




def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	snake_case_		    =     len(_A							)
	snake_case_		    =     len(matrix[0]							)
	snake_case_		    =     min(_A     ,	_A							)

	for row in range(_A							):
		# Check if diagonal element is not zero
		if matrix[row][row] != 0:
			# Eliminate all the elements below the diagonal
			for col in range(row + 1     ,	_A							):
				snake_case_		    =     matrix[col][row] / matrix[row][row]
				for i in range(_A     ,	_A							):
					matrix[col][i] -= multiplier * matrix[row][i]
		else:
			# Find a non-zero diagonal element to swap rows
			snake_case_		    =     True
			for i in range(row + 1     ,	_A							):
				if matrix[i][row] != 0:
					snake_case_    ,      snake_case_		    =     matrix[i], matrix[row]
					snake_case_		    =     False
					break
			if reduce:
				rank -= 1
				for i in range(_A							):
					snake_case_		    =     matrix[i][rank]

            # Reduce the row pointer by one to stay on the same row
			row -= 1

	return rank


if __name__ == "__main__":
		import doctest

		doctest.testmod()






from timeit import timeit

lowercase__				:     Union[str, Any] 		=						{
    "MALAYALAM": True,
    "String": False,
    "rotor": True,
    "level": True,
    "A": True,
    "BB": True,
    "ABC": False,
    "amanaplanacanalpanama": True,  # "a man a plan a canal panama"
}
# Ensure our test data is valid
assert all((key == key[::-1]) is value for key, value in test_data.items())


def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	snake_case_		    =     0
	snake_case_		    =     len(_A							) - 1
	while start_i < end_i:
		if s[start_i] == s[end_i]:
			start_i += 1
			end_i -= 1
		else:
			return False
	return True


def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	snake_case_		    =     len(_A							) // 2
	snake_case_		    =     len(_A							)

	# We need to traverse till half of the length of string
	# as we can get access of the i'th last element from
	# i'th index.
	# eg: [0,1,2,3,4,5] => 4th index can be accessed
	# with the help of 1st index (i==n-i-1)
	# where n is length of string
	return all(s[i] == s[n - i - 1] for i in range(_A							)							)


def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	if len(_A							) <= 2:
		return True
	if s[0] == s[len(_A							) - 1]:
		return is_palindrome_recursive(s[1:-1]							)
	else:
		return False


def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	return s == s[::-1]


def 						lowerCamelCase__    (		_A							):







	'''simple docstring'''





	snake_case_		    =     f"all({name}(key) is value for key, value in test_data.items())"
	snake_case_		    =     f"from __main__ import test_data, {name}"
	snake_case_		    =     500000
	snake_case_		    =     timeit(stmt=_A     ,	setup=_A     ,	number=_A							)
	print(f"{name:<35} finished {number:,} runs in {result:.5f} seconds"							)


if __name__ == "__main__":
		for key, value in test_data.items():
				assert is_palindrome(key) is is_palindrome_recursive(key)
				assert is_palindrome(key) is is_palindrome_slice(key)
				print(f'''{key:21} {value}''')
		print("a man a plan a canal panama")

		# finished 500,000 runs in 0.46793 seconds
		benchmark_function("is_palindrome_slice")
		# finished 500,000 runs in 0.85234 seconds
		benchmark_function("is_palindrome")
		# finished 500,000 runs in 1.32028 seconds
		benchmark_function("is_palindrome_recursive")
		# finished 500,000 runs in 2.08679 seconds
		benchmark_function("is_palindrome_traversal")
