       List[str]  ,							UpperCAmelCase__			:       Optional[Any]  ,							UpperCAmelCase__			:       int  )				->Optional[Any]:
        if self.__height != self.__width:
              raise Exception('''Matrix is not square'''  )
        UpperCAmelCase_            =  self.__matrix[:x] + self.__matrix[x + 1 :]
        for i in range(len(lowercase__  )  ):
              UpperCAmelCase_            =  minor[i][:y] + minor[i][y + 1 :]
        return Matrix(lowercase__  ,							self.__width - 1  ,							self.__height - 1  ).determinant()






  def  lowerCAmelCase__ (      self			:       Optional[int]  ,							UpperCAmelCase__			:       List[str]  ,							UpperCAmelCase__			:       Tuple  )				->Any:
        if self.__height != self.__width:
              raise Exception('''Matrix is not square'''  )
        if 0 <= x < self.__height and 0 <= y < self.__width:
              return (-1) ** (x + y) * self.minor(lowercase__  ,							lowercase__  )
        else:
              raise Exception('''Indices out of bounds'''  )






  def  lowerCAmelCase__ (      self			:       Union[str, Any]  )				->Optional[Any]:
        if self.__height != self.__width:
              raise Exception('''Matrix is not square'''  )
        if self.__height < 1:
              raise Exception('''Matrix has no element'''  )
        elif self.__height == 1:
              return self.__matrix[0][0]
        elif self.__height == 2:
              return (
                  self.__matrix[0][0] * self.__matrix[1][1]
                  - self.__matrix[0][1] * self.__matrix[1][0]
              )
        else:
              UpperCAmelCase_            =  [
                  self.__matrix[0][y] * self.cofactor(0  ,							lowercase__  ) for y in range(self.__width  )
              ]
              return sum(lowercase__  )






def  __lowerCamelCase       (      _UpperCamelCase  :  int					):


      '''simple docstring'''


      UpperCAmelCase_            =  [[0] * n for _ in range(SCREAMING_SNAKE_CASE__					)]
      return Matrix(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					)





def  __lowerCamelCase       (      _UpperCamelCase  :  int							,    _UpperCamelCase  :  int							,    _UpperCamelCase  :  int							,    _UpperCamelCase  :  int					):


      '''simple docstring'''


      random.seed(SCREAMING_SNAKE_CASE__					)
      UpperCAmelCase_            =  [
          [random.randint(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					) for _ in range(SCREAMING_SNAKE_CASE__					)] for _ in range(SCREAMING_SNAKE_CASE__					)
      ]
      return Matrix(SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__							,    SCREAMING_SNAKE_CASE__					)






'''simple docstring'''
from ...utils import logging
from ..ta.modeling_tf_ta import TFTaEncoderModel, TFTaForConditionalGeneration, TFTaModel
from .configuration_mta import MTaConfig


lowercase__  :      Dict        =					logging.get_logger(__name__)

lowercase__  :      List[Any]        =					"T5Config"







class lowerCamelCase							(	lowerCamelCase					):




  '''simple docstring'''



  lowerCAmelCase__										=	'''mt5'''
  lowerCAmelCase__										=	MTaConfig







class lowerCamelCase							(	lowerCamelCase					):




  '''simple docstring'''



  lowerCAmelCase__										=	'''mt5'''
  lowerCAmelCase__										=	MTaConfig







class lowerCamelCase							(	lowerCamelCase					):




  '''simple docstring'''



  lowerCAmelCase__										=	'''mt5'''
  lowerCAmelCase__										=	MTaConfig





