


"""simple docstring"""





from __future__ import annotations

from typing import TypedDict



class 		snake_case_(       lowercase_			):
     __UpperCamelCase  =					42
     __UpperCamelCase  =					42



def      _snake_case						(						_snake_case				:			Dict			):



      if not isinstance(lowerCamelCase_ ,   lowerCamelCase_			):
            raise TypeError('''The parameter s type must be str.'''			)

      return [s[i:] + s[:i] for i in range(len(lowerCamelCase_			)			)]


def      _snake_case						(						_snake_case				:			Optional[int]			):



      if not isinstance(lowerCamelCase_ ,   lowerCamelCase_			):
            raise TypeError('''The parameter s type must be str.'''			)
      if not s:
            raise ValueError('''The parameter s must not be empty.'''			)

      lowerCAmelCase					:	Tuple       =   all_rotations(lowerCamelCase_			)
      rotations.sort()  # sort the list of rotations in alphabetically order
      # make a string composed of the last char of each rotation
      lowerCAmelCase					:	BWTTransformDict       =   {
          "bwt_string": "".join([word[-1] for word in rotations]			),
          "idx_original_string": rotations.index(lowerCamelCase_			),
      }
      return response


def      _snake_case						(						_snake_case				:			Optional[Any] ,   _snake_case				:			Optional[Any]			):



      if not isinstance(lowerCamelCase_ ,   lowerCamelCase_			):
            raise TypeError('''The parameter bwt_string type must be str.'''			)
      if not bwt_string:
            raise ValueError('''The parameter bwt_string must not be empty.'''			)
      try:
            lowerCAmelCase					:	List[Any]       =   int(lowerCamelCase_			)
      except ValueError:
            raise TypeError(
                '''The parameter idx_original_string type must be int or passive'''
                ''' of cast to int.'''			)
      if idx_original_string < 0:
            raise ValueError('''The parameter idx_original_string must not be lower than 0.'''			)
      if idx_original_string >= len(lowerCamelCase_			):
            raise ValueError(
                '''The parameter idx_original_string must be lower than''' ''' len(bwt_string).'''			)

      lowerCAmelCase					:	List[str]       =   [""""""] * len(lowerCamelCase_			)
      for _ in range(len(lowerCamelCase_			)			):
            for i in range(len(lowerCamelCase_			)			):
                  lowerCAmelCase					:	Optional[Any]       =   bwt_string[i] + ordered_rotations[i]
            ordered_rotations.sort()
      return ordered_rotations[idx_original_string]


if __name__ == "__main__":
 snake_case__		:     Union[str, Any]    				=				'''Provide a string that I will generate its BWT transform: '''
 snake_case__		:     Tuple    				=				input(entry_msg).strip()
 snake_case__		:     int    				=				bwt_transform(s)
 print(
     f"""Burrows Wheeler transform for string \'{s}\' results """
     f"""in \'{result["bwt_string"]}\'"""
 )
 snake_case__		:     Optional[int]    				=				reverse_bwt(result['''bwt_string'''], result['''idx_original_string'''])
 print(
     f"""Reversing Burrows Wheeler transform for entry \'{result["bwt_string"]}\' """
     f"""we get original string \'{original_string}\'"""
 )






"""simple docstring"""





# using dfs for finding eulerian path traversal


def      _snake_case						(						_snake_case				:			Optional[Any] ,   _snake_case				:			List[Any] ,   _snake_case				:			str ,   _snake_case				:			List[Any]=None			):
      lowerCAmelCase					:	Any       =   (path or []) + [u]
      for v in graph[u]:
            if visited_edge[u][v] is False:
                  lowerCAmelCase,      lowerCAmelCase					:	Union[str, Any]       =   True, True
                  lowerCAmelCase					:	int       =   dfs(_snake_case ,   _snake_case ,   _snake_case ,   _snake_case			)
      return path


def      _snake_case						(						_snake_case				:			Optional[int] ,   _snake_case				:			Dict			):
      lowerCAmelCase					:	Tuple       =   0
      lowerCAmelCase					:	Optional[Any]       =   -1
      for i in range(_snake_case			):
            if i not in graph.keys():
                  continue
            if len(graph[i]			) % 2 == 1:
                  odd_degree_nodes += 1
                  lowerCAmelCase					:	Optional[Any]       =   i
      if odd_degree_nodes == 0:
            return 1, odd_node
      if odd_degree_nodes == 2:
            return 2, odd_node
      return 3, odd_node


def      _snake_case						(						_snake_case				:			Tuple ,   _snake_case				:			List[Any]			):
      lowerCAmelCase					:	Any       =   [[False for _ in range(max_node + 1			)] for _ in range(max_node + 1			)]
      lowerCAmelCase,      lowerCAmelCase					:	Optional[int]       =   check_circuit_or_path(_snake_case ,   _snake_case			)
      if check == 3:
            print('''graph is not Eulerian'''			)
            print('''no path'''			)
            return
      lowerCAmelCase					:	Dict       =   1
      if check == 2:
            lowerCAmelCase					:	int       =   odd_node
            print('''graph has a Euler path'''			)
      if check == 1:
            print('''graph has a Euler cycle'''			)
      lowerCAmelCase					:	List[str]       =   dfs(_snake_case ,   _snake_case ,   _snake_case			)
      print(_snake_case			)


def      _snake_case						(						):
      lowerCAmelCase					:	Optional[Any]       =   {1: [2, 3, 4], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [4]}
      lowerCAmelCase					:	Union[str, Any]       =   {1: [2, 3, 4, 5], 2: [1, 3], 3: [1, 2], 4: [1, 5], 5: [1, 4]}
      lowerCAmelCase					:	List[Any]       =   {1: [2, 3, 4], 2: [1, 3, 4], 3: [1, 2], 4: [1, 2, 5], 5: [4]}
      lowerCAmelCase					:	Optional[Any]       =   {1: [2, 3], 2: [1, 3], 3: [1, 2]}
      lowerCAmelCase					:	Any       =   {
          1: [],
          2: []
          # all degree is zero
      }
      lowerCAmelCase					:	List[str]       =   10
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)
      check_euler(_snake_case ,   _snake_case			)


if __name__ == "__main__":
 main()


