

"""simple docstring"""






def    UpperCamelCase       (      _lowerCAmelCase  :    Optional[int] = 2000000			)					->      str:
	_UpperCAmelCase     :				List[str]          =       [0 for i in range(n + 1			)]
	_UpperCAmelCase     :				List[Any]          =       1
	_UpperCAmelCase     :				Optional[int]          =       1

	for i in range(2,	int(n**0.5			) + 1			):
		if primality_list[i] == 0:
			for j in range(i * i,	n + 1,	A_			):
				_UpperCAmelCase     :				Any          =       1
	_UpperCAmelCase     :				Union[str, Any]          =       0
	for i in range(A_			):
		if primality_list[i] == 0:
			sum_of_primes += i
	return sum_of_primes


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








"""simple docstring"""





from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase

def     __SCREAMING_SNAKE_CASE    ( A_					):
	lowerCAmelCase__							,lowerCAmelCase__      :		Dict    							=      analyze_text(A_					)
	lowerCAmelCase__      :		Any    							=      list(''' ''' + ascii_lowercase					)
	# what is our total sum of probabilities.
	lowerCAmelCase__      :		Optional[Any]    							=      sum(single_char_strings.values()					)

	# one length string
	lowerCAmelCase__      :		int    							=      0
	# for each alpha we go in our dict and if it is in it we calculate entropy
	for ch in my_alphas:
		if ch in single_char_strings:
			lowerCAmelCase__      :		Union[str, Any]    							=      single_char_strings[ch]
			lowerCAmelCase__      :		Dict    							=      my_str / all_sum
			my_fir_sum += prob * math.loga(A_					)  # entropy formula.

    # print entropy
	print(f'{round(-1 * my_fir_sum					):.1f}'					)

	# two len string
	lowerCAmelCase__      :		List[Any]    							=      sum(two_char_strings.values()					)
	lowerCAmelCase__      :		Optional[int]    							=      0
	# for each alpha (two in size) calculate entropy.
	for cha in my_alphas:
		for cha in my_alphas:
			lowerCAmelCase__      :		int    							=      cha + cha
			if sequence in two_char_strings:
				lowerCAmelCase__      :		Optional[Any]    							=      two_char_strings[sequence]
				lowerCAmelCase__      :		int    							=      int(A_					) / all_sum
				my_sec_sum += prob * math.loga(A_					)

    # print second entropy
	print(f'{round(-1 * my_sec_sum					):.1f}'					)

	# print the difference between them
	print(f'{round((-1 * my_sec_sum) - (-1 * my_fir_sum)					):.1f}'					)

def     __SCREAMING_SNAKE_CASE    ( A_					):
	lowerCAmelCase__      :		List[str]    							=      Counter()  # type: ignore
	lowerCAmelCase__      :		Optional[int]    							=      Counter()  # type: ignore
	single_char_strings[text[-1]] += 1

	# first case when we have space at start.
	two_char_strings[" " + text[0]] += 1
	for i in range(0		,	len(A_					) - 1					):
		single_char_strings[text[i]] += 1
		two_char_strings[text[i : i + 2]] += 1
	return single_char_strings, two_char_strings

def     __SCREAMING_SNAKE_CASE    ( ):
	import doctest

	doctest.testmod()
	# text = (
	#     "Had repulsive dashwoods suspicion sincerity but advantage now him. Remark "
	#     "easily garret nor nay. Civil those mrs enjoy shy fat merry. You greatest "
	#     "jointure saw horrible. He private he on be imagine suppose. Fertile "
	#     "beloved evident through no service elderly is. Blind there if every no so "
	#     "at. Own neglected you preferred way sincerity delivered his attempted. To "
	#     "of message cottage windows do besides against uncivil.  Delightful "
	#     "unreserved impossible few estimating men favourable see entreaties. She "
	#     "propriety immediate was improving. He or entrance humoured likewise "
	#     "moderate. Much nor game son say feel. Fat make met can must form into "
	#     "gate. Me we offending prevailed discovery. "
	# )

	# calculate_prob(text)


if __name__ == "__main__":
							main()




