





"""simple docstring"""






from __future__ import annotations

import math
from collections import Counter
from string import ascii_lowercase

def       __A (     a_  :str)						->						None:
    __a	:  Union[str, Any]         =					analyze_text(a_)
    __a	:  List[str]         =					list(''' ''' + ascii_lowercase)
    # what is our total sum of probabilities.
    __a	:  Any         =					sum(single_char_strings.values())

    # one length string
    __a	:  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:
            __a	:  Dict         =					single_char_strings[ch]
            __a	:  List[str]         =					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
    __a	:  int         =					sum(two_char_strings.values())
    __a	:  Tuple         =					0
    # for each alpha (two in size) calculate entropy.
    for cha in my_alphas:
        for cha in my_alphas:
            __a	:  Any         =					cha + cha
            if sequence in two_char_strings:
                __a	:  str         =					two_char_strings[sequence]
                __a	:  Dict         =					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       __A (     a_  :str)						->						tuple[dict, dict]:
    __a	:  Union[str, Any]         =					Counter()  # type: ignore
    __a	:  Any         =					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       __A (     )						->						Dict:
    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()






"""simple docstring"""






def       __A (     a_  :int = 1_00_00_00)						->						int:
				__a	:  Tuple         =					[i - 1 for i in range(limit + 1)]

				for i in range(2				,    limit + 1):
								if phi[i] == i - 1:
												for j in range(2 * i				,    limit + 1				,    a_):
																phi[j] -= phi[j] // i

				return sum(phi[2 : limit + 1])


if __name__ == "__main__":
		print(solution())