




from __future__ import annotations

import math







def 		_A(       UpperCamelCase__							:			int				)    -> bool:
							'''simple docstring'''


							if 1 < number < 4:
														# 2 and 3 are primes
														return True
							elif number < 2 or number % 2 == 0 or number % 3 == 0:
														# Negatives, 0, 1, all even numbers, all multiples of 3 are not primes
														return False

							# All primes number are in format of 6k +/- 1
							for i in range(5				,       int(math.sqrt(UpperCamelCase__				) + 1				)				,       6				):
														if number % i == 0 or number % (i + 2) == 0:
																					return False
							return True


UpperCAmelCase__				     = [num for num in range(3, 100001, 2) if not is_prime(num)]







def 		_A(       UpperCamelCase__							:			int				)    -> list[int]:
							'''simple docstring'''


							if not isinstance(UpperCamelCase__				,       UpperCamelCase__				):
														raise ValueError('''n must be an integer'''				)
							if n <= 0:
														raise ValueError('''n must be >= 0'''				)

							__lowercase      =    []
							for num in range(len(UpperCamelCase__				)				):
														__lowercase      =    0
														while 2 * i * i <= odd_composites[num]:
																					__lowercase      =    odd_composites[num] - 2 * i * i
																					if is_prime(UpperCamelCase__				):
																												break
																					i += 1
														else:
																					list_nums.append(odd_composites[num]				)
																					if len(UpperCamelCase__				) == n:
																												return list_nums

							return []







def 		_A(       )    -> int:
							'''simple docstring'''


							return compute_nums(1				)[0]


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












import itertools
import string
from collections.abc import Generator, Iterable







def 		_A(       UpperCamelCase__							:			Iterable[str]				,       UpperCamelCase__							:			int				)    -> Generator[tuple[str, ...], None, None]:
							'''simple docstring'''


							__lowercase      =    iter(UpperCamelCase__				)
							while True:
														__lowercase      =    tuple(itertools.islice(UpperCamelCase__				,       UpperCamelCase__				)				)
														if not chunk:
																					return
														yield chunk







def 		_A(       UpperCamelCase__							:			str				)    -> str:
							'''simple docstring'''


							__lowercase      =    ''''''.join([c.upper() for c in dirty if c in string.ascii_letters]				)
							__lowercase      =    ''''''

							if len(UpperCamelCase__				) < 2:
														return dirty

							for i in range(len(UpperCamelCase__				) - 1				):
														clean += dirty[i]

														if dirty[i] == dirty[i + 1]:
																					clean += "X"

							clean += dirty[-1]

							if len(UpperCamelCase__				) & 1:
														clean += "X"

							return clean







def 		_A(       UpperCamelCase__							:			str				)    -> list[str]:
							'''simple docstring'''


							__lowercase      =    '''ABCDEFGHIKLMNOPQRSTUVWXYZ'''
							# we're using a list instead of a '2d' array because it makes the math
							# for setting up the table and doing the actual encoding/decoding simpler
							__lowercase      =    []

							# copy key chars into the table if they are in `alphabet` ignoring duplicates
							for char in key.upper():
														if char not in table and char in alphabet:
																					table.append(UpperCamelCase__				)

    # fill the rest of the table in with the remaining alphabet chars
							for char in alphabet:
														if char not in table:
																					table.append(UpperCamelCase__				)

							return table







def 		_A(       UpperCamelCase__							:			str				,       UpperCamelCase__							:			str				)    -> str:
							'''simple docstring'''


							__lowercase      =    generate_table(UpperCamelCase__				)
							__lowercase      =    prepare_input(UpperCamelCase__				)
							__lowercase      =    ''''''

							# https://en.wikipedia.org/wiki/Playfair_cipher#Description
							for chara, chara in chunker(UpperCamelCase__				,       2				):
														__lowercase     ,     __lowercase      =    divmod(table.index(UpperCamelCase__				)				,       5				)
														__lowercase     ,     __lowercase      =    divmod(table.index(UpperCamelCase__				)				,       5				)

														if rowa == rowa:
																					ciphertext += table[rowa * 5 + (cola + 1) % 5]
																					ciphertext += table[rowa * 5 + (cola + 1) % 5]
														elif cola == cola:
																					ciphertext += table[((rowa + 1) % 5) * 5 + cola]
																					ciphertext += table[((rowa + 1) % 5) * 5 + cola]
														else:  # rectangle
																					ciphertext += table[rowa * 5 + cola]
																					ciphertext += table[rowa * 5 + cola]

							return ciphertext







def 		_A(       UpperCamelCase__							:			str				,       UpperCamelCase__							:			str				)    -> str:
							'''simple docstring'''


							__lowercase      =    generate_table(UpperCamelCase__				)
							__lowercase      =    ''''''

							# https://en.wikipedia.org/wiki/Playfair_cipher#Description
							for chara, chara in chunker(UpperCamelCase__				,       2				):
														__lowercase     ,     __lowercase      =    divmod(table.index(UpperCamelCase__				)				,       5				)
														__lowercase     ,     __lowercase      =    divmod(table.index(UpperCamelCase__				)				,       5				)

														if rowa == rowa:
																					plaintext += table[rowa * 5 + (cola - 1) % 5]
																					plaintext += table[rowa * 5 + (cola - 1) % 5]
														elif cola == cola:
																					plaintext += table[((rowa - 1) % 5) * 5 + cola]
																					plaintext += table[((rowa - 1) % 5) * 5 + cola]
														else:  # rectangle
																					plaintext += table[rowa * 5 + cola]
																					plaintext += table[rowa * 5 + cola]

							return plaintext






