



from collections import defaultdict
from math import ceil, sqrt



def 		lowerCAmelCase__    (					UpperCamelCase_				:       int = 1_0_0_0_0_0_0 ,       UpperCamelCase_				:       int = 1_0	)->  int:
    A__		 =					defaultdict(UpperCamelCase_	)

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

        hole_width_lower_bound += (outer_width - hole_width_lower_bound) % 2

        for hole_width in range(UpperCamelCase_ ,       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 <= 1_0	)


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





import numpy as np
from matplotlib import pyplot as plt
from sklearn.datasets import load_iris
from sklearn.metrics import ConfusionMatrixDisplay
from sklearn.model_selection import train_test_split
from xgboost import XGBClassifier



def 		lowerCAmelCase__    (					UpperCamelCase_				:       dict	)->  tuple:
    return (data["data"], data["target"])



def 		lowerCAmelCase__    (					UpperCamelCase_				:       np.ndarray ,       UpperCamelCase_				:       np.ndarray	)->  XGBClassifier:
    A__		 =					XGBClassifier()
    classifier.fit(UpperCamelCase_ ,       UpperCamelCase_	)
    return classifier



def 		lowerCAmelCase__    (					)->  None:
    A__		 =					load_iris()
    A__ ,	A__		 =					data_handling(UpperCamelCase_	)
    A__ ,	A__ ,	A__ ,	A__		 =					train_test_split(
        UpperCamelCase_ ,       UpperCamelCase_ ,       test_size=0.25	)

    A__		 =					iris['''target_names''']

    # Create an XGBoost Classifier from the training data
    A__		 =					xgboost(UpperCamelCase_ ,       UpperCamelCase_	)

    # Display the confusion matrix of the classifier with both training and test sets
    ConfusionMatrixDisplay.from_estimator(
        UpperCamelCase_ ,       UpperCamelCase_ ,       UpperCamelCase_ ,       display_labels=UpperCamelCase_ ,       cmap='''Blues''' ,       normalize='''true''' ,       )
    plt.title('''Normalized Confusion Matrix - IRIS Dataset'''	)
    plt.show()


if __name__ == "__main__":
   import doctest

   doctest.testmod(verbose=True)
   main()
