





from __future__ import annotations






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				tuple[int, int]       , UpperCamelCase__:				int     ):
		SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   position
		SCREAMING_SNAKE_CASE__								=   [
		    (y + 1, x + 2),
		    (y - 1, x + 2),
		    (y + 1, x - 2),
		    (y - 1, x - 2),
		    (y + 2, x + 1),
		    (y + 2, x - 1),
		    (y - 2, x + 1),
		    (y - 2, x - 1),
		]
		SCREAMING_SNAKE_CASE__								=   []

		for position in positions:
				SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   position
				if 0 <= y_test < n and 0 <= x_test < n:
						permissible_positions.append(UpperCamelCase__     )

		return permissible_positions






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				list[list[int]]     ):
		return not any(elem == 0 for row in board for elem in row     )






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				list[list[int]]       , UpperCamelCase__:				tuple[int, int]       , UpperCamelCase__:				int     ):

		if is_complete(UpperCamelCase__     ):
				return True

		for position in get_valid_pos(UpperCamelCase__       , len(UpperCamelCase__     )     ):
				SCREAMING_SNAKE_CASE__						,    SCREAMING_SNAKE_CASE__								=   position

				if board[y][x] == 0:
						SCREAMING_SNAKE_CASE__								=   curr + 1
						if open_knight_tour_helper(UpperCamelCase__       , UpperCamelCase__       , curr + 1     ):
								return True
						SCREAMING_SNAKE_CASE__								=   0

		return False






def 					SCREAMING_SNAKE_CASE__				(							UpperCamelCase__:				int     ):
		SCREAMING_SNAKE_CASE__								=   [[0 for i in range(UpperCamelCase__     )] for j in range(UpperCamelCase__     )]

		for i in range(UpperCamelCase__     ):
				for j in range(UpperCamelCase__     ):
						SCREAMING_SNAKE_CASE__								=   1
						if open_knight_tour_helper(UpperCamelCase__       , (i, j)       , 1     ):
								return board
						SCREAMING_SNAKE_CASE__								=   0

		SCREAMING_SNAKE_CASE__								=   f'''Open Kight Tour cannot be performed on a board of size {n}'''
		raise ValueError(UpperCamelCase__     )


if __name__ == "__main__":
	import doctest

	doctest.testmod()

from ..utils import (
    OptionalDependencyNotAvailable,
    is_flax_available,
    is_scipy_available,
    is_torch_available,
    is_torchsde_available,
)


try:
   if not is_torch_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_pt_objects import *  # noqa F403
else:
   from .scheduling_consistency_models import CMStochasticIterativeScheduler
   from .scheduling_ddim import DDIMScheduler
   from .scheduling_ddim_inverse import DDIMInverseScheduler
   from .scheduling_ddim_parallel import DDIMParallelScheduler
   from .scheduling_ddpm import DDPMScheduler
   from .scheduling_ddpm_parallel import DDPMParallelScheduler
   from .scheduling_deis_multistep import DEISMultistepScheduler
   from .scheduling_dpmsolver_multistep import DPMSolverMultistepScheduler
   from .scheduling_dpmsolver_multistep_inverse import DPMSolverMultistepInverseScheduler
   from .scheduling_dpmsolver_singlestep import DPMSolverSinglestepScheduler
   from .scheduling_euler_ancestral_discrete import EulerAncestralDiscreteScheduler
   from .scheduling_euler_discrete import EulerDiscreteScheduler
   from .scheduling_heun_discrete import HeunDiscreteScheduler
   from .scheduling_ipndm import IPNDMScheduler
   from .scheduling_k_dpm_2_ancestral_discrete import KDPMaAncestralDiscreteScheduler
   from .scheduling_k_dpm_2_discrete import KDPMaDiscreteScheduler
   from .scheduling_karras_ve import KarrasVeScheduler
   from .scheduling_pndm import PNDMScheduler
   from .scheduling_repaint import RePaintScheduler
   from .scheduling_sde_ve import ScoreSdeVeScheduler
   from .scheduling_sde_vp import ScoreSdeVpScheduler
   from .scheduling_unclip import UnCLIPScheduler
   from .scheduling_unipc_multistep import UniPCMultistepScheduler
   from .scheduling_utils import KarrasDiffusionSchedulers, SchedulerMixin
   from .scheduling_vq_diffusion import VQDiffusionScheduler

try:
   if not is_flax_available():
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_flax_objects import *  # noqa F403
else:
   from .scheduling_ddim_flax import FlaxDDIMScheduler
   from .scheduling_ddpm_flax import FlaxDDPMScheduler
   from .scheduling_dpmsolver_multistep_flax import FlaxDPMSolverMultistepScheduler
   from .scheduling_karras_ve_flax import FlaxKarrasVeScheduler
   from .scheduling_lms_discrete_flax import FlaxLMSDiscreteScheduler
   from .scheduling_pndm_flax import FlaxPNDMScheduler
   from .scheduling_sde_ve_flax import FlaxScoreSdeVeScheduler
   from .scheduling_utils_flax import (
       FlaxKarrasDiffusionSchedulers,
       FlaxSchedulerMixin,
       FlaxSchedulerOutput,
       broadcast_to_shape_from_left,
   )


try:
   if not (is_torch_available() and is_scipy_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_torch_and_scipy_objects import *  # noqa F403
else:
   from .scheduling_lms_discrete import LMSDiscreteScheduler

try:
   if not (is_torch_available() and is_torchsde_available()):
      raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
   from ..utils.dummy_torch_and_torchsde_objects import *  # noqa F403
else:
   from .scheduling_dpmsolver_sde import DPMSolverSDEScheduler





