






"""simple docstring"""






def  __lowerCamelCase					(					lowerCAmelCase__ = 6008_5147_5143				):

				try:
								A__							 =       int(lowerCAmelCase__				)
				except (TypeError, ValueError):
								raise TypeError('Parameter n must be int or castable to int.'				)
				if n <= 0:
								raise ValueError('Parameter n must be greater than or equal to one.'				)
				A__							 =       1
				A__							 =       2
				while i * i <= n:
								while n % i == 0:
												A__							 =       i
												n //= i
								i += 1
				if n > 1:
								A__							 =       n
				return int(lowerCAmelCase__				)


if __name__ == "__main__":
					print(f'''{solution() = }''')










"""simple docstring"""






from math import ceil



def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__				):
				A__							 =       list(range(0       ,lowerCAmelCase__				)				)

				A__							 =       [item for sublist in list(device_map.values()				) for item in sublist]

				# Duplicate check
				A__							 =       []
				for i in device_map_blocks:
								if device_map_blocks.count(lowerCAmelCase__				) > 1 and i not in duplicate_blocks:
												duplicate_blocks.append(lowerCAmelCase__				)
    # Missing blocks
				A__							 =       [i for i in blocks if i not in device_map_blocks]
				A__							 =       [i for i in device_map_blocks if i not in blocks]

				if len(lowerCAmelCase__				) != 0:
								raise ValueError(
								    'Duplicate attention blocks specified in device_map. Attention blocks must be specified to one device.'
								    ' These attention blocks were specified more than once: ' + str(lowerCAmelCase__				)				)
				if len(lowerCAmelCase__				) != 0:
								raise ValueError(
								    'There are attention blocks for this model that are not specified in the device_map. Add these attention '
								    'blocks to a device on the device_map: ' + str(lowerCAmelCase__				)				)
				if len(lowerCAmelCase__				) != 0:
								raise ValueError(
								    'The device_map contains more attention blocks than this model has. Remove these from the device_map:'
								    + str(lowerCAmelCase__				)				)







def  __lowerCamelCase					(					lowerCAmelCase__       ,lowerCAmelCase__				):
				A__							 =       list(range(lowerCAmelCase__				)				)
				A__							 =       int(ceil(n_layers / len(lowerCAmelCase__				)				)				)
				A__							 =       [layers[i : i + n_blocks] for i in range(0       ,lowerCAmelCase__       ,lowerCAmelCase__				)]

				return dict(zip(lowerCAmelCase__       ,lowerCAmelCase__				)				)


