



'''simple docstring'''




import sys



def      a      (			lowerCamelCase__   ):
			'''simple docstring'''





			A_     :						Optional[Any]     =					len(lowerCamelCase__   )
			A_     :						Union[str, Any]     =					[[0 for x in range(lowerCamelCase__   )] for x in range(lowerCamelCase__   )]
			A_     :						int     =					[[0 for x in range(lowerCamelCase__   )] for x in range(lowerCamelCase__   )]

			for chain_length in range(2						,				lowerCamelCase__   ):
						for a in range(1						,				n - chain_length + 1   ):
									A_     :						Any     =					a + chain_length - 1

									A_     :						int     =					sys.maxsize
									for c in range(lowerCamelCase__						,				lowerCamelCase__   ):
												A_     :						str     =					(
												    matrix[a][c] + matrix[c + 1][b] + array[a - 1] * array[c] * array[b]
												)
												if cost < matrix[a][b]:
															A_     :						List[str]     =					cost
															A_     :						List[Any]     =					c
			return matrix, sol



def      a      (			lowerCamelCase__						,				lowerCamelCase__						,				lowerCamelCase__   ):
			'''simple docstring'''





			if i == j:
						print("""A""" + str(lowerCamelCase__   )						,				end=""" """   )
			else:
						print("""("""						,				end=""" """   )
						print_optiomal_solution(lowerCamelCase__						,				lowerCamelCase__						,				optimal_solution[i][j]   )
						print_optiomal_solution(lowerCamelCase__						,				optimal_solution[i][j] + 1						,				lowerCamelCase__   )
						print(""")"""						,				end=""" """   )



def      a      (			):
			'''simple docstring'''





			A_     :						Dict     =					[30, 35, 15, 5, 10, 20, 25]
			A_     :						Tuple     =					len(lowerCamelCase__   )
			# Size of matrix created from above array will be
			# 30*35 35*15 15*5 5*10 10*20 20*25
			A_,   A_     :						Any     =					matrix_chain_order(lowerCamelCase__   )

			print("""No. of Operation required: """ + str(matrix[1][n - 1]   )   )
			print_optiomal_solution(lowerCamelCase__						,				1						,				n - 1   )


if __name__ == "__main__":
						main()




'''simple docstring'''




import unittest
from typing import Tuple

import torch

from diffusers.utils import floats_tensor, randn_tensor, torch_all_close, torch_device
from diffusers.utils.testing_utils import require_torch







@require_torch
class      _lowerCAmelCase							:


	@property
	def    _a     (self							):
				return self.get_dummy_input()


	@property
	def    _a     (self							):
				if self.block_type == "down":
							return (4, 32, 16, 16)
				elif self.block_type == "mid":
							return (4, 32, 32, 32)
				elif self.block_type == "up":
							return (4, 32, 64, 64)

				raise ValueError(F'\'{self.block_type}\' is not a supported block_type. Set it to \'up\', \'mid\', or \'down\'.'							)


	def    _a     (self	,				lowercase=True	,				lowercase=False	,				lowercase=False	,				lowercase=False	,				):
				A_     :						List[str]     =					4
				A_     :						int     =					32
				A_     :						Optional[int]     =					(32, 32)

				A_     :						Optional[Any]     =					torch.manual_seed(0							)
				A_     :						int     =					torch.device(lowercase							)
				A_     :						int     =					(batch_size, num_channels) + sizes
				A_     :						Optional[int]     =					randn_tensor(lowercase	,				generator=lowercase	,				device=lowercase							)
				A_     :						Union[str, Any]     =					{"""hidden_states""": hidden_states}

				if include_temb:
							A_     :						str     =					128
							A_     :						List[Any]     =					randn_tensor((batch_size, temb_channels)	,				generator=lowercase	,				device=lowercase							)

				if include_res_hidden_states_tuple:
							A_     :						List[str]     =					torch.manual_seed(1							)
							A_     :						int     =					(randn_tensor(lowercase	,				generator=lowercase	,				device=lowercase							),)

				if include_encoder_hidden_states:
							A_     :						List[str]     =					floats_tensor((batch_size, 32, 32)							).to(lowercase							)

				if include_skip_sample:
							A_     :						Dict     =					randn_tensor(((batch_size, 3) + sizes)	,				generator=lowercase	,				device=lowercase							)

				return dummy_input


	def    _a     (self							):
				A_     :						Tuple     =					{
				    """in_channels""": 32,
				    """out_channels""": 32,
				    """temb_channels""": 128,
				}
				if self.block_type == "up":
							A_     :						Any     =					32

				if self.block_type == "mid":
							init_dict.pop("""out_channels"""							)

				A_     :						Optional[int]     =					self.dummy_input
				return init_dict, inputs_dict


	def    _a     (self	,				lowercase							):
				A_,   A_     :						Optional[Any]     =					self.prepare_init_args_and_inputs_for_common()
				A_     :						int     =					self.block_class(**lowercase							)
				unet_block.to(lowercase							)
				unet_block.eval()

				with torch.no_grad():
							A_     :						List[str]     =					unet_block(**lowercase							)

				if isinstance(lowercase	,				lowercase							):
							A_     :						Union[str, Any]     =					output[0]

				self.assertEqual(output.shape	,				self.output_shape							)

				A_     :						int     =					output[0, -1, -3:, -3:]
				A_     :						List[Any]     =					torch.tensor(lowercase							).to(lowercase							)
				assert torch_all_close(output_slice.flatten()	,				lowercase	,				atol=5E-3							)


	@unittest.skipIf(torch_device == """mps"""	,				"""Training is not supported in mps"""							)
	def    _a     (self							):
				A_,   A_     :						Tuple     =					self.prepare_init_args_and_inputs_for_common()
				A_     :						List[str]     =					self.block_class(**lowercase							)
				model.to(lowercase							)
				model.train()
				A_     :						Any     =					model(**lowercase							)

				if isinstance(lowercase	,				lowercase							):
							A_     :						str     =					output[0]

				A_     :						Union[str, Any]     =					torch.device(lowercase							)
				A_     :						Tuple     =					randn_tensor(output.shape	,				device=lowercase							)
				A_     :						List[str]     =					torch.nn.functional.mse_loss(lowercase	,				lowercase							)
				loss.backward()