

from collections import defaultdict
from math import ceil, sqrt



def       __lowerCAmelCase      (						A = 1000000       ,     A = 10    ):
	UpperCAmelCase_       				=			defaultdict(A    )

	for outer_width in range(3       ,     (t_limit // 4) + 2    ):
		if outer_width * outer_width > t_limit:
			UpperCAmelCase_       				=			max(
			    ceil(sqrt(outer_width * outer_width - t_limit    )    )       ,     1    )
		else:
			UpperCAmelCase_       				=			1

		hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

		for hole_width in range(A       ,     outer_width - 1       ,     2    ):
			count[outer_width * outer_width - hole_width * hole_width] += 1

	return sum(1 for n in count.values() if 1 <= n <= 10    )


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


import importlib

import torch
import yaml
from omegaconf import OmegaConf
from taming.models.vqgan import VQModel



def       __lowerCAmelCase      (						A       ,     A=False    ):
	UpperCAmelCase_       				=			OmegaConf.load(A    )
	if display:
		print(yaml.dump(OmegaConf.to_container(A    )    )    )
	return config



def       __lowerCAmelCase      (						A       ,     A=None       ,     A=None    ):
	if conf_path is None:
		UpperCAmelCase_       				=			"./model_checkpoints/vqgan_only.yaml"
	UpperCAmelCase_       				=			load_config(A       ,     display=A    )
	UpperCAmelCase_       				=			VQModel(**config.model.params    )
	if ckpt_path is None:
		UpperCAmelCase_       				=			"./model_checkpoints/vqgan_only.pt"
	UpperCAmelCase_       				=			torch.load(A       ,     map_location=A    )
	if ".ckpt" in ckpt_path:
		UpperCAmelCase_       				=			sd["state_dict"]
	model.load_state_dict(A       ,     strict=A    )
	model.to(A    )
	del sd
	return model



def       __lowerCAmelCase      (						A       ,     A    ):
	UpperCAmelCase_				,   UpperCAmelCase_				,   UpperCAmelCase_       				=			model.encode(A    )
	print(F"VQGAN --- {model.__class__.__name__}: latent shape: {z.shape[2:]}"    )
	UpperCAmelCase_       				=			model.decode(A    )
	return xrec



def       __lowerCAmelCase      (						A       ,     A=False    ):
	UpperCAmelCase_				,   UpperCAmelCase_       				=			string.rsplit("."       ,     1    )
	if reload:
		UpperCAmelCase_       				=			importlib.import_module(A    )
		importlib.reload(A    )
	return getattr(importlib.import_module(A       ,     package=A    )       ,     cls    )



def       __lowerCAmelCase      (						A    ):
	if "target" not in config:
		raise KeyError("Expected key `target` to instantiate."    )
	return get_obj_from_str(config["target"]    )(**config.get("params"       ,     {}    )    )



def       __lowerCAmelCase      (						A       ,     A       ,     A=True       ,     A=True    ):
	UpperCAmelCase_       				=			instantiate_from_config(A    )
	if sd is not None:
		model.load_state_dict(A    )
	if gpu:
		model.cuda()
	if eval_mode:
		model.eval()
	return {"model": model}




def       __lowerCAmelCase      (						A       ,     A       ,     A       ,     A    ):
	# load the specified checkpoint
	if ckpt:
		UpperCAmelCase_       				=			torch.load(A       ,     map_location="cpu"    )
		UpperCAmelCase_       				=			pl_sd["global_step"]
		print(F"loaded model from global step {global_step}."    )
	else:
		UpperCAmelCase_       				=			{"state_dict": None}
		UpperCAmelCase_       				=			None
	UpperCAmelCase_       				=			load_model_from_config(config.model       ,     pl_sd["state_dict"]       ,     gpu=A       ,     eval_mode=A    )["model"]
	return model, global_step