code: 
  
  
  from math import radians as angle_to_radians
  from math import sin
  
  # Acceleration Constant on Earth (unit m/s^2)
  SCREAMING_SNAKE_CASE : int          =    9.8_06_65
  
  
  
  
  
  def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: float	,	SCREAMING_SNAKE_CASE_				: float      ):
  
  
  
  
  
  
         """simple docstring"""
  
  
  
         if not isinstance(SCREAMING_SNAKE_CASE_	,	(int, float)      ):
                raise TypeError("""Invalid velocity. Should be a positive number."""      )
  
         if not isinstance(SCREAMING_SNAKE_CASE_	,	(int, float)      ):
                raise TypeError("""Invalid angle. Range is 1-90 degrees."""      )
  
         # Ensure valid angle
         if angle > 90 or angle < 1:
                raise ValueError("""Invalid angle. Range is 1-90 degrees."""      )
  
         # Ensure valid velocity
         if init_velocity < 0:
                raise ValueError("""Invalid velocity. Should be a positive number."""      )
  
  
  
  
  
  def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: float	,	SCREAMING_SNAKE_CASE_				: float      ):
  
  
  
  
  
  
         """simple docstring"""
  
  
  
         check_args(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      )
         a_       :   int			=	angle_to_radians(2 * angle      )
         return round(init_velocity**2 * sin(SCREAMING_SNAKE_CASE_      ) / g	,	2      )
  
  
  
  
  
  def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: float	,	SCREAMING_SNAKE_CASE_				: float      ):
  
  
  
  
  
  
         """simple docstring"""
  
  
  
         check_args(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      )
         a_       :   List[Any]			=	angle_to_radians(SCREAMING_SNAKE_CASE_      )
         return round(init_velocity**2 * sin(SCREAMING_SNAKE_CASE_      ) ** 2 / (2 * g)	,	2      )
  
  
  
  
  
  def 						_lowerCamelCase		(							SCREAMING_SNAKE_CASE_				: float	,	SCREAMING_SNAKE_CASE_				: float      ):
  
  
  
  
  
  
         """simple docstring"""
  
  
  
         check_args(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      )
         a_       :   Tuple			=	angle_to_radians(SCREAMING_SNAKE_CASE_      )
         return round(2 * init_velocity * sin(SCREAMING_SNAKE_CASE_      ) / g	,	2      )
  
  
  
  
  
  def 						_lowerCamelCase		(							):
  
  
  
  
  
  
         """simple docstring"""
  
  
  
         a_       :   Any			=	25, 20
         assert horizontal_distance(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      ) == 40.97
         assert max_height(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      ) == 3.73
         assert total_time(SCREAMING_SNAKE_CASE_	,	SCREAMING_SNAKE_CASE_      ) == 1.74
  
  
  if __name__ == "__main__":
   from doctest import testmod
  
   testmod()
  
   # Get input from user
   SCREAMING_SNAKE_CASE : str          =    float(input("Initial Velocity: ").strip())
  
   # Get input from user
   SCREAMING_SNAKE_CASE : int          =    float(input("angle: ").strip())
  
   # Print results
   print()
   print("Results: ")
   print(F"""Horizontal Distance: {horizontal_distance(init_vel, angle)!s} [m]""")
   print(F"""Maximum Height: {max_height(init_vel, angle)!s} [m]""")
   print(F"""Total Time: {total_time(init_vel, angle)!s} [s]""")
  
  
  
style_context: 
  
  
  from dataclasses import dataclass
  from typing import Any, Dict, Optional
  
  import torch
  import torch.nn.functional as F
  from torch import nn
  
  from ..configuration_utils import ConfigMixin, register_to_config
  from ..models.embeddings import ImagePositionalEmbeddings
  from ..utils import BaseOutput, deprecate
  from .attention import BasicTransformerBlock
  from .embeddings import PatchEmbed
  from .modeling_utils import ModelMixin
  
  
  
  
  
  @dataclass
  class 					snake_case__  ( __A       ):
  	UpperCAmelCase   :							torch.FloatTensor
  
  
  
  
  
  class 					snake_case__  ( __A      ,    __A       ):
  
  
  
  
  
  	@register_to_config
  	def __init__(  self				,    UpperCamelCase_ = 16				,    UpperCamelCase_ = 88				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = 1				,    UpperCamelCase_ = 0.0				,    UpperCamelCase_ = 32				,    UpperCamelCase_ = None				,    UpperCamelCase_ = False				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = "geglu"				,    UpperCamelCase_ = None				,    UpperCamelCase_ = False				,    UpperCamelCase_ = False				,    UpperCamelCase_ = False				,    UpperCamelCase_ = "layer_norm"				,    UpperCamelCase_ = True				,    )		->			Union[str, Any]:
  								"""simple docstring"""
  
  
  
  
  
  
  								super().__init__()
  								a_       :   Dict			=	use_linear_projection
  								a_       :   Tuple			=	num_attention_heads
  								a_       :   List[Any]			=	attention_head_dim
  								a_       :   Dict			=	num_attention_heads * attention_head_dim
  
  								# 1. Transformer2DModel can process both standard continuous images of shape `(batch_size, num_channels, width, height)` as well as quantized image embeddings of shape `(batch_size, num_image_vectors)`
  								# Define whether input is continuous or discrete depending on configuration
  								a_       :   List[Any]			=	(in_channels is not None) and (patch_size is None)
  								a_       :   Dict			=	num_vector_embeds is not None
  								a_       :   Union[str, Any]			=	in_channels is not None and patch_size is not None
  
  								if norm_type == "layer_norm" and num_embeds_ada_norm is not None:
  															a_       :   int			=	(
  															    f"""The configuration file of this model: {self.__class__} is outdated. `norm_type` is either not set or"""
  															    """ incorrectly set to `'layer_norm'`.Make sure to set `norm_type` to `'ada_norm'` in the config."""
  															    """ Please make sure to update the config accordingly as leaving `norm_type` might led to incorrect"""
  															    """ results in future versions. If you have downloaded this checkpoint from the Hugging Face Hub, it"""
  															    """ would be very nice if you could open a Pull request for the `transformer/config.json` file"""
  															)
  															deprecate("""norm_type!=num_embeds_ada_norm"""				,    """1.0.0"""				,    UpperCamelCase_				,    standard_warn=UpperCamelCase_							)
  															a_       :   List[Any]			=	"""ada_norm"""
  
  								if self.is_input_continuous and self.is_input_vectorized:
  															raise ValueError(
  															    f"""Cannot define both `in_channels`: {in_channels} and `num_vector_embeds`: {num_vector_embeds}. Make"""
  															    """ sure that either `in_channels` or `num_vector_embeds` is None."""							)
  								elif self.is_input_vectorized and self.is_input_patches:
  															raise ValueError(
  															    f"""Cannot define both `num_vector_embeds`: {num_vector_embeds} and `patch_size`: {patch_size}. Make"""
  															    """ sure that either `num_vector_embeds` or `num_patches` is None."""							)
  								elif not self.is_input_continuous and not self.is_input_vectorized and not self.is_input_patches:
  															raise ValueError(
  															    f"""Has to define `in_channels`: {in_channels}, `num_vector_embeds`: {num_vector_embeds}, or patch_size:"""
  															    f""" {patch_size}. Make sure that `in_channels`, `num_vector_embeds` or `num_patches` is not None."""							)
  
  								# 2. Define input layers
  								if self.is_input_continuous:
  															a_       :   List[Any]			=	in_channels
  
  															a_       :   List[str]			=	torch.nn.GroupNorm(num_groups=UpperCamelCase_				,    num_channels=UpperCamelCase_				,    eps=1e-6				,    affine=UpperCamelCase_							)
  															if use_linear_projection:
  																						a_       :   int			=	nn.Linear(UpperCamelCase_				,    UpperCamelCase_							)
  															else:
  																						a_       :   Optional[Any]			=	nn.Convad(UpperCamelCase_				,    UpperCamelCase_				,    kernel_size=1				,    stride=1				,    padding=0							)
  								elif self.is_input_vectorized:
  															assert sample_size is not None, "Transformer2DModel over discrete input must provide sample_size"
  															assert num_vector_embeds is not None, "Transformer2DModel over discrete input must provide num_embed"
  
  															a_       :   Optional[Any]			=	sample_size
  															a_       :   str			=	sample_size
  															a_       :   str			=	num_vector_embeds
  															a_       :   str			=	self.height * self.width
  
  															a_       :   int			=	ImagePositionalEmbeddings(
  															    num_embed=UpperCamelCase_				,    embed_dim=UpperCamelCase_				,    height=self.height				,    width=self.width							)
  								elif self.is_input_patches:
  															assert sample_size is not None, "Transformer2DModel over patched input must provide sample_size"
  
  															a_       :   Dict			=	sample_size
  															a_       :   List[Any]			=	sample_size
  
  															a_       :   Tuple			=	patch_size
  															a_       :   Optional[Any]			=	PatchEmbed(
  															    height=UpperCamelCase_				,    width=UpperCamelCase_				,    patch_size=UpperCamelCase_				,    in_channels=UpperCamelCase_				,    embed_dim=UpperCamelCase_				,    )
  
  								# 3. Define transformers blocks
  								a_       :   List[Any]			=	nn.ModuleList(
  								    [
  								        BasicTransformerBlock(
  								            UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_				,    dropout=UpperCamelCase_				,    cross_attention_dim=UpperCamelCase_				,    activation_fn=UpperCamelCase_				,    num_embeds_ada_norm=UpperCamelCase_				,    attention_bias=UpperCamelCase_				,    only_cross_attention=UpperCamelCase_				,    upcast_attention=UpperCamelCase_				,    norm_type=UpperCamelCase_				,    norm_elementwise_affine=UpperCamelCase_				,    )
  								        for d in range(UpperCamelCase_							)
  								    ]							)
  
  								# 4. Define output layers
  								a_       :   str			=	in_channels if out_channels is None else out_channels
  								if self.is_input_continuous:
  															# TODO: should use out_channels for continuous projections
  															if use_linear_projection:
  																						a_       :   Optional[int]			=	nn.Linear(UpperCamelCase_				,    UpperCamelCase_							)
  															else:
  																						a_       :   Any			=	nn.Convad(UpperCamelCase_				,    UpperCamelCase_				,    kernel_size=1				,    stride=1				,    padding=0							)
  								elif self.is_input_vectorized:
  															a_       :   Optional[int]			=	nn.LayerNorm(UpperCamelCase_							)
  															a_       :   str			=	nn.Linear(UpperCamelCase_				,    self.num_vector_embeds - 1							)
  								elif self.is_input_patches:
  															a_       :   int			=	nn.LayerNorm(UpperCamelCase_				,    elementwise_affine=UpperCamelCase_				,    eps=1e-6							)
  															a_       :   str			=	nn.Linear(UpperCamelCase_				,    2 * inner_dim							)
  															a_       :   Optional[int]			=	nn.Linear(UpperCamelCase_				,    patch_size * patch_size * self.out_channels							)
  
  
  
  
  
  	def     A				(  self				,    UpperCamelCase_				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = None				,    UpperCamelCase_ = True				,    )		->			str:
  								"""simple docstring"""
  
  
  
  
  
  
  								if attention_mask is not None and attention_mask.ndim == 2:
  															# assume that mask is expressed as:
  															#   (1 = keep,      0 = discard)
  															# convert mask into a bias that can be added to attention scores:
  															#       (keep = +0,     discard = -10000.0)
  															a_       :   str			=	(1 - attention_mask.to(hidden_states.dtype							)) * -1_0000.0
  															a_       :   Union[str, Any]			=	attention_mask.unsqueeze(1							)
  
  								# convert encoder_attention_mask to a bias the same way we do for attention_mask
  								if encoder_attention_mask is not None and encoder_attention_mask.ndim == 2:
  															a_       :   Any			=	(1 - encoder_attention_mask.to(hidden_states.dtype							)) * -1_0000.0
  															a_       :   List[str]			=	encoder_attention_mask.unsqueeze(1							)
  
  								# 1. Input
  								if self.is_input_continuous:
  															a_		,				a_		,				a_		,				a_       :   str			=	hidden_states.shape
  															a_       :   Optional[Any]			=	hidden_states
  
  															a_       :   Optional[int]			=	self.norm(UpperCamelCase_							)
  															if not self.use_linear_projection:
  																						a_       :   int			=	self.proj_in(UpperCamelCase_							)
  																						a_       :   str			=	hidden_states.shape[1]
  																						a_       :   List[str]			=	hidden_states.permute(0				,    2				,    3				,    1							).reshape(UpperCamelCase_				,    height * width				,    UpperCamelCase_							)
  															else:
  																						a_       :   int			=	hidden_states.shape[1]
  																						a_       :   Optional[int]			=	hidden_states.permute(0				,    2				,    3				,    1							).reshape(UpperCamelCase_				,    height * width				,    UpperCamelCase_							)
  																						a_       :   Tuple			=	self.proj_in(UpperCamelCase_							)
  								elif self.is_input_vectorized:
  															a_       :   List[str]			=	self.latent_image_embedding(UpperCamelCase_							)
  								elif self.is_input_patches:
  															a_       :   Optional[int]			=	self.pos_embed(UpperCamelCase_							)
  
  								# 2. Blocks
  								for block in self.transformer_blocks:
  															a_       :   int			=	block(
  															    UpperCamelCase_				,    attention_mask=UpperCamelCase_				,    encoder_hidden_states=UpperCamelCase_				,    encoder_attention_mask=UpperCamelCase_				,    timestep=UpperCamelCase_				,    cross_attention_kwargs=UpperCamelCase_				,    class_labels=UpperCamelCase_				,    )
  
  								# 3. Output
  								if self.is_input_continuous:
  															if not self.use_linear_projection:
  																						a_       :   Dict			=	hidden_states.reshape(UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_							).permute(0				,    3				,    1				,    2							).contiguous()
  																						a_       :   List[Any]			=	self.proj_out(UpperCamelCase_							)
  															else:
  																						a_       :   Optional[int]			=	self.proj_out(UpperCamelCase_							)
  																						a_       :   int			=	hidden_states.reshape(UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_				,    UpperCamelCase_							).permute(0				,    3				,    1				,    2							).contiguous()
  
  															a_       :   int			=	hidden_states + residual
  								elif self.is_input_vectorized:
  															a_       :   str			=	self.norm_out(UpperCamelCase_							)
  															a_       :   str			=	self.out(UpperCamelCase_							)
  															# (batch, self.num_vector_embeds - 1, self.num_latent_pixels)
  															a_       :   int			=	logits.permute(0				,    2				,    1							)
  
  															# log(p(x_0))
  															a_       :   int			=	F.log_softmax(logits.double()				,    dim=1							).float()
  								elif self.is_input_patches:
  															# TODO: cleanup!
  															a_       :   Union[str, Any]			=	self.transformer_blocks[0].norma.emb(
  															    UpperCamelCase_				,    UpperCamelCase_				,    hidden_dtype=hidden_states.dtype							)
  															a_		,				a_       :   int			=	self.proj_out_a(F.silu(UpperCamelCase_							)							).chunk(2				,    dim=1							)
  															a_       :   Union[str, Any]			=	self.norm_out(UpperCamelCase_							) * (1 + scale[:, None]) + shift[:, None]
  															a_       :   Union[str, Any]			=	self.proj_out_a(UpperCamelCase_							)
  
  															# unpatchify
  															a_       :   Any			=	int(hidden_states.shape[1] ** 0.5							)
  															a_       :   str			=	hidden_states.reshape(
  															    shape=(-1, height, width, self.patch_size, self.patch_size, self.out_channels)							)
  															a_       :   Union[str, Any]			=	torch.einsum("""nhwpqc->nchpwq"""				,    UpperCamelCase_							)
  															a_       :   List[Any]			=	hidden_states.reshape(
  															    shape=(-1, self.out_channels, height * self.patch_size, width * self.patch_size)							)
  
  								if not return_dict:
  															return (output,)
  
  								return TransformeraDModelOutput(sample=UpperCamelCase_							)
  
  
  