


from __future__ import annotations

a			:			int												=					list[list[int]]

# assigning initial values to the grid
a			:			Matrix												=					[
    [3, 0, 6, 5, 0, 8, 4, 0, 0],
    [5, 2, 0, 0, 0, 0, 0, 0, 0],
    [0, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]

# a grid with no solution
a			:			Matrix												=					[
    [5, 0, 6, 5, 0, 8, 4, 0, 3],
    [5, 2, 0, 0, 0, 0, 0, 0, 2],
    [1, 8, 7, 0, 0, 0, 0, 3, 1],
    [0, 0, 3, 0, 1, 0, 0, 8, 0],
    [9, 0, 0, 8, 6, 3, 0, 0, 5],
    [0, 5, 0, 0, 9, 0, 6, 0, 0],
    [1, 3, 0, 0, 0, 0, 2, 5, 0],
    [0, 0, 0, 0, 0, 0, 0, 7, 4],
    [0, 0, 5, 2, 0, 6, 3, 0, 0],
]


def 		lowercase_	(  _UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase	):


			'''simple docstring'''







			for i in range(9	):
						if grid[row][i] == n or grid[i][column] == n:
									return False

			for i in range(3	):
						for j in range(3	):
									if grid[(row - row % 3) + i][(column - column % 3) + j] == n:
												return False

			return True


def 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			for i in range(9	):
						for j in range(9	):
									if grid[i][j] == 0:
												return i, j
			return None


def 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			if location := find_empty_location(_UpperCamelCase	):
						__lowercase       ,			__lowercase			       = location
			else:
						# If the location is ``None``, then the grid is solved.
						return grid

			for digit in range(1							,      10	):
						if is_safe(_UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase							,      _UpperCamelCase	):
									__lowercase			       = digit

									if sudoku(_UpperCamelCase	) is not None:
												return grid

									__lowercase			       = 0

			return None


def 		lowercase_	(  _UpperCamelCase	):


			'''simple docstring'''







			for row in grid:
						for cell in row:
									print(_UpperCamelCase							,      end=''' '''	)
						print()


if __name__ == "__main__":
	# make a copy of grid so that you can compare with the unmodified grid
	for example_grid in (initial_grid, no_solution):
		print('''\nExample grid:\n''' + '''=''' * 20)
		print_solution(example_grid)
		print('''\nExample grid solution:''')
		a			:			Optional[Any]												=					sudoku(example_grid)
		if solution is not None:
			print_solution(solution)
		else:
			print('''Cannot find a solution.''')






from collections import Counter
from timeit import timeit


def 		lowercase_	(  _UpperCamelCase = ""							,      ):


			'''simple docstring'''







			return sum(c % 2 for c in Counter(input_str.replace(''' '''							,      ''''''	).lower()	).values()	) < 2


def 		lowercase_	(  _UpperCamelCase = ""	):


			'''simple docstring'''







			if len(_UpperCamelCase	) == 0:
						return True
			__lowercase			       = input_str.replace(''' '''							,      ''''''	).lower()
			# character_freq_dict: Stores the frequency of every character in the input string
			__lowercase			       = {}

			for character in lower_case_input_str:
						__lowercase			       = character_freq_dict.get(_UpperCamelCase							,      0	) + 1
			__lowercase			       = 0

			for character_count in character_freq_dict.values():
						if character_count % 2:
									odd_char += 1
			if odd_char > 1:
						return False
			return True


def 		lowercase_	(  _UpperCamelCase = ""	):


			'''simple docstring'''







			print('''\nFor string = '''							,      _UpperCamelCase							,      ''':'''	)
			print(
			    '''> can_string_be_rearranged_as_palindrome_counter()'''							,      '''\tans ='''							,      can_string_be_rearranged_as_palindrome_counter(_UpperCamelCase	)							,      '''\ttime ='''							,      timeit(
			        '''z.can_string_be_rearranged_as_palindrome_counter(z.check_str)'''							,      setup='''import __main__ as z'''							,      )							,      '''seconds'''							,      )
			print(
			    '''> can_string_be_rearranged_as_palindrome()'''							,      '''\tans ='''							,      can_string_be_rearranged_as_palindrome(_UpperCamelCase	)							,      '''\ttime ='''							,      timeit(
			        '''z.can_string_be_rearranged_as_palindrome(z.check_str)'''							,      setup='''import __main__ as z'''							,      )							,      '''seconds'''							,      )


if __name__ == "__main__":
	a			:			int												=					input(
	    '''Enter string to determine if it can be rearranged as a palindrome or not: '''
	).strip()
	benchmark(check_str)
	a			:			Tuple												=					can_string_be_rearranged_as_palindrome_counter(check_str)
	print(f'''{check_str} can {'' if status else 'not '}be rearranged as a palindrome''')


