



'''simple docstring'''






from __future__ import annotations

A_				:					Optional[Any]							=      [2, 1, 4, 5, 6, 0, 8, 9, 1, 2, 0, 6, 4, 2, 0, 6, 5, 3, 2, 7]



class 				lowercase			:


 """simple docstring"""


 def __init__(				self    ,a_				)						->  None:
        _UpperCAmelCase    :		int     	=					-1
        _UpperCAmelCase    :		int     	=					-1
        _UpperCAmelCase    :		list[int]     	=					[-1] * length
        _UpperCAmelCase    :		Node | None     	=					None
        _UpperCAmelCase    :		Node | None     	=					None







 def __repr__(				self				)						->  str:
        return f'''Node(min_value={self.minn} max_value={self.maxx})'''







def        snake_case_   (	lowerCAmelCase_						)->						Node | None:





       '''simple docstring'''


       _UpperCAmelCase    :		Optional[Any]     	=					Node(len(lowerCAmelCase_						)						)
       _UpperCAmelCase	,_UpperCAmelCase    :		List[str]     	=					min(lowerCAmelCase_						), max(lowerCAmelCase_						)
       # Leaf node case where the node contains only one unique value
       if root.minn == root.maxx:
              return root
       _UpperCAmelCase    :		Any     	=					(root.minn + root.maxx) // 2

       _UpperCAmelCase    :		list[int]     	=					[]
       _UpperCAmelCase    :		list[int]     	=					[]

       for index, num in enumerate(lowerCAmelCase_						):
              if num <= pivot:
                     left_arr.append(lowerCAmelCase_						)
              else:
                     right_arr.append(lowerCAmelCase_						)
              _UpperCAmelCase    :		List[str]     	=					len(lowerCAmelCase_						)
       _UpperCAmelCase    :		List[str]     	=					build_tree(lowerCAmelCase_						)
       _UpperCAmelCase    :		str     	=					build_tree(lowerCAmelCase_						)
       return root




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)->						int:





       '''simple docstring'''


       if index < 0 or node is None:
              return 0
       # Leaf node cases
       if node.minn == node.maxx:
              return index + 1 if node.minn == num else 0
       _UpperCAmelCase    :		Any     	=					(node.minn + node.maxx) // 2
       if num <= pivot:
              # go the left subtree and map index to the left subtree
              return rank_till_index(node.left			,  lowerCAmelCase_			,  node.map_left[index] - 1						)
       else:
              # go to the right subtree and map index to the right subtree
              return rank_till_index(node.right			,  lowerCAmelCase_			,  index - node.map_left[index]						)




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)->						int:





       '''simple docstring'''


       if start > end:
              return 0
       _UpperCAmelCase    :		Any     	=					rank_till_index(lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)
       _UpperCAmelCase    :		Tuple     	=					rank_till_index(lowerCAmelCase_			,  lowerCAmelCase_			,  start - 1						)
       return rank_till_end - rank_before_start




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)->						int:





       '''simple docstring'''


       if index > (end - start) or start > end or node is None:
              return -1
       # Leaf node case
       if node.minn == node.maxx:
              return node.minn
       # Number of elements in the left subtree in interval [start, end]
       _UpperCAmelCase    :		List[str]     	=					node.map_left[end] - (
           node.map_left[start - 1] if start else 0
       )
       if num_elements_in_left_tree > index:
              return quantile(
                  node.left			,  lowerCAmelCase_			,  (node.map_left[start - 1] if start else 0)			,  node.map_left[end] - 1			,  )
       else:
              return quantile(
                  node.right			,  index - num_elements_in_left_tree			,  start - (node.map_left[start - 1] if start else 0)			,  end - node.map_left[end]			,  )




def        snake_case_   (	lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_			,  lowerCAmelCase_						)->						int:





       '''simple docstring'''


       if (
           start > end
           or node is None
           or start_num > end_num
           or node.minn > end_num
           or node.maxx < start_num
       ):
              return 0
       if start_num <= node.minn and node.maxx <= end_num:
              return end - start + 1
       _UpperCAmelCase    :		Union[str, Any]     	=					range_counting(
           node.left			,  (node.map_left[start - 1] if start else 0)			,  node.map_left[end] - 1			,  lowerCAmelCase_			,  lowerCAmelCase_			,  )
       _UpperCAmelCase    :		Union[str, Any]     	=					range_counting(
           node.right			,  start - (node.map_left[start - 1] if start else 0)			,  end - node.map_left[end]			,  lowerCAmelCase_			,  lowerCAmelCase_			,  )
       return left + right


if __name__ == "__main__":
   import doctest

   doctest.testmod()







"""simple docstring"""


def   a__			(					__lowercase )						->						bool:
				# must be
				_A       	=      [list(__lowercase ) for row in matrix]
				if matrix and isinstance(__lowercase  ,      __lowercase ):
								if isinstance(matrix[0]  ,      __lowercase ):
												_A       	=      0
												for row in matrix:
																if prev_len == 0:
																				_A       	=      len(__lowercase )
																				_A       	=      True
																else:
																				_A       	=      prev_len == len(__lowercase )
								else:
												_A       	=      True
				else:
								_A       	=      False

				return result






def   a__			(					__lowercase )						->						None:
				if check_matrix(__lowercase ) and len(__lowercase ) > 0:
								_A       	=      [list(__lowercase ) for row in a]
								_A       	=      len(__lowercase )
								if isinstance(a[0]  ,      __lowercase ):
												_A       	=      len(a[0] )
								else:
												for dat in a:
																print(__lowercase )
												return

								# horizotal printing increasing
								for i in range(0  ,      __lowercase ):
												print(a[0][i] )
								# vertical printing down
								for i in range(1  ,      __lowercase ):
												print(a[i][mat_col - 1] )
								# horizotal printing decreasing
								if mat_row > 1:
												for i in range(mat_col - 2  ,      -1  ,      -1 ):
																print(a[mat_row - 1][i] )
        # vertical printing up
								for i in range(mat_row - 2  ,      0  ,      -1 ):
												print(a[i][0] )
								_A       	=      [row[1 : mat_col - 1] for row in a[1 : mat_row - 1]]
								if len(__lowercase ) > 0:
												spiral_print_clockwise(__lowercase )
								else:
												return
				else:
								print("Not a valid matrix" )
								return






def   a__			(					__lowercase )						->						list[int]:
				if matrix:
								return list(matrix.pop(0 ) ) + spiral_traversal(list(zip(*__lowercase ) )[::-1] )
				else:
								return []


# driver code
if __name__ == "__main__":
		import doctest

		doctest.testmod()

		a_											=     [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12]]
		spiral_print_clockwise(a)