
"""simple docstring"""







from __future__ import annotations

from typing import Any
def       __UpperCAmelCase		(		*a_      :		list[list[int]]					)  ->							list[list[int]]:
   if all(_check_not_integer(a_					) for m in matrix_s					):
      for i in matrix_s[1:]:
         _verify_matrix_sizes(matrix_s[0]     ,	a_					)
      return [[sum(a_					) for t in zip(*a_					)] for m in zip(*a_					)]
   raise TypeError("Expected a matrix, got int/list instead"					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		list[list[int]]					)  ->							list[list[int]]:
   if (
       _check_not_integer(a_					)
       and _check_not_integer(a_					)
       and _verify_matrix_sizes(a_     ,	a_					)
   ):
      return [[i - j for i, j in zip(*a_					)] for m in zip(a_     ,	a_					)]
   raise TypeError("Expected a matrix, got int/list instead"					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		int | float					)  ->							list[list[float]]:
   return [[x * n for x in row] for row in matrix]
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		list[list[int]]					)  ->							list[list[int]]:
   if _check_not_integer(a_					) and _check_not_integer(a_					):
      _UpperCAmelCase						,				_UpperCAmelCase 						=       _verify_matrix_sizes(a_     ,	a_					)

   if cols[0] != rows[1]:
      _UpperCAmelCase 						=       (
          "Cannot multiply matrix of dimensions "
          F'''({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'''
      )
      raise ValueError(a_					)
   return [
       [sum(m * n for m, n in zip(a_     ,	a_					)					) for j in zip(*a_					)] for i in matrix_a
   ]
def       __UpperCAmelCase		(		a_      :		int					)  ->							list[list[int]]:
   _UpperCAmelCase 						=       int(a_					)
   return [[int(row == column					) for column in range(a_					)] for row in range(a_					)]
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		bool = True					)  ->							list[list[int]] | map[list[int]]:
   if _check_not_integer(a_					):
      if return_map:
         return map(a_     ,	zip(*a_					)					)
      else:
         return list(map(a_     ,	zip(*a_					)					)					)
   raise TypeError("Expected a matrix, got int/list instead"					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		int     ,	a_      :		int					)  ->							list[list[int]]:
   _UpperCAmelCase 						=       matrix[:row] + matrix[row + 1 :]
   return [row[:column] + row[column + 1 :] for row in minor]
def       __UpperCAmelCase		(		a_      :		list[list[int]]					)  ->							Any:
   if len(a_					) == 1:
      return matrix[0][0]

   return sum(
       x * determinant(minor(a_     ,	0     ,	a_					)					) * (-1) ** i
       for i, x in enumerate(matrix[0]					)					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]					)  ->							list[list[float]] | None:
   _UpperCAmelCase 						=       determinant(a_					)
   if det == 0:
      return None

   _UpperCAmelCase 						=       [
       [determinant(minor(a_     ,	a_     ,	a_					)					) for j in range(len(a_					)					)]
       for i in range(len(a_					)					)
   ]

   _UpperCAmelCase 						=       [
       [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]					)]
       for row in range(len(a_					)					)
   ]
   _UpperCAmelCase 						=       list(transpose(a_					)					)
   return scalar_multiply(a_     ,	1 / det					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]					)  ->							bool:
   return not isinstance(a_     ,	a_					) and not isinstance(matrix[0]     ,	a_					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]					)  ->							tuple[int, int]:
   return len(a_					), len(matrix[0]					)
def       __UpperCAmelCase		(		a_      :		list[list[int]]     ,	a_      :		list[list[int]]					)  ->							tuple[tuple[int, int], tuple[int, int]]:
   _UpperCAmelCase 						=       _shape(a_					) + _shape(a_					)
   if shape[0] != shape[3] or shape[1] != shape[2]:
      _UpperCAmelCase 						=       (
          "operands could not be broadcast together with shape "
          F'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
      )
      raise ValueError(a_					)
   return (shape[0], shape[2]), (shape[1], shape[3])
def       __UpperCAmelCase		(		)  ->							None:
   _UpperCAmelCase 						=       [[12, 10], [3, 9]]
   _UpperCAmelCase 						=       [[3, 4], [7, 4]]
   _UpperCAmelCase 						=       [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
   _UpperCAmelCase 						=       [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
   print(F'''Add Operation, {add(a_     ,	a_					) = } \n'''					)
   print(
       F'''Multiply Operation, {multiply(a_     ,	a_					) = } \n'''     ,	)
   print(F'''Identity: {identity(5					)}\n'''					)
   print(F'''Minor of {matrix_c} = {minor(a_     ,	1     ,	2					)} \n'''					)
   print(F'''Determinant of {matrix_b} = {determinant(a_					)} \n'''					)
   print(F'''Inverse of {matrix_d} = {inverse(a_					)}\n'''					)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()



"""simple docstring"""







def       __UpperCAmelCase		(		a_      :		list[int]					)  ->							int:

   # validate:
   if not isinstance(a_     ,	a_					) or not all(
       isinstance(a_     ,	a_					) and item >= 0 for item in citations					):
      raise ValueError("The citations should be a list of non negative integers."					)

   citations.sort()
   _UpperCAmelCase 						=       len(a_					)

   for i in range(a_					):
      if citations[len_citations - 1 - i] <= i:
         return i

   return len_citations


if __name__ == "__main__":
  import doctest

  doctest.testmod()

