




'''simple docstring'''

import math
from typing import Optional

import numpy as np
import torch
from torch import nn

from .activations import get_activation




def    snake_case__     (  a       ,      a       ,      a = False       ,      a = 1       ,      a = 1       ,      a = 1_0000       ,      )			->       Optional[int]:





			'''simple docstring'''






			assert len(timesteps.shape	) == 1, "Timesteps should be a 1d-array"

			snake_case__          =						embedding_dim // 2
			snake_case__          =						-math.log(a	) * torch.arange(
			    start=0       ,      end=a       ,      dtype=torch.floataa       ,      device=timesteps.device	)
			snake_case__          =						exponent / (half_dim - downscale_freq_shift)

			snake_case__          =						torch.exp(a	)
			snake_case__          =						timesteps[:, None].float() * emb[None, :]

			# scale embeddings
			snake_case__          =						scale * emb

			# concat sine and cosine embeddings
			snake_case__          =						torch.cat([torch.sin(a	), torch.cos(a	)]       ,      dim=-1	)

			# flip sine and cosine embeddings
			if flip_sin_to_cos:
						snake_case__          =						torch.cat([emb[:, half_dim:], emb[:, :half_dim]]       ,      dim=-1	)

			# zero pad
			if embedding_dim % 2 == 1:
						snake_case__          =						torch.nn.functional.pad(a       ,      (0, 1, 0, 0)	)
			return emb




def    snake_case__     (  a       ,      a       ,      a=False       ,      a=0	)			->       Dict:





			'''simple docstring'''






			snake_case__          =						np.arange(a       ,      dtype=np.floataa	)
			snake_case__          =						np.arange(a       ,      dtype=np.floataa	)
			snake_case__          =						np.meshgrid(a       ,      a	)  # here w goes first
			snake_case__          =						np.stack(a       ,      axis=0	)

			snake_case__          =						grid.reshape([2, 1, grid_size, grid_size]	)
			snake_case__          =						get_ad_sincos_pos_embed_from_grid(a       ,      a	)
			if cls_token and extra_tokens > 0:
						snake_case__          =						np.concatenate([np.zeros([extra_tokens, embed_dim]	), pos_embed]       ,      axis=0	)
			return pos_embed




def    snake_case__     (  a       ,      a	)			->       List[str]:





			'''simple docstring'''






			if embed_dim % 2 != 0:
						raise ValueError("""embed_dim must be divisible by 2"""	)

			# use half of dimensions to encode grid_h
			snake_case__          =						get_ad_sincos_pos_embed_from_grid(embed_dim // 2       ,      grid[0]	)  # (H*W, D/2)
			snake_case__          =						get_ad_sincos_pos_embed_from_grid(embed_dim // 2       ,      grid[1]	)  # (H*W, D/2)

			snake_case__          =						np.concatenate([emb_h, emb_w]       ,      axis=1	)  # (H*W, D)
			return emb




def    snake_case__     (  a       ,      a	)			->       Tuple:





			'''simple docstring'''






			if embed_dim % 2 != 0:
						raise ValueError("""embed_dim must be divisible by 2"""	)

			snake_case__          =						np.arange(embed_dim // 2       ,      dtype=np.floataa	)
			omega /= embed_dim / 2.0
			snake_case__          =						1.0 / 1_0000**omega  # (D/2,)

			snake_case__          =						pos.reshape(-1	)  # (M,)
			snake_case__          =						np.einsum("""m,d->md"""       ,      a       ,      a	)  # (M, D/2), outer product

			snake_case__          =						np.sin(a	)  # (M, D/2)
			snake_case__          =						np.cos(a	)  # (M, D/2)

			snake_case__          =						np.concatenate([emb_sin, emb_cos]       ,      axis=1	)  # (M, D)
			return emb





class __magic_name__(						nn.Module      ):






						def __init__(   self						:						str					,   __UpperCamelCase						:						Union[str, Any]=2_2_4					,   __UpperCamelCase						:						Tuple=2_2_4					,   __UpperCamelCase						:						List[str]=1_6					,   __UpperCamelCase						:						Tuple=3					,   __UpperCamelCase						:						str=7_6_8					,   __UpperCamelCase						:						Optional[int]=False					,   __UpperCamelCase						:						List[Any]=True					,   __UpperCamelCase						:						Dict=True					,   ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						(height // patch_size) * (width // patch_size)
									snake_case__          =						flatten
									snake_case__          =						layer_norm

									snake_case__          =						nn.Convad(
									    __UpperCamelCase					,   __UpperCamelCase					,   kernel_size=(patch_size, patch_size)					,   stride=__UpperCamelCase					,   bias=__UpperCamelCase       )
									if layer_norm:
												snake_case__          =						nn.LayerNorm(__UpperCamelCase					,   elementwise_affine=__UpperCamelCase					,   eps=1E-6       )
									else:
												snake_case__          =						None

									snake_case__          =						get_ad_sincos_pos_embed(__UpperCamelCase					,   int(num_patches**0.5       )       )
									self.register_buffer("""pos_embed"""					,   torch.from_numpy(__UpperCamelCase       ).float().unsqueeze(0       )					,   persistent=__UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Tuple					,   __UpperCamelCase						:						Optional[int]       ):



									'''simple docstring'''






									snake_case__          =						self.proj(__UpperCamelCase       )
									if self.flatten:
												snake_case__          =						latent.flatten(2       ).transpose(1					,   2       )  # BCHW -> BNC
									if self.layer_norm:
												snake_case__          =						self.norm(__UpperCamelCase       )
									return latent + self.pos_embed







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Union[str, Any]					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						str = "silu"					,   __UpperCamelCase						:						int = None					,   __UpperCamelCase						:						Optional[str] = None					,   __UpperCamelCase						:						Any=None					,   ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )

									if cond_proj_dim is not None:
												snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase					,   bias=__UpperCamelCase       )
									else:
												snake_case__          =						None

									snake_case__          =						get_activation(__UpperCamelCase       )

									if out_dim is not None:
												snake_case__          =						out_dim
									else:
												snake_case__          =						time_embed_dim
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )

									if post_act_fn is None:
												snake_case__          =						None
									else:
												snake_case__          =						get_activation(__UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						int					,   __UpperCamelCase						:						List[str]					,   __UpperCamelCase						:						Any=None       ):



									'''simple docstring'''






									if condition is not None:
												snake_case__          =						sample + self.cond_proj(__UpperCamelCase       )
									snake_case__          =						self.linear_a(__UpperCamelCase       )

									if self.act is not None:
												snake_case__          =						self.act(__UpperCamelCase       )

									snake_case__          =						self.linear_a(__UpperCamelCase       )

									if self.post_act is not None:
												snake_case__          =						self.post_act(__UpperCamelCase       )
									return sample







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Optional[int]					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						bool					,   __UpperCamelCase						:						float       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						num_channels
									snake_case__          =						flip_sin_to_cos
									snake_case__          =						downscale_freq_shift







						def       __lowerCAmelCase(   self						:						Union[str, Any]					,   __UpperCamelCase						:						Any       ):



									'''simple docstring'''






									snake_case__          =						get_timestep_embedding(
									    __UpperCamelCase					,   self.num_channels					,   flip_sin_to_cos=self.flip_sin_to_cos					,   downscale_freq_shift=self.downscale_freq_shift					,   )
									return t_emb







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						List[str]					,   __UpperCamelCase						:						int = 2_5_6					,   __UpperCamelCase						:						float = 1.0					,   __UpperCamelCase						:						Any=True					,   __UpperCamelCase						:						Tuple=True					,   __UpperCamelCase						:						int=False       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						nn.Parameter(torch.randn(__UpperCamelCase       ) * scale					,   requires_grad=__UpperCamelCase       )
									snake_case__          =						log
									snake_case__          =						flip_sin_to_cos

									if set_W_to_weight:
												# to delete later
												snake_case__          =						nn.Parameter(torch.randn(__UpperCamelCase       ) * scale					,   requires_grad=__UpperCamelCase       )

												snake_case__          =						self.W







						def       __lowerCAmelCase(   self						:						Optional[Any]					,   __UpperCamelCase						:						Any       ):



									'''simple docstring'''






									if self.log:
												snake_case__          =						torch.log(__UpperCamelCase       )

									snake_case__          =						x[:, None] * self.weight[None, :] * 2 * np.pi

									if self.flip_sin_to_cos:
												snake_case__          =						torch.cat([torch.cos(__UpperCamelCase       ), torch.sin(__UpperCamelCase       )]					,   dim=-1       )
									else:
												snake_case__          =						torch.cat([torch.sin(__UpperCamelCase       ), torch.cos(__UpperCamelCase       )]					,   dim=-1       )
									return out







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Any					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int					,   ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						height
									snake_case__          =						width
									snake_case__          =						num_embed
									snake_case__          =						embed_dim

									snake_case__          =						nn.Embedding(self.num_embed					,   __UpperCamelCase       )
									snake_case__          =						nn.Embedding(self.height					,   __UpperCamelCase       )
									snake_case__          =						nn.Embedding(self.width					,   __UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Optional[Any]					,   __UpperCamelCase						:						List[Any]       ):



									'''simple docstring'''






									snake_case__          =						self.emb(__UpperCamelCase       )

									snake_case__          =						self.height_emb(torch.arange(self.height					,   device=index.device       ).view(1					,   self.height       )       )

									# 1 x H x D -> 1 x H x 1 x D
									snake_case__          =						height_emb.unsqueeze(2       )

									snake_case__          =						self.width_emb(torch.arange(self.width					,   device=index.device       ).view(1					,   self.width       )       )

									# 1 x W x D -> 1 x 1 x W x D
									snake_case__          =						width_emb.unsqueeze(1       )

									snake_case__          =						height_emb + width_emb

									# 1 x H x W x D -> 1 x L xD
									snake_case__          =						pos_emb.view(1					,   self.height * self.width					,   -1       )

									snake_case__          =						emb + pos_emb[:, : emb.shape[1], :]

									return emb







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Dict					,   __UpperCamelCase						:						Union[str, Any]					,   __UpperCamelCase						:						Optional[Any]					,   __UpperCamelCase						:						Union[str, Any]       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						dropout_prob > 0
									snake_case__          =						nn.Embedding(num_classes + use_cfg_embedding					,   __UpperCamelCase       )
									snake_case__          =						num_classes
									snake_case__          =						dropout_prob






						def       __lowerCAmelCase(   self						:						List[Any]					,   __UpperCamelCase						:						Union[str, Any]					,   __UpperCamelCase						:						Optional[int]=None       ):



									'''simple docstring'''






									if force_drop_ids is None:
												snake_case__          =						torch.rand(labels.shape[0]					,   device=labels.device       ) < self.dropout_prob
									else:
												snake_case__          =						torch.tensor(force_drop_ids == 1       )
									snake_case__          =						torch.where(__UpperCamelCase					,   self.num_classes					,   __UpperCamelCase       )
									return labels







						def       __lowerCAmelCase(   self						:						Optional[int]					,   __UpperCamelCase						:						torch.LongTensor					,   __UpperCamelCase						:						Tuple=None       ):



									'''simple docstring'''






									snake_case__          =						self.dropout_prob > 0
									if (self.training and use_dropout) or (force_drop_ids is not None):
												snake_case__          =						self.token_drop(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						self.embedding_table(__UpperCamelCase       )
									return embeddings







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						int					,   __UpperCamelCase						:						int = 1_0_2_4					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 1_0					,   ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						num_image_text_embeds
									snake_case__          =						nn.Linear(__UpperCamelCase					,   self.num_image_text_embeds * cross_attention_dim       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Union[str, Any]					,   __UpperCamelCase						:						torch.FloatTensor					,   __UpperCamelCase						:						torch.FloatTensor       ):



									'''simple docstring'''






									snake_case__          =						text_embeds.shape[0]

									# image
									snake_case__          =						self.image_embeds(__UpperCamelCase       )
									snake_case__          =						image_text_embeds.reshape(__UpperCamelCase					,   self.num_image_text_embeds					,   -1       )

									# text
									snake_case__          =						self.text_proj(__UpperCamelCase       )

									return torch.cat([image_text_embeds, text_embeds]					,   dim=1       )







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						str					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 3_2					,   ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						num_image_text_embeds
									snake_case__          =						nn.Linear(__UpperCamelCase					,   self.num_image_text_embeds * cross_attention_dim       )
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Union[str, Any]					,   __UpperCamelCase						:						torch.FloatTensor       ):



									'''simple docstring'''






									snake_case__          =						image_embeds.shape[0]

									# image
									snake_case__          =						self.image_embeds(__UpperCamelCase       )
									snake_case__          =						image_embeds.reshape(__UpperCamelCase					,   self.num_image_text_embeds					,   -1       )
									snake_case__          =						self.norm(__UpperCamelCase       )
									return image_embeds







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Tuple					,   __UpperCamelCase						:						Any					,   __UpperCamelCase						:						Optional[int]					,   __UpperCamelCase						:						Union[str, Any]=0.1       ):



									'''simple docstring'''






									super().__init__()

									snake_case__          =						Timesteps(num_channels=2_5_6					,   flip_sin_to_cos=__UpperCamelCase					,   downscale_freq_shift=1       )
									snake_case__          =						TimestepEmbedding(in_channels=2_5_6					,   time_embed_dim=__UpperCamelCase       )
									snake_case__          =						LabelEmbedding(__UpperCamelCase					,   __UpperCamelCase					,   __UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Union[str, Any]					,   __UpperCamelCase						:						List[Any]					,   __UpperCamelCase						:						Dict					,   __UpperCamelCase						:						Tuple=None       ):



									'''simple docstring'''






									snake_case__          =						self.time_proj(__UpperCamelCase       )
									snake_case__          =						self.timestep_embedder(timesteps_proj.to(dtype=__UpperCamelCase       )       )  # (N, D)

									snake_case__          =						self.class_embedder(__UpperCamelCase       )  # (N, D)

									snake_case__          =						timesteps_emb + class_labels  # (N, D)

									return conditioning







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						int					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int					,   __UpperCamelCase						:						int = 6_4       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )
									snake_case__          =						AttentionPooling(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						List[Any]					,   __UpperCamelCase						:						Tuple       ):



									'''simple docstring'''






									snake_case__          =						self.norma(__UpperCamelCase       )
									snake_case__          =						self.pool(__UpperCamelCase       )
									snake_case__          =						self.proj(__UpperCamelCase       )
									snake_case__          =						self.norma(__UpperCamelCase       )
									return hidden_states







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Any					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 1_5_3_6       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						List[Any]					,   __UpperCamelCase						:						torch.FloatTensor					,   __UpperCamelCase						:						torch.FloatTensor       ):



									'''simple docstring'''






									snake_case__          =						self.text_proj(__UpperCamelCase       )
									snake_case__          =						self.text_norm(__UpperCamelCase       )

									# image
									snake_case__          =						self.image_proj(__UpperCamelCase       )

									return time_image_embeds + time_text_embeds







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						str					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 1_5_3_6       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )







						def       __lowerCAmelCase(   self						:						Tuple					,   __UpperCamelCase						:						torch.FloatTensor       ):



									'''simple docstring'''






									snake_case__          =						self.image_proj(__UpperCamelCase       )
									snake_case__          =						self.image_norm(__UpperCamelCase       )
									return time_image_embeds







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Dict					,   __UpperCamelCase						:						int = 7_6_8					,   __UpperCamelCase						:						int = 1_5_3_6       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase       )
									snake_case__          =						nn.LayerNorm(__UpperCamelCase       )
									snake_case__          =						nn.Sequential(
									    nn.Convad(3					,   1_6					,   3					,   padding=1       )					,   nn.SiLU()					,   nn.Convad(1_6					,   1_6					,   3					,   padding=1       )					,   nn.SiLU()					,   nn.Convad(1_6					,   3_2					,   3					,   padding=1					,   stride=2       )					,   nn.SiLU()					,   nn.Convad(3_2					,   3_2					,   3					,   padding=1       )					,   nn.SiLU()					,   nn.Convad(3_2					,   9_6					,   3					,   padding=1					,   stride=2       )					,   nn.SiLU()					,   nn.Convad(9_6					,   9_6					,   3					,   padding=1       )					,   nn.SiLU()					,   nn.Convad(9_6					,   2_5_6					,   3					,   padding=1					,   stride=2       )					,   nn.SiLU()					,   nn.Convad(2_5_6					,   4					,   3					,   padding=1       )					,   )







						def       __lowerCAmelCase(   self						:						List[Any]					,   __UpperCamelCase						:						torch.FloatTensor					,   __UpperCamelCase						:						torch.FloatTensor       ):



									'''simple docstring'''






									snake_case__          =						self.image_proj(__UpperCamelCase       )
									snake_case__          =						self.image_norm(__UpperCamelCase       )
									snake_case__          =						self.input_hint_block(__UpperCamelCase       )
									return time_image_embeds, hint







class __magic_name__(						nn.Module      ):






						def __init__(   self						:						Union[str, Any]					,   __UpperCamelCase						:						str					,   __UpperCamelCase						:						Dict					,   __UpperCamelCase						:						Any=None       ):



									'''simple docstring'''






									super().__init__()
									snake_case__          =						dtype
									snake_case__          =						nn.Parameter(torch.randn(1					,   __UpperCamelCase       ) / embed_dim**0.5       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase					,   dtype=self.dtype       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase					,   dtype=self.dtype       )
									snake_case__          =						nn.Linear(__UpperCamelCase					,   __UpperCamelCase					,   dtype=self.dtype       )
									snake_case__          =						num_heads
									snake_case__          =						embed_dim // self.num_heads







						def       __lowerCAmelCase(   self						:						List[str]					,   __UpperCamelCase						:						Tuple       ):



									'''simple docstring'''






									snake_case__    ,			snake_case__    ,			snake_case__          =						x.size()

									def shape(__UpperCamelCase						:						int       ):
												# (bs, length, width) --> (bs, length, n_heads, dim_per_head)
												snake_case__          =						x.view(__UpperCamelCase					,   -1					,   self.num_heads					,   self.dim_per_head       )
												# (bs, length, n_heads, dim_per_head) --> (bs, n_heads, length, dim_per_head)
												snake_case__          =						x.transpose(1					,   2       )
												# (bs, n_heads, length, dim_per_head) --> (bs*n_heads, length, dim_per_head)
												snake_case__          =						x.reshape(bs * self.num_heads					,   -1					,   self.dim_per_head       )
												# (bs*n_heads, length, dim_per_head) --> (bs*n_heads, dim_per_head, length)
												snake_case__          =						x.transpose(1					,   2       )
												return x

									snake_case__          =						x.mean(dim=1					,   keepdim=__UpperCamelCase       ) + self.positional_embedding.to(x.dtype       )
									snake_case__          =						torch.cat([class_token, x]					,   dim=1       )  # (bs, length+1, width)

									# (bs*n_heads, class_token_length, dim_per_head)
									snake_case__          =						shape(self.q_proj(__UpperCamelCase       )       )
									# (bs*n_heads, length+class_token_length, dim_per_head)
									snake_case__          =						shape(self.k_proj(__UpperCamelCase       )       )
									snake_case__          =						shape(self.v_proj(__UpperCamelCase       )       )

									# (bs*n_heads, class_token_length, length+class_token_length):
									snake_case__          =						1 / math.sqrt(math.sqrt(self.dim_per_head       )       )
									snake_case__          =						torch.einsum("""bct,bcs->bts"""					,   q * scale					,   k * scale       )  # More stable with f16 than dividing afterwards
									snake_case__          =						torch.softmax(weight.float()					,   dim=-1       ).type(weight.dtype       )

									# (bs*n_heads, dim_per_head, class_token_length)
									snake_case__          =						torch.einsum("""bts,bcs->bct"""					,   __UpperCamelCase					,   __UpperCamelCase       )

									# (bs, length+1, width)
									snake_case__          =						a.reshape(__UpperCamelCase					,   -1					,   1       ).transpose(1					,   2       )

									return a[:, 0, :]  # cls_token



'''simple docstring'''

from __future__ import annotations






def __UpperCamelCase (      __lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	__lowerCamelCase		:			float | int   ,	)   ->  list[float | int]:







     '''simple docstring'''






     if not all((nth_term, start_term_a, common_ratio_r)					):
          return []
     _a            =		[]
     _a            =		1
     _a            =		common_ratio_r
     for _ in range(int(__lowerCamelCase					)					):
          if not series:
               series.append(__lowerCamelCase					)
          else:
               power += 1
               series.append(float(start_term_a * multiple					)					)
               _a            =		pow(float(__lowerCamelCase					)   ,	__lowerCamelCase					)
     return series


if __name__ == "__main__":
   import doctest

   doctest.testmod()

   lowercase__					  =		float(input("Enter the last number (n term) of the Geometric Series"))
   lowercase__					  =		float(input("Enter the starting term (a) of the Geometric Series"))
   lowercase__					  =		float(
       input("Enter the common ratio between two terms (r) of the Geometric Series")
   )
   print("Formula of Geometric Series => a + ar + ar^2 ... +ar^n")
   print(geometric_series(nth_term, start_term_a, common_ratio_r))

