s3100-2011/lectures/l2 
[ganesh@line-ganesh l2]$ python3
python3
Python 3.2.1 (v3.2.1:ac1f7e5c0510, Jul  9 2011, 01:03:53) 
[GCC 4.2.1 (Apple Inc. build 5666) (dot 3)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> def Phi():
    """This is the ZERO language for concatenation (viewed as multiplication)
    """
    return set() # Don't write it as {} because this is ambiguous - dict/set 

def Phi():
...     """This is the ZERO language for concatenation (viewed as multiplication)
...     """
...     return set() # Don't write it as {} because this is ambiguous - dict/set 
... 
>>> Phi()
Phi()
set()
>>> def Unit():
    """This is the UNIT language for concatenation (viewed as multiplication)
    """
    return {""} # Set with epsilon

def Unit():
...     """This is the UNIT language for concatenation (viewed as multiplication)
...     """
...     return {""} # Set with epsilon
... 
>>> Unit()
Unit()
{''}
>>> def cat(L1,L2):
    """Concat two languages
    cat(a,b) --> set(['abab', 'bc22', 'ab11', 'ab22', 'bcab', 'bc11']) 
    where a=set(['ab', 'bc']) b=set(['11', 'ab', '22'])
    """
    return set({x+y for x in L1 for y in L2})

def cat(L1,L2):
...     """Concat two languages
...     cat(a,b) --> set(['abab', 'bc22', 'ab11', 'ab22', 'bcab', 'bc11']) 
...     where a=set(['ab', 'bc']) b=set(['11', 'ab', '22'])
...     """
...     return set({x+y for x in L1 for y in L2})
... 
>>> cat(Phi(), Unit())
cat(Phi(), Unit())
set()
>>> cat(Unit(), Unit())
cat(Unit(), Unit())
{''}
>>> cat(Phi(), {"aaa", "aba"})
cat(Phi(), {"aaa", "aba"})
set()
>>> cat(Unit(), {"aaa", "aba"})
cat(Unit(), {"aaa", "aba"})
{'aba', 'aaa'}
>>> def exp(L,n):
    """Exponentiate a language
    exp(a,2) --> set(['abab', 'bcab', 'bcbc', 'abbc']) where  a = set(['ab', 'bc'])
    """
    return Unit() if n == 0 else cat(L, exp(L, n-1))

def exp(L,n):
...     """Exponentiate a language
...     exp(a,2) --> set(['abab', 'bcab', 'bcbc', 'abbc']) where  a = set(['ab', 'bc'])
...     """
...     return Unit() if n == 0 else cat(L, exp(L, n-1))
... 
>>> exp({'aa','ab'}, 23
exp({'aa','ab'}, 23
... )
)


  C-c C-cTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 6, in cat
  File "<stdin>", line 6, in <setcomp>
KeyboardInterrupt
>>> 
>>> exp({'aa','ab'}, 23)
exp({'aa','ab'}, 23)
  C-c C-cTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 6, in cat
KeyboardInterrupt
>>> ^D
[ganesh@line-ganesh l2]$ !!
!!
python3
Python 3.2.1 (v3.2.1:ac1f7e5c0510, Jul  9 2011, 01:03:53) 
[GCC 4.2.1 (Apple Inc. build 5666) (dot 3)] on darwin
Type "help", "copyright", "credits" or "license" for more information.
>>> exp
exp
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
NameError: name 'exp' is not defined
>>> def exp(L,n):
    """Exponentiate a language
    exp(a,2) --> set(['abab', 'bcab', 'bcbc', 'abbc']) where  a = set(['ab', 'bc'])
    """
    return Unit() if n == 0 else cat(L, exp(L, n-1))

def exp(L,n):
...     """Exponentiate a language
...     exp(a,2) --> set(['abab', 'bcab', 'bcbc', 'abbc']) where  a = set(['ab', 'bc'])
...     """
...     return Unit() if n == 0 else cat(L, exp(L, n-1))
... 
>>> def cat(L1,L2):
    """Concat two languages
    cat(a,b) --> set(['abab', 'bc22', 'ab11', 'ab22', 'bcab', 'bc11']) 
    where a=set(['ab', 'bc']) b=set(['11', 'ab', '22'])
    """
    return set({x+y for x in L1 for y in L2})

def cat(L1,L2):
...     """Concat two languages
...     cat(a,b) --> set(['abab', 'bc22', 'ab11', 'ab22', 'bcab', 'bc11']) 
...     where a=set(['ab', 'bc']) b=set(['11', 'ab', '22'])
...     """
...     return set({x+y for x in L1 for y in L2})
... 
>>> def Phi():
    """This is the ZERO language for concatenation (viewed as multiplication)
    """
    return set() # Don't write it as {} because this is ambiguous - dict/set 

def Phi():
...     """This is the ZERO language for concatenation (viewed as multiplication)
...     """
...     return set() # Don't write it as {} because this is ambiguous - dict/set 
... 
>>> def Unit():
    """This is the UNIT language for concatenation (viewed as multiplication)
    """
    return {""} # Set with epsilon

def Unit():
...     """This is the UNIT language for concatenation (viewed as multiplication)
...     """
...     return {""} # Set with epsilon
... 
>>> cat({'a','b'}, {'0','1'})
cat({'a','b'}, {'0','1'})
{'a1', 'a0', 'b0', 'b1'}
>>> exp({'a','b'}, 22)
exp({'a','b'}, 22)


  C-c C-c

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'bbabbaaabbaabaababaabb', 'bbabbaaabbaabaababaaba', 'baaaabbabbbaaaabaabaab', 'baaaabbabbbaaaabaabaaa', 'abaaaabababbbbaaaaabba', 'abaaaabababbbbaaaaabbb', 'bbbbbaababababaabaaaba', 'bbbbbaababababaabaaabb', 'ababbaaaababbabbbabaab', 'ababbaaaababbabbbabaaa', 'bbaaaabbaabbbaabbabbbb', 'bbaaaabbaabbbaabbabbba', 'abaaabbbbbaababaabbabb', 'abaaabbbbbaababaabbaba', 'aaaaaaaabbababbabbaaba', 'aaaaaaaabbababbabbaabb', 'aababbaabbbaabaaaaabba', 'aababbaabbbaabaaaaabbb', 'aabababbbabbababbaabbb', 'aabababbbabbababbaabba', 'abbaaaaaaaabbaabbabaab', 'abbaaaaaaaabbaabbabaaa', 'bbaabaabbbbaaaaaabaaaa', 'aaabbbaaaababaabaabbab', 'abbabaaaababbbbbabbbab', 'abbabaaaababbbbbabbbaa', 'aaaaabaabaaaabbababaaa', 'abbbbbbaaaaaabbbabbaaa', 'abbbbbbaaaaaabbbabbaab', 'aaaaabaabaaaabbababaab', 'baabaaaabaabaaaababbbb', 'baabaaaabaabaaaababbba', 'baaaabaabbbbbaaaaabaab', 'baaaabaabbbbbaaaaabaaa', 'aaaababbbbaaaaaaabaaab', 'aaaaababaabbbbbababbab', 'aaaaababaabbbbbababbaa', 'aaaababbbbaaaaaaabaaaa', 'aaaaabbbabbaaaaaaaaaab', 'aaaaabbbabbaaaaaaaaaaa', 'bbababaaabbaabbaabaaba', 'bbababaaabbaabbaabaabb', 'aaabbababbbbbbaaaabaaa', 'aaabbababbbbbbaaaabaab', 'aaabbbaabababbabbaaaba', 'aaabbbaabababbabbaaabb', 'babaabbaaaababbaaabaab', 'babaabbaaaababbaaabaaa', 'aaaaaabaabbbabbabbaaaa', 'abbabbbababaabbbaabbba', 'aaaaaabaabbbabbabbaaab', 'babaabbaabaaabbabbaaaa', 'babaabbaabaaabbabbaaab', 'baaaabbbabaababababaab', 'babbaaabbbbaaaabaaaabb', 'abbaaabbbabbaaabbaaaaa', 'abbaaabbbabbaaabbaaaab', 'abaabbaabbbbaabbbaabba', 'abaabbaabbbbaabbbaabbb', 'baaaabbbabaababababaaa', 'bbbaabaaaaaabbbabbabbb', 'bbbaababbbbbaaaaababab', 'bbbaababbbbbaaaaababaa', 'abaaabbbaaaabbabaaaaab', 'abaaabbbaaaabbabaaaaaa', 'babaababbbbbbabbbabbaa', 'baababbbabbababbaaabaa', 'baababbbabbababbaaabab', 'babaababbbbbbabbbabbab', 'bbbababaaaaaabaaabbaab', 'bbbababaaaaaabaaabbaaa', 'babaaaaabbbbaaabaaabba', 'babaaaaabbbbaaabaaabbb', 'bbabaaaaabbaaaabaaaaba', 'bbabaaaaabbaaaabaaaabb', 'abbaaabaabbabbbaaababb', 'abbaaabaabbabbbaaababa', 'ababaababbabbaabbbaaaa', 'ababaababbabbaabbbaaab', 'abbaabaaabbbbaabbabbba', 'abaaabbaabaababbbbbbaa', 'abaaabbaabaababbbbbbab', 'abbaabaaabbbbaabbabbbb', 'aaaabababbbbbabaaaaaba', 'bbbaabbbaabaaabbaababa', 'bbbaabbbaabaaabbaababb', 'abababbabbaabbabbabbbb', 'abababbabbaabbabbabbba', 'aaaaabbaabbabaabaababb', 'aaaaabbaabbabaabaababa', 'bbaaabbaaabaabbaabaaaa', 'baabbaaaabaaabbbbabbab', 'baabbaaaabaaabbbbabbaa', 'bbaaabbaaabaabbaabaaab', 'baababababbbbbbabbbabb', 'baababababbbbbbabbbaba', 'aabbbaabbabbbbabaabbba', 'aabbbaabbabbbbabaabbbb', 'aabbabaaabaabbbaabbbaa', 'aabbabaaabaabbbaabbbab', 'babbabbbaabaaabbbbbbba', 'babbabbbaabaaabbbbbbbb', 'abaabbbabbbbabbbaaaaaa', 'abaabbbabbbbabbbaaaaab', 'bbaaabaabbababbaaaabba', 'bbaaabaabbababbaaaabbb', 'babaabbbaaaababbaaaaab', 'bbaaabbabaabbbbbbabbaa', 'bbaaabbabaabbbbbbabbab', 'babaabbbaaaababbaaaaaa', 'baabbbbbbaabbbbbbbaaab', 'baabbbbbbaabbbbbbbaaaa', 'abbaaabaabababaaaabaaa', 'abbaaabaabababaaaabaab', 'baabbbbbbaaaaabbbaaaaa', 'aaaabbaababbbbaabaabba', 'aababaabbbaaaaaabbbaab', 'aababaabbbaaaaaabbbaaa', 'aaaabbaababbbbaabaabbb', 'abbbaababbababbbbabaaa', 'abbbaababbababbbbabaab', 'abaaabbabbbbabaaaabaab', 'abaaabbabbbbabaaaabaaa', 'abbabbbbbaaababbaaabab', 'abbabbbbbaaababbaaabaa', 'babbabbbabbbbbbbbabbba', 'babbabbbabbbbbbbbabbbb', 'bbabbbabbbbaaabbabbbba', 'bbabbbabbbbaaabbabbbbb', 'babbbabbbaabbbabbbabab', 'babbbabbbaabbbabbbabaa', 'aaabbbaabbaababbaaaaaa', 'aaabbbaabbaababbaaaaab', 'babbabaabbaaabababbbbb', 'babbabaabbaaabababbbba', 'abbbaaaaaaaababbabbbab', 'abbbaaaaaaaababbabbbaa', 'abbaabbabbbaaaaabababb', 'abbaabbabbbaaaaabababa', 'abaaabaaabbbbbabbabaaa', 'aabbabbaaabbbbabaabaab', 'aabbabbaaabbbbabaabaaa', 'abaaabaaabbbbbabbabaab', 'babaabbbabababaabbbaab', 'baababababaaababaabbbb', 'abaaabababababaababaaa', 'abaaabababababaababaab', 'aabbaabbabbbbbbabbbbbb', 'aaaaababaabaabaabaabbb', 'aabbaabbabbbbbbabbbbba', 'bbbabaababbaabbabbbbba', 'abbabbababaaaabbbbbbab', 'abbabbababaaaabbbbbbaa', 'aabbbababbaabaababaaba', 'aabbbababbaabaababaabb', 'abaaaababbbbabbabbabaa', 'abaaaababbbbabbabbabab', 'abaabbbabbababaabbbaba', 'abaabbbabbababaabbbabb', 'aaabaababbaaabaaaaabaa', 'bbbbabbaabbaababbbbbba', 'bbbbabbaabbaababbbbbbb', 'aaabaababbaaabaaaaabab', 'aabbbbbbabbabaaaabbbaa', 'aabbbbbbabbabaaaabbbab', 'aabaaabaaaababbbabbaba', 'aabaaabaaaababbbabbabb', 'abbabaaaababbabaabaaaa', 'abbabaaaababbabaabaaab', 'aababaabbaabbbabbbaabb', 'baabbaabbbaabaababbaab', 'aababaabbaabbbabbbaaba', 'bbabaaaaaaaaaabbbbbaba', 'bbabaaaaaaaaaabbbbbabb', 'aaabbabbabbabbaabaabbb', 'aaabbabbabbabbaabaabba', 'aabaaabbabbbaabababbba', 'aabaaabbabbbaabababbbb', 'abbabbabaaabbbababaaab', 'abbabbabaaabbbababaaaa', 'aabbbbabaaabaabbbabaab', 'aabbbbabaaabaabbbabaaa', 'abbaabbaaaaababaababaa', 'abbaabbaaaaababaababab', 'babaabbabaabababaababa', 'aabbbabaabbaabbaabbaba', 'aabbbabaabbaabbaabbabb', 'babaabbabaabababaababb', 'aaabaabbaabaaaabbbbaba  C-c C-c', 'aaabaabbaabaaaabbbbabb', 'bbabababaababaabbbbbab', 'bbabababaababaabbbbbaa', 'abaababbabbabaababbbba', 'aabaaaabaabbaabbabaaba', 'aabaaaabaabbaabbabaabb', 'baabbbbaababbabbbbaaaa', 'abbabbaabbaaabbaabbaba', 'aabbbbbabbaaababbaaabb', 'aabbbbbabbaaababbaaaba', 'aaabaaabbbbbbabaaaaaaa', 'abbbababbbbbbbabbbabaa', 'ababbbbaabaaabbaaababa', 'bbabbbbabaaaabbbbbbabb', 'ababbabababbbbaabaabbb', 'abbbbbbaabbabaaabbabbb', 'abaabaabbabaaabbabbbab', 'abaabaabbabaaabbabbbaa', 'aaabbbababaaababbaaaaa', 'aaabbbababaaababbaaaab', 'aabbbaaaaaaaaabbbbabba', 'aabbbaaaaaaaaabbbbabbb', 'aabbbbbabbabbbbaabbbbb', 'aabbbbbabbabbbbaabbbba', 'bbbbbbaabbbabbabbbbaab', 'bbbbbbbaaaaaaaabaabbab', 'bbbbbbbaaaaaaaabaabbaa', 'bbbbbbaabbbabbabbbbaaa', 'baabaabbbbaaabbaababba', 'baabaabbbbaaabbaababbb', 'babbaaabababababbbabaa', 'babbaaabababababbbabab', 'baabaaaabaababbbabbaab', 'ababbbbabbbaaabaababba', 'baabaaaabaababbbabbaaa', 'babbbaabbbbbbbbbbaabbb', 'babbbaabbbbbbbbbbaabba', 'abbaabbaababbaaababbab', 'abbaabbaababbaaababbaa', 'abaaabTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
KeyboardInterrupt
>>> 

>>> 
>>> 
>>> exp({'0','1'}, 2)
exp({'0','1'}, 2)
{'11', '10', '00', '01'}
>>> exp({'0','1'}, 2)
exp({'0','1'}, 2)
{'11', '10', '00', '01'}
>>> exp({'0','1'}, 22)
exp({'0','1'}, 22)
  C-c C-cTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 5, in exp
  File "<stdin>", line 5, in exp
  File "<stdin>", line 6, in cat
KeyboardInterrupt
>>> exp({'0','1'}, 2)
exp({'0','1'}, 2)
{'11', '10', '00', '01'}
>>> exp({'0','1'}, 10)
exp({'0','1'}, 10)
{'0101001001', '0101001000', '0110010001', '0110010000', '1001001001', '1001001000', '0101010010', '0101010011', '0011111111', '0011111110', '1110101111', '1110101110', '1101111000', '1101111001', '1100101110', '1100101111', '1000100011', '1000010110', '1000010111', '1011001110', '1011001111', '1011110001', '1111111001', '1011110000', '1110000010', '1110000011', '0010000010', '0010000011', '1010001111', '1010001110', '1011101100', '1011101101', '1111100111', '0010111110', '0010111111', '0110100101', '0011110110', '0011110111', '0110001001', '0110001000', '1111011110', '1111011111', '0000111111', '0000111110', '1010100001', '1010100000', '0011011000', '0011011001', '1001000101', '1001000100', '0110011101', '0110011100', '0111010011', '0111010010', '0001101100', '0001101101', '1101011100', '1101011101', '1000001101', '1000001100', '0111001000', '0111001001', '0010011100', '0010011101', '0000110011', '0000110010', '1011110111', '0001110111', '0001110110', '1011110110', '1110001110', '1110001111', '0010001110', '0010001111', '1000111001', '0001100000', '0001100001', '1000110111', '1000110110', '0110100000', '0100100110', '0100100111', '0100111101', '0100111100', '1010000101', '1010000100', '0011001100', '0011001101', '1101101100', '1101101101', '0110000101', '0110000100', '0001111111', '1111001010', '1111001011', '1110110100', '1110110101', '1100110011', '1100110010', '1011011010', '1011011011', '1100111010', '0011010110', '1101000100', '1101000101', '1111110000', '1110111111', '1001010001', '1001010000', '0000100001', '0000100000', '1101100000', '1101100001', '1000011001', '1000011000', '0001001101', '0001001100', '0010110100', '1010111111', '1010111110', '1000101111', '1000101110', '0001111011', '0001111010', '1111000011', '1111000010', '1001011101', '1001011100', '0000011110', '1101111101', '0000011111', '1101111100', '0010100110', '0010100111', '1000111011', '1000111010', '1111010001', '1111010000', '0011000000', '0011000001', '1011000001', '1011000000', '1100100001', '1100100000', '1010011100', '0000001011', '0101010001', '0101010000', '1110111000', '1110111001', '0011011011', '0011011010', '1101001000', '1101001001', '1011010110', '1011010111', '1001111100', '1011100001', '1100111100', '1100101101', '1100101100', '0001111110', '1000010101', '1011111111', '0110010100', '1011001100', '1001001100', '1001001101', '1110011010', '1110011011', '0010000001', '0010000000', '1110000001', '1110000000', '1000000100', '1000000101', '1011101111', '1011101110', '0010111101', '0010111100', '0100110000', '0111000010', '0111000011', '0011110101', '0011110100', '1000100000', '1000100001', '1000111110', '1000111111', '1111011101', '1111011100', '1000001000', '1000001001', '1010001100', '1010001101', '0110001100', '0110001101', '0001101111', '0001101110', '1101011111', '1101011110', '0111001011', '0111001010', '0111110010', '0111110011', '0010011111', '0010011110', '1010100100', '1010100101', '1011100100', '1001101110', '1001101111', '0110011000', '0110011001', '1110010110', '1110010111', '0110110000', '1110001101', '1110001100', '0010001101', '0110110001', '0010110110', '0001100011', '0001100010', '1010010010', '1010010011', '0100100101', '0100100100', '0101110000', '0101110001', '0011001111', '1011101001', '1011101000', '0000001111', '1101101111', '1101101110', '0000001110', '1111001001', '1111001000', '1110110111', '1110110110', '1011011001', '1011011000', '1100111001', '1100111000', '1101000111', '1101000110', '0011010010', '0011010011', '0100111000', '0100111001', '1010000000', '1010000001', '0110000000', '0110000001', '1011111110', '1101100011', '1101100010', '0110100010', '1101101010', '1101101011', '0110100011', '0001011100', '0101100100', '0111111110', '0111111111', '0101100101', '1010011011', '1010011010', '1011100101', '1001010100', '1001010101', '0000010100', '0000010101', '1100100100', '1100100101', '0010100101', '0010100100', '1000011100', '1000011101', '0001001000', '0001001001', '0011111001', '0011111000', '1111110101', '0110101101', '0110101100', '0011000011', '0011000010', '1001011000', '1001011001', '0100000010', '0100000011', '1110111011', '1110111010', '0000000101', '0000000100', '1101001011', '1101001010', '0010001100', '1000010100', '1111010100', '1111010101', '0011101000', '0011101001', '0010111000', '0010111001', '0110010111', '0110010110', '1001001111', '1001001110', '1001100001', '1001100000', '0101010100', '0101010101', '1110011001', '0111011011', '0001010000', '0001010001', '1000000111', '1000000110', '0001000010', '0001000011', '0111000001', '0111000000', '1100001010', '1100001011', '1000010000', '1000010001', '1011001000', '1011001001', '0100011010', '0100011011', '1100010111', '0010000100', '0010000101', '1100010110', '1110000100', '1110000101', '1000001011', '1000001010', '1000000010', '1000000011', '1110100000', '1110100001', '1100011110', '1100011111', '0011110000', '0011110001', '0110001111', '0110001110', '0100001110', '0100001111', '1101110000', '0111110001', '0111110000', '1010100111', '1010100110', '1001101101', '1001101100', '0110011011', '0110011010', '1110010101', '1110010100', '1101101001', '1101101000', '1010010001', '1010010000', '1010011101', '1011100110', '1011100111', '1100000110', '1100000111', '0101110011', '0101110010', '0101111010', '0101111011', '1110001000', '1110001001', '0010001000', '0010001001', '0100010110', '0100010111', '0111101010', '0111101011', '0010101100', '0010101101', '0010110101', '0110110101', '0110110100', '0011001110', '1011011100', '1010101010', '0100100000', '0100100001', '0011010001', '0011010000', '0100111011', '0100111010', '1100111101', '1010000011', '1010000010', '0110000011', '0110000010', '0100110010', '0100110011', '1010001010', '1010001011', '0111100110', '0111100111', '1111001100', '1111001101', '1001111010', '1001111011', '0111111101', '0111111100', '0001011111', '0001011110', '1010101011', '0000001101', '1101110010', '1101110011', '1000100110', '1111100010', '1111100011', '1001010111', '1001010110', '0000010111', '0000010110', '1100100111', '1100100110', '0000001100', '0001001011', '0001001010', '1000011111', '1000011110', '0101100010', '0101100011', '0101110110', '0101110111', '0101000110', '0101000111', '1001011011', '1001011010', '0100000001', '0100000000', '0010100000', '0010100001', '0000001001', '0000001000', '0010110010', '0010110011', '1111010111', '1111010110', '0110110110', '0110110111', '1011000111', '0011101011', '1011000110', '0011100010', '0011100011', '1010110000', '1010110001', '0111011001', '0111011000', '0101010111', '0101010110', '0110101001', '0001010011', '0001010010', '1011010000', '1011010001', '0001000001', '0001000000', '1111101110', '1111101111', '0000011011', '0000011010', '1100001001', '1100001000', '1000101010', '1011111000', '1000010010', '0100011001', '0100011000', '1110011100', '1110011101', '0101011101', '0101011100', '0010000111', '0010000110', '0010111011', '0010111010', '0101101111', '1000000001', '1000000000', '1100011101', '1100011100', '0111000100', '0111000101', '0110011110', '1110100011', '1100010000', '0011110011', '0011110010', '0100001101', '0100001100', '0000000000', '0110111100', '0110111101', '0100101010', '0100101011', '0011101110', '0011101111', '1011000010', '1111111010', '1111111011', '0111110100', '0111110101', '1011000011', '1100000101', '1100000100', '1001101000', '1001101001', '0101111001', '0101111000', '0100010101', '0100010100', '1110010000', '1110010001', '0010001011', '0010001010', '0111101001', '0111101000', '1110001011', '1110001010', '0010101111', '0010101110', '1010010100', '1010010101', '0100100011', '0100100010', '0001011101', '1011010011', '1010011110', '0000101110', '0000101111', '1011010010', '1010001001', '1010001000', '1111001111', '1111001110', '1001111001', '1001111000', '0111100101', '0111100100', '1101110001', '1100111110', '1010101000', '1011011111', '1011011110', '1010101001', '0001011010', '0001011011', '1111100001', '1111100000', '0100101111', '0100101110', '0101100001', '0101100000', '1111110110', '1111110111', '0111111000', '0111111001', '1101011010', '1110100100', '0101110101', '0101110100', '0101101000', '0101101001', '0010100011', '0010100010', '1110011000', '1110101010', '1110101011', '0010101010', '0010101011', '0010110001', '0010110000', '0011111010', '0011111011', '0110101011', '0110101010', '1100010100', '1100010101', '1001100100', '0011100001', '0011100000', '0100000100', '0100000101', '1010110011', '1010110010', '1001110101', '1001110100', '1001100101', '0011001001', '0000000011', '0000000010', '1010101101', '1010101100', '0101000101', '0101000100', '1111101101', '1111101100', '0011010111', '1000100111', '1100111011', '1011000100', '1011000101', '1110011111', '1110011110', '1011111011', '1011111010', '0101101101', '0111011101', '1001100111', '1001100110', '0000111010', '0000111011', '0001000100', '0001000101', '0111000111', '0111000110', '1000010011', '0101101100', '1100001100', '1100001101', '1101010000', '1101010001', '0100011100', '0100011101', '1110100110', '1110100111', '0111010110', '0111010111', '0101011000', '0101011001', '1111111111', '0000110110', '0000110111', '0110111111', '0110111110', '1100011000', '1100011001', '0011101101', '0011101100', '0001110010', '0001110011', '0011101010', '0100001000', '0100001001', '0111101100', '0111101101', '1000100010', '0111110111', '0111110110', '1000110010', '1000110011', '1001101011', '1001101010', '0010010000', '0010010001', '1110010011', '1110010010', '1100110110', '1100110111', '1010010111', '1010010110', '1001110110', '1001110111', '1111111110', '1100000000', '1100000001', '0000101101', '0000101100', '0101111100', '0101111101', '0100010000', '1111111000', '0110110011', '0110110010', '1010111010', '1010111011', '0110111010', '0110111011', '0000011100', '0110100001', '1000101011', '0001011001', '0001011000', '1111000110', '1111000111', '0100110100', '0100110101', '0000001010', '0000000001', '1110000111', '1011100000', '1111110100', '0111100000', '0111100001', '1101110100', '1101110101', '0111111011', '0111111010', '1011110010', '1011110011', '0101001100', '0101001101', '1111100100', '1111100101', '0100101100', '0100101101', '0010101001', '0010101000', '1110101001', '1110101000', '0011011110', '0011011111', '1101111110', '1101111111', '1001000000', '1001000001', '0101000000', '0101000001', '1111101000', '1111101001', '0100000111', '0100000110', '1010110110', '1010110111', '1011101010', '1011101011', '0100010001', '1011010101', '1011010100', '0011100100', '0011100101', '0111011111', '0111011110', '1001110000', '1001110001', '1011001011', '1011001010', '0000111001', '0000111000', '0001000111', '0001000110', '0100101001', '0100101000', '1100001111', '1100001110', '1101010011', '1101010010', '1110100101', '1101011011', '0101011011', '0101011010', '0111010101', '0111010100', '0100011111', '0100011110', '0111001110', '0111001111', '0001101010', '0001101011', '1011111001', '0000110101', '0000110100', '1100011011', '1100011010', '1100010010', '1100010011', '0001110001', '0001110000', '0000100100', '0000100101', '0100001011', '0100001010', '0001100110', '0001100111', '0101101110', '1000110001', '1000110000', '1110110010', '1110000110', '1110110011', '0011001010', '0011001011', '0010010011', '0010010010', '0010011010', '0010011011', '1111111100', '1111111101', '1100110101', '1100110100', '1010011000', '1101000010', '1101000011', '1010011001', '1100000011', '1100000010', '0101111111', '0101111110', '0100010011', '0100010010', '0111101111', '0111101110', '1101100110', '1101100111', '0010010110', '1011111100', '0110111001', '0110111000', '1010111001', '1010011111', '1000101001', '1000101000', '0111011010', '0001111101', '0001111100', '0100110111', '0000101001', '1111000101', '1111000100', '1011100011', '1011100010', '0111100011', '0111100010', '1101110111', '1101110110', '0000010001', '0000010000', '1000111101', '1000111100', '0110100100', '1111100110', '0011000110', '0011000111', '0110101110', '0101001111', '0101001110', '0110101111', '1110100010', '0011011101', '0011011100', '1110111110', '1111110001', '0101100111', '0101100110', '1111011000', '1111011001', '1101001110', '1101001111', '1100101000', '1100101001', '0101000011', '0101000010', '1111101011', '1111101010', '1001000011', '1001000010', '1001001010', '1001001011', '0101001010', '0101001011', '0110010010', '0110010011', '1101010110', '0100110001', '1101010111', '1110101100', '1110101101', '1010110101', '1010110100', '0011111100', '0011111101', '1000101100', '1000100101', '1000100100', '1000101101', '0011100111', '0011100110', '0001010101', '0001010100', '1001110011', '1001110010', '1011011101', '0010010111', '1000001110', '1000001111', '0110001010', '0110001011', '0101101011', '0101101010', '0001101001', '0001101000', '1101011001', '1101011000', '0111001101', '0111001100', '1101111011', '0000111100', '0000111101', '1010100010', '1010100011', '0000000110', '0000000111', '1100010001', '0110011111', '1001000110', '1001000111', '0000100111', '0000100110', '0000011000', '0000011001', '0111010000', '0111010001', '1010111000', '0001010110', '1011111101', '0001100101', '0001100100', '0000110000', '0000110001', '1001111101', '0001010111', '0001110100', '0001110101', '1100111111', '0011001000', '1111110011', '0000011101', '1111110010', '0010011001', '0010011000', '1110110001', '1110110000', '1101000001', '1101000000', '1000110100', '1000110101', '0101011110', '0101011111', '0100111110', '0100111111', '0010110111', '0000101000', '0110101000', '0100110110', '1010000110', '1010000111', '0110000110', '0110000111', '1101010101', '1101010100', '0010010101', '0010010100', '1100110000', '1100110001', '0011010100', '0011010101', '1010101110', '1010101111', '1001100010', '1001100011', '0000101011', '0000101010', '1001010010', '1001010011', '1011001101', '0000100010', '0000100011', '0110010101', '1000011010', '1000011011', '0000010010', '0000010011', '1000111000', '0001001110', '0001001111', '1101111010', '1010111100', '1010111101', '0110100111', '0110100110', '0011000101', '0011000100', '0001111000', '0001111001', '1101100101', '1101100100', '1001111111', '1111000000', '1111000001', '1001111110', '1001011110', '1001011111', '1110111101', '1110111100', '0111011100', '1101001101', '1101001100', '1111011011', '1111011010', '1111010010', '1111010011', '1011110100', '1011110101', '1100101011', '1100101010', '1100100010', '1100100011'}
>>> exp({'0','1'}, 8)
exp({'0','1'}, 8)
{'10110001', '10110000', '00000100', '01000001', '01000000', '01111000', '01111001', '00010100', '00010101', '10011111', '10011110', '10111110', '10010101', '10010100', '10111111', '00011110', '00011111', '11001001', '11001000', '01100011', '01100010', '00110011', '00110010', '10100011', '10100010', '10101010', '10101011', '00001111', '00001110', '11111111', '11111110', '01010110', '01010111', '00111010', '00111011', '01101010', '01101011', '10001011', '10001010', '11100100', '11100101', '11101110', '11101111', '10110111', '10000010', '10000011', '00100100', '00100101', '11011110', '11011111', '00000011', '10110110', '00101110', '00101111', '01000111', '01000110', '10111000', '10111001', '01011100', '01011101', '00011000', '00011001', '11001111', '11001110', '11000101', '11000100', '10011010', '10011011', '01001101', '01001100', '11010100', '11010101', '11110101', '11110100', '01110001', '01110000', '01010000', '01010001', '01101100', '01101101', '10010000', '10010001', '00111100', '00111101', '00110110', '00110111', '10101100', '10101101', '01100110', '01100111', '00001010', '00001011', '10100110', '10100111', '11011000', '11011001', '11111010', '11111011', '10000100', '10000101', '01111101', '01111100', '00101000', '00101001', '00010001', '00010000', '10111101', '10111100', '11101000', '11101001', '00000000', '10001110', '10001111', '01011001', '01011000', '00000110', '00000111', '11000011', '11000010', '01000010', '01000011', '10011100', '10011101', '01001011', '01001010', '01110111', '01110110', '11110011', '11110010', '11001010', '11001011', '11010001', '11010000', '10001000', '10001001', '00100001', '00100000', '00110000', '00110001', '11100001', '11100000', '01100000', '01100001', '10100000', '10100001', '10110010', '00001100', '00001101', '11111100', '11111101', '01111011', '01111010', '10111011', '10111010', '00010111', '00010110', '00011101', '00011100', '10110100', '10110101', '01000100', '01000101', '00000101', '10101001', '10101000', '01101001', '01101000', '11001100', '11001101', '11000110', '11000111', '00111001', '00111000', '10110011', '01001110', '01001111', '11110110', '11110111', '11100111', '11100110', '11101101', '11101100', '01110010', '01110011', '10000001', '10000000', '00100111', '00100110', '00101101', '00101100', '00011011', '00011010', '01011111', '01011110', '00000001', '01010101', '01010100', '01110100', '01110101', '01111110', '01111111', '10011001', '10011000', '00010010', '00010011', '10010110', '11010111', '11010110', '10010111', '11011101', '11011100', '01010011', '01010010', '01011010', '01011011', '01101111', '01101110', '10010011', '10010010', '00000010', '11000000', '11000001', '00111111', '00111110', '00110101', '00110100', '10101111', '10101110', '01100101', '01100100', '10100101', '10100100', '00001001', '00001000', '01001000', '01001001', '11110000', '11110001', '11011011', '11011010', '11111001', '11111000', '11010010', '11010011', '10000111', '10000110', '10001101', '10001100', '00101011', '00101010', '00100010', '00100011', '11101011', '11101010', '11100010', '11100011'}
>>> exp({'0','1'}, 10)
exp({'0','1'}, 10)
{'0101001001', '0101001000', '0110010001', '0110010000', '1001001001', '1001001000', '0101010010', '0101010011', '0011111111', '0011111110', '1110101111', '1110101110', '1101111000', '1101111001', '1100101110', '1100101111', '1000100011', '1000010110', '1000010111', '1011001110', '1011001111', '1011110001', '1111111001', '1011110000', '1110000010', '1110000011', '0010000010', '0010000011', '1010001111', '1010001110', '1011101100', '1011101101', '1111100111', '0010111110', '0010111111', '0110100101', '0011110110', '0011110111', '0110001001', '0110001000', '1111011110', '1111011111', '0000111111', '0000111110', '1010100001', '1010100000', '0011011000', '0011011001', '1001000101', '1001000100', '0110011101', '0110011100', '0111010011', '0111010010', '0001101100', '0001101101', '1101011100', '1101011101', '1000001101', '1000001100', '0111001000', '0111001001', '0010011100', '0010011101', '0000110011', '0000110010', '1011110111', '0001110111', '0001110110', '1011110110', '1110001110', '1110001111', '0010001110', '0010001111', '1000111001', '0001100000', '0001100001', '1000110111', '1000110110', '0110100000', '0100100110', '0100100111', '0100111101', '0100111100', '1010000101', '1010000100', '0011001100', '0011001101', '1101101100', '1101101101', '0110000101', '0110000100', '0001111111', '1111001010', '1111001011', '1110110100', '1110110101', '1100110011', '1100110010', '1011011010', '1011011011', '1100111010', '0011010110', '1101000100', '1101000101', '1111110000', '1110111111', '1001010001', '1001010000', '0000100001', '0000100000', '1101100000', '1101100001', '1000011001', '1000011000', '0001001101', '0001001100', '0010110100', '1010111111', '1010111110', '1000101111', '1000101110', '0001111011', '0001111010', '1111000011', '1111000010', '1001011101', '1001011100', '0000011110', '1101111101', '0000011111', '1101111100', '0010100110', '0010100111', '1000111011', '1000111010', '1111010001', '1111010000', '0011000000', '0011000001', '1011000001', '1011000000', '1100100001', '1100100000', '1010011100', '0000001011', '0101010001', '0101010000', '1110111000', '1110111001', '0011011011', '0011011010', '1101001000', '1101001001', '1011010110', '1011010111', '1001111100', '1011100001', '1100111100', '1100101101', '1100101100', '0001111110', '1000010101', '1011111111', '0110010100', '1011001100', '1001001100', '1001001101', '1110011010', '1110011011', '0010000001', '0010000000', '1110000001', '1110000000', '1000000100', '1000000101', '1011101111', '1011101110', '0010111101', '0010111100', '0100110000', '0111000010', '0111000011', '0011110101', '0011110100', '1000100000', '1000100001', '1000111110', '1000111111', '1111011101', '1111011100', '1000001000', '1000001001', '1010001100', '1010001101', '0110001100', '0110001101', '0001101111', '0001101110', '1101011111', '1101011110', '0111001011', '0111001010', '0111110010', '0111110011', '0010011111', '0010011110', '1010100100', '1010100101', '1011100100', '1001101110', '1001101111', '0110011000', '0110011001', '1110010110', '1110010111', '0110110000', '1110001101', '1110001100', '0010001101', '0110110001', '0010110110', '0001100011', '0001100010', '1010010010', '1010010011', '0100100101', '0100100100', '0101110000', '0101110001', '0011001111', '1011101001', '1011101000', '0000001111', '1101101111', '1101101110', '0000001110', '1111001001', '1111001000', '1110110111', '1110110110', '1011011001', '1011011000', '1100111001', '1100111000', '1101000111', '1101000110', '0011010010', '0011010011', '0100111000', '0100111001', '1010000000', '1010000001', '0110000000', '0110000001', '1011111110', '1101100011', '1101100010', '0110100010', '1101101010', '1101101011', '0110100011', '0001011100', '0101100100', '0111111110', '0111111111', '0101100101', '1010011011', '1010011010', '1011100101', '1001010100', '1001010101', '0000010100', '0000010101', '1100100100', '1100100101', '0010100101', '0010100100', '1000011100', '1000011101', '0001001000', '0001001001', '0011111001', '0011111000', '1111110101', '0110101101', '0110101100', '0011000011', '0011000010', '1001011000', '1001011001', '0100000010', '0100000011', '1110111011', '1110111010', '0000000101', '0000000100', '1101001011', '1101001010', '0010001100', '1000010100', '1111010100', '1111010101', '0011101000', '0011101001', '0010111000', '0010111001', '0110010111', '0110010110', '1001001111', '1001001110', '1001100001', '1001100000', '0101010100', '0101010101', '1110011001', '0111011011', '0001010000', '0001010001', '1000000111', '1000000110', '0001000010', '0001000011', '0111000001', '0111000000', '1100001010', '1100001011', '1000010000', '1000010001', '1011001000', '1011001001', '0100011010', '0100011011', '1100010111', '0010000100', '0010000101', '1100010110', '1110000100', '1110000101', '1000001011', '1000001010', '1000000010', '1000000011', '1110100000', '1110100001', '1100011110', '1100011111', '0011110000', '0011110001', '0110001111', '0110001110', '0100001110', '0100001111', '1101110000', '0111110001', '0111110000', '1010100111', '1010100110', '1001101101', '1001101100', '0110011011', '0110011010', '1110010101', '1110010100', '1101101001', '1101101000', '1010010001', '1010010000', '1010011101', '1011100110', '1011100111', '1100000110', '1100000111', '0101110011', '0101110010', '0101111010', '0101111011', '1110001000', '1110001001', '0010001000', '0010001001', '0100010110', '0100010111', '0111101010', '0111101011', '0010101100', '0010101101', '0010110101', '0110110101', '0110110100', '0011001110', '1011011100', '1010101010', '0100100000', '0100100001', '0011010001', '0011010000', '0100111011', '0100111010', '1100111101', '1010000011', '1010000010', '0110000011', '0110000010', '0100110010', '0100110011', '1010001010', '1010001011', '0111100110', '0111100111', '1111001100', '1111001101', '1001111010', '1001111011', '0111111101', '0111111100', '0001011111', '0001011110', '1010101011', '0000001101', '1101110010', '1101110011', '1000100110', '1111100010', '1111100011', '1001010111', '1001010110', '0000010111', '0000010110', '1100100111', '1100100110', '0000001100', '0001001011', '0001001010', '1000011111', '1000011110', '0101100010', '0101100011', '0101110110', '0101110111', '0101000110', '0101000111', '1001011011', '1001011010', '0100000001', '0100000000', '0010100000', '0010100001', '0000001001', '0000001000', '0010110010', '0010110011', '1111010111', '1111010110', '0110110110', '0110110111', '1011000111', '0011101011', '1011000110', '0011100010', '0011100011', '1010110000', '1010110001', '0111011001', '0111011000', '0101010111', '0101010110', '0110101001', '0001010011', '0001010010', '1011010000', '1011010001', '0001000001', '0001000000', '1111101110', '1111101111', '0000011011', '0000011010', '1100001001', '1100001000', '1000101010', '1011111000', '1000010010', '0100011001', '0100011000', '1110011100', '1110011101', '0101011101', '0101011100', '0010000111', '0010000110', '0010111011', '0010111010', '0101101111', '1000000001', '1000000000', '1100011101', '1100011100', '0111000100', '0111000101', '0110011110', '1110100011', '1100010000', '0011110011', '0011110010', '0100001101', '0100001100', '0000000000', '0110111100', '0110111101', '0100101010', '0100101011', '0011101110', '0011101111', '1011000010', '1111111010', '1111111011', '0111110100', '0111110101', '1011000011', '1100000101', '1100000100', '1001101000', '1001101001', '0101111001', '0101111000', '0100010101', '0100010100', '1110010000', '1110010001', '0010001011', '0010001010', '0111101001', '0111101000', '1110001011', '1110001010', '0010101111', '0010101110', '1010010100', '1010010101', '0100100011', '0100100010', '0001011101', '1011010011', '1010011110', '0000101110', '0000101111', '1011010010', '1010001001', '1010001000', '1111001111', '1111001110', '1001111001', '1001111000', '0111100101', '0111100100', '1101110001', '1100111110', '1010101000', '1011011111', '1011011110', '1010101001', '0001011010', '0001011011', '1111100001', '1111100000', '0100101111', '0100101110', '0101100001', '0101100000', '1111110110', '1111110111', '0111111000', '0111111001', '1101011010', '1110100100', '0101110101', '0101110100', '0101101000', '0101101001', '0010100011', '0010100010', '1110011000', '1110101010', '1110101011', '0010101010', '0010101011', '0010110001', '0010110000', '0011111010', '0011111011', '0110101011', '0110101010', '1100010100', '1100010101', '1001100100', '0011100001', '0011100000', '0100000100', '0100000101', '1010110011', '1010110010', '1001110101', '1001110100', '1001100101', '0011001001', '0000000011', '0000000010', '1010101101', '1010101100', '0101000101', '0101000100', '1111101101', '1111101100', '0011010111', '1000100111', '1100111011', '1011000100', '1011000101', '1110011111', '1110011110', '1011111011', '1011111010', '0101101101', '0111011101', '1001100111', '1001100110', '0000111010', '0000111011', '0001000100', '0001000101', '0111000111', '0111000110', '1000010011', '0101101100', '1100001100', '1100001101', '1101010000', '1101010001', '0100011100', '0100011101', '1110100110', '1110100111', '0111010110', '0111010111', '0101011000', '0101011001', '1111111111', '0000110110', '0000110111', '0110111111', '0110111110', '1100011000', '1100011001', '0011101101', '0011101100', '0001110010', '0001110011', '0011101010', '0100001000', '0100001001', '0111101100', '0111101101', '1000100010', '0111110111', '0111110110', '1000110010', '1000110011', '1001101011', '1001101010', '0010010000', '0010010001', '1110010011', '1110010010', '1100110110', '1100110111', '1010010111', '1010010110', '1001110110', '1001110111', '1111111110', '1100000000', '1100000001', '0000101101', '0000101100', '0101111100', '0101111101', '0100010000', '1111111000', '0110110011', '0110110010', '1010111010', '1010111011', '0110111010', '0110111011', '0000011100', '0110100001', '1000101011', '0001011001', '0001011000', '1111000110', '1111000111', '0100110100', '0100110101', '0000001010', '0000000001', '1110000111', '1011100000', '1111110100', '0111100000', '0111100001', '1101110100', '1101110101', '0111111011', '0111111010', '1011110010', '1011110011', '0101001100', '0101001101', '1111100100', '1111100101', '0100101100', '0100101101', '0010101001', '0010101000', '1110101001', '1110101000', '0011011110', '0011011111', '1101111110', '1101111111', '1001000000', '1001000001', '0101000000', '0101000001', '1111101000', '1111101001', '0100000111', '0100000110', '1010110110', '1010110111', '1011101010', '1011101011', '0100010001', '1011010101', '1011010100', '0011100100', '0011100101', '0111011111', '0111011110', '1001110000', '1001110001', '1011001011', '1011001010', '0000111001', '0000111000', '0001000111', '0001000110', '0100101001', '0100101000', '1100001111', '1100001110', '1101010011', '1101010010', '1110100101', '1101011011', '0101011011', '0101011010', '0111010101', '0111010100', '0100011111', '0100011110', '0111001110', '0111001111', '0001101010', '0001101011', '1011111001', '0000110101', '0000110100', '1100011011', '1100011010', '1100010010', '1100010011', '0001110001', '0001110000', '0000100100', '0000100101', '0100001011', '0100001010', '0001100110', '0001100111', '0101101110', '1000110001', '1000110000', '1110110010', '1110000110', '1110110011', '0011001010', '0011001011', '0010010011', '0010010010', '0010011010', '0010011011', '1111111100', '1111111101', '1100110101', '1100110100', '1010011000', '1101000010', '1101000011', '1010011001', '1100000011', '1100000010', '0101111111', '0101111110', '0100010011', '0100010010', '0111101111', '0111101110', '1101100110', '1101100111', '0010010110', '1011111100', '0110111001', '0110111000', '1010111001', '1010011111', '1000101001', '1000101000', '0111011010', '0001111101', '0001111100', '0100110111', '0000101001', '1111000101', '1111000100', '1011100011', '1011100010', '0111100011', '0111100010', '1101110111', '1101110110', '0000010001', '0000010000', '1000111101', '1000111100', '0110100100', '1111100110', '0011000110', '0011000111', '0110101110', '0101001111', '0101001110', '0110101111', '1110100010', '0011011101', '0011011100', '1110111110', '1111110001', '0101100111', '0101100110', '1111011000', '1111011001', '1101001110', '1101001111', '1100101000', '1100101001', '0101000011', '0101000010', '1111101011', '1111101010', '1001000011', '1001000010', '1001001010', '1001001011', '0101001010', '0101001011', '0110010010', '0110010011', '1101010110', '0100110001', '1101010111', '1110101100', '1110101101', '1010110101', '1010110100', '0011111100', '0011111101', '1000101100', '1000100101', '1000100100', '1000101101', '0011100111', '0011100110', '0001010101', '0001010100', '1001110011', '1001110010', '1011011101', '0010010111', '1000001110', '1000001111', '0110001010', '0110001011', '0101101011', '0101101010', '0001101001', '0001101000', '1101011001', '1101011000', '0111001101', '0111001100', '1101111011', '0000111100', '0000111101', '1010100010', '1010100011', '0000000110', '0000000111', '1100010001', '0110011111', '1001000110', '1001000111', '0000100111', '0000100110', '0000011000', '0000011001', '0111010000', '0111010001', '1010111000', '0001010110', '1011111101', '0001100101', '0001100100', '0000110000', '0000110001', '1001111101', '0001010111', '0001110100', '0001110101', '1100111111', '0011001000', '1111110011', '0000011101', '1111110010', '0010011001', '0010011000', '1110110001', '1110110000', '1101000001', '1101000000', '1000110100', '1000110101', '0101011110', '0101011111', '0100111110', '0100111111', '0010110111', '0000101000', '0110101000', '0100110110', '1010000110', '1010000111', '0110000110', '0110000111', '1101010101', '1101010100', '0010010101', '0010010100', '1100110000', '1100110001', '0011010100', '0011010101', '1010101110', '1010101111', '1001100010', '1001100011', '0000101011', '0000101010', '1001010010', '1001010011', '1011001101', '0000100010', '0000100011', '0110010101', '1000011010', '1000011011', '0000010010', '0000010011', '1000111000', '0001001110', '0001001111', '1101111010', '1010111100', '1010111101', '0110100111', '0110100110', '0011000101', '0011000100', '0001111000', '0001111001', '1101100101', '1101100100', '1001111111', '1111000000', '1111000001', '1001111110', '1001011110', '1001011111', '1110111101', '1110111100', '0111011100', '1101001101', '1101001100', '1111011011', '1111011010', '1111010010', '1111010011', '1011110100', '1011110101', '1100101011', '1100101010', '1100100010', '1100100011'}
>>> exp(Phi(), 0)
exp(Phi(), 0)
{''}
>>> exp(Unit(), 0)
exp(Unit(), 0)
{''}
>>> exp(exp({'a','b'}, 9), 0)
exp(exp({'a','b'}, 9), 0)
{''}
>>> cat(exp(exp({'a','b'}, 9), 0), Unit())
cat(exp(exp({'a','b'}, 9), 0), Unit())
{''}
>>> def star(L,n):
    """Star a language, bounding the iteration to the given n
    star(a,2) --> set(['abab', 'bcbc', 'ab', 'abbc', '', 'bc', 'bcab']), 
    where  a = set(['ab', 'bc'])
    """
    return Unit() if n == 0 else exp(L,n) | star(L,n-1)

def star(L,n):
...     """Star a language, bounding the iteration to the given n
...     star(a,2) --> set(['abab', 'bcbc', 'ab', 'abbc', '', 'bc', 'bcab']), 
...     where  a = set(['ab', 'bc'])
...     """
...     return Unit() if n == 0 else exp(L,n) | star(L,n-1)
... 
>>> star({'0','1'},0)
star({'0','1'},0)
{''}
>>> star({'0','1'},1)
star({'0','1'},1)
{'1', '0', ''}
>>> star({'0','1'},2)
star({'0','1'},2)
{'11', '10', '00', '01', '', '0', '1'}
>>> star({'0','1'},3)
star({'0','1'},3)
{'11', '10', '00', '01', '', '0', '1', '010', '011', '001', '000', '111', '110', '100', '101'}
>>> star({'0','1'},4)
star({'0','1'},4)
{'', '0110', '0111', '0000', '0001', '0011', '0010', '0101', '0100', '010', '011', '001', '000', '111', '110', '100', '101', '11', '10', '00', '01', '0', '1111', '1110', '1', '1100', '1101', '1010', '1011', '1001', '1000'}
>>> star({'0','1'},20)
star({'0','1'},20)
  C-c C-cTraceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "<stdin>", line 6, in star
  File "<stdin>", line 5, in exp
  File "<stdin>", line 6, in cat
  File "<stdin>", line 6, in <setcomp>
KeyboardInterrupt
>>> star({'0','1'},12)
star({'0','1'},12)
{'100100100001', '100100100000', '110000', '010111001', '000100011001', '000100011000', '010111000', '000001101001', '000001101000', '1001001001', '1001001000', '111111011011', '111111011010', '101010010110', '101010010111', '110111000111', '110111000110', '010011000010', '010011000011', '11111001111', '11111001110', '00111010111', '', '11111011', '01011101101', '01011101100', '11000100010', '00101000001', '001001001100', '001001001101', '001011001101', '001011001100', '1001110011', '101101100111', '101101100110', '10111101111', '10111101110', '11011101111', '11011101110', '001101111000', '001101111001', '011101100100', '011101100101', '001010000011', '011111101011', '10011001', '101111011001', '101111011000', '010010001101', '1110000010', '1110000011', '01111100101', '01111100100', '111110101010', '111110101011', '111111001', '111111000', '000110010111', '000110010110', '011011010', '011011011', '011010011', '011010010', '010000001101', '010000001100', '101011100', '101011101', '11100100111', '11100100110', '000010011001', '000010011000', '100011111101', '100011111100', '0110001001', '0110001000', '01101111010', '00011001101', '00011001100', '11101111001', '01101111011', '000011100', '000011101', '1001000000', '010000000', '010000001', '100010', '100011', '01100101100', '01100101101', '1111011110', '00111010110', '101010001101', '101010001100', '11101110000', '0000000100', '01001001101', '01001001100', '0011111111', '0011111110', '100', '101', '100101011', '100101010', '110101100001', '110101100000', '101100100101', '101100100100', '110011110011', '110011110010', '0100011', '0100010', '011110110110', '011110110111', '010011100111', '001100101110', '001100101111', '1110101', '101100001110', '0001101100', '0001101101', '101100001111', '10110010001', '10110010000', '001101110010', '001101110011', '111111110101', '111111110100', '111110100000', '011101001001', '011101001000', '0010011100', '110001011101', '0000110011', '0000110010', '10000', '0001110111', '0001110110', '10001', '001111101000', '001111101001', '0001011101', '01011001111', '10000111111', '10000111110', '01011001110', '001110110100', '001110110101', '01000101100', '0010001110', '0010001111', '01000010100', '01000010101', '11110001111', '00000011001', '0110011110', '10111110100', '101000101101', '101000101100', '111011110111', '111011110110', '001111000000', '001111000001', '001011101111', '001011101110', '00000011000', '0110011111', '110010011001', '110010011000', '00001010', '00001011', '11110101111', '00110101011', '111110011001', '111110011000', '11110101110', '101110111111', '101110111110', '011100101100', '011100101101', '01101000110', '01101000111', '1111100', '1111101', '00010001', '00010000', '101111100011', '11110000100', '11110000101', '101000111111', '101000111110', '100010101000', '100010101001', '100001000101', '100001000100', '000000110011', '000000110010', '001001011000', '001001011001', '1001010001', '1001010000', '11101011111', '11110111', '0000100001', '0000100000', '10111111111', '111001111100', '111001111101', '1111101100', '111011011001', '111011011000', '001011010101', '001011010100', '1001101100', '00001110110', '111100000111', '10110010', '10110011', '11001', '100111100100', '100111100101', '0110011010', '101010111011', '101010111010', '00100110011', '00100110010', '100110110010', '100110110011', '1000101111', '1000101110', '000011110101', '000011110100', '01011110111', '110000000110', '110000000111', '000100111', '011111101010', '000110001111', '000110001110', '110101010111', '110101010110', '001010000010', '010000010101', '010000010100', '011110000000', '011110000001', '110101001', '110101000', '01111010011', '01111010010', '001001101', '110000011101', '110000011100', '10011101001', '111001010001', '111001010000', '01000100011', '111111000011', '111111000010', '10001101011', '001010001010', '01010101110', '010100111010', '001010001011', '11001111100', '10011100110', '011100110111', '011100110110', '010101010110', '010101010111', '110011', '110010', '101111000100', '101111000101', '101010010101', '101001111111', '11111001100', '11111001101', '010011000001', '010011000000', '00111010100', '00111010101', '100110111011', '01011101110', '01011101111', '100110111010', '11100010001', '11100010000', '10100011101', '010110111110', '010110111111', '001001001111', '001001001110', '10011000101', '10011000100', '001010101', '1001111100', '1001111101', '10111101100', '10111101101', '11011101100', '11011101101', '11110101100', '11110101101', '01100100100', '001101111011', '001101111010', '111010001100', '111010001101', '11100001010', '11100001011', '111010100010', '111010100011', '111101011010', '111101011011', '01111100110', '01111100111', '1101110100', '001010001001', '001010001000', '10001100101', '10001100100', '1101110101', '11011000111', '11011000110', '1110000001', '1110000000', '111110101001', '111110101000', '111000001110', '111000001111', '00111001001', '00111001000', '1000000100', '1000000101', '0111111011', '1011101111', '1011101110', '011010000', '011010001', '01011001', '110100011', '110100010', '01011000', '10000100101', '10111110001', '10000100110', '11000110', '11000111', '010011111000', '010011111001', '101001', '00011001110', '1011101100', '1011101101', '101000001100', '101000001101', '101100101', '101100100', '001010010100', '001010010101', '001010001', '001010000', '100001', '100000', '1111011101', '1111011100', '111010111', '111010110', '01101100001', '11011001010', '01001001110', '01001001111', '11010', '11011', '100101000', '00110100110', '00110100111', '001001010', '001001011', '100101111000', '100101111001', '101011101110', '101011101111', '011110110101', '011110110100', '001100101101', '001100101100', '0001101111', '0001101110', '01001011100', '01001011101', '001101110001', '001101110000', '10001001', '10110010010', '10110010011', '01100011001', '11100111110', '0010011111', '0010011110', '1010100100', '1010100101', '10100101010', '10100101011', '100110010000', '100110010001', '000101110110', '000101110111', '01110000101', '01110000100', '001111101011', '001111101010', '0101110011', '001110110111', '001110110110', '01101000000', '01100000111', '10000111100', '10000111101', '011101111', '0010001101', '01100000110', '1100010111', '011101110', '11011101', '11011100', '01111011010', '01101000001', '01111011011', '11101010101', '11101010100', '00010000011', '00010000010', '100001011000', '100001011001', '11000100100', '001111000011', '001111000010', '0100100101', '0100100100', '01001111010', '11111111111', '11111111110', '00100011', '010100101110', '010100101111', '00001001', '00001000', '001110011010', '001110011011', '100011100000', '100011100001', '100010110000', '011010011101', '00111011100', '011100101111', '011100101110', '110011111001', '1110110111', '110011111000', '110100011100', '110100011101', '100010101011', '100010101010', '011100011001', '10010010', '100111111100', '100111111101', '001001011011', '001001011010', '1010000000', '1010000001', '0111101010', '11110111011', '0111101011', '111001111111', '111001111110', '10110001', '10110000', '10011011101', '10011011100', '101001000100', '101001000101', '100001110110', '100001110111', '010001100001', '010110100110', '010110100111', '0101100100', '0111111110', '0111111111', '100111100111', '100111100110', '0101100101', '1010011011', '1010011010', '10010000010', '101011001', '10010000011', '00100110000', '101011101101', '11111', '10001011001', '100110110001', '100110110000', '000111111110', '000111111111', '110000000101', '110000000100', '1110101000', '10100101111', '10100101110', '111010010100', '111010010101', '10110011011', '0000010100', '0000010101', '10110011010', '110101010', '110101011', '01101110101', '01101110100', '101011011000', '101011011001', '1000011100', '1000011101', '011110000011', '011110000010', '00111000000', '00011110000', '01111010000', '01111010001', '1111011111', '010100111001', '010100111000', '010011011001', '010011011000', '101010', '001100011110', '001100011111', '010101010101', '010101010100', '10011100100', '10011100101', '01101101000', '01101101001', '10111110101', '001001101110', '001001101111', '011111110100', '011111110101', '000101101110', '000101101111', '101111000111', '101111000110', '101001111101', '101001111100', '110110010010', '110110010011', '100000110100', '100000110101', '11100010010', '11100010011', '11011110', '11111110000', '010000000010', '010000000011', '001101101010', '001101101011', '101010011', '101010010', '01111111110', '01111111111', '010110111101', '010110111100', '10001111101', '10001111100', '100100111100', '100100111101', '01000111111', '11111110001', '0110010111', '0110010110', '111010100001', '111010100000', '111010001111', '111010001110', '010010100', '111101011001', '111101011000', '01011010010', '10001100110', '10001100111', '010011100000', '010011100001', '00111001010', '00111001011', '111000001101', '111000001100', '110100000', '110100001', '101100001000', '101100001001', '00111000011', '00111000010', '110001111110', '110001111111', '11111101', '000100111101', '10111110010', '10111110011', '000100111100', '11111011101', '111001001', '111001000', '11111011100', '010011111011', '010011111010', '11000101', '11000100', '100111011000', '00110011001', '00110011000', '011110', '100111011001', '1011001000', '1011001001', '1000000110', '101000001111', '101000001110', '0100011010', '0100011011', '111101000100', '111101000101', '100101100000', '100101100001', '001010010111', '001010010110', '11000000001', '001001101011', '010001010010', '010001010011', '01011000011', '01011000010', '001001101010', '001011011', '001011010', '1001101111', '001000010000', '001000010001', '011100100110', '10010000110', '011100100111', '11000000000', '1011', '10010000', '10010001', '100101111011', '100101111010', '111101100000', '111101100001', '100111010100', '100111010101', '010001001101', '011110101', '001001001', '001000001011', '101011101100', '001001000', '110', '10100010110', '10100010111', '000101101011', '01100011010', '01100011011', '010010100010', '010010100011', '00110110111', '00110110110', '01100010011', '01100010010', '11000100000', '1010100111', '1010100110', '01001101111', '01001101110', '00100000011', '100110010011', '100110010010', '01110000110', '01110000111', '000101110101', '000101110100', '110101111100', '110101111101', '11111100111', '11111100110', '000101001', '1110111110', '01010011010', '01001000011', '11101010110', '11101010111', '001110000100', '001110000101', '10000001111', '10000001110', '00010000000', '00010000001', '11111100', '100001011011', '100001011010', '1110111111', '11111111100', '11111111101', '100001010010', '100001010011', '010010101110', '010100101101', '010100101100', '1010011100', '010010101111', '01001011111', '11001000010', '01101100000', '01001011110', '11010001101', '100011100011', '100011100010', '011010011111', '011010011110', '001110011001', '001110011000', '11010100000', '11111000111', '011011011011', '001100000110', '001100000111', '101110011110', '101110011111', '101001100110', '101001100111', '11101110111', '11101110110', '0001011', '0001010', '1000000', '01101000011', '110100011111', '110100011110', '101001011100', '101001011101', '100110000', '1100111100', '0010011101', '00110101100', '00110101101', '100111111111', '100111111110', '1010000011', '1010000010', '111000111110', '111000111111', '01101000010', '000001011100', '000001011101', '011010111000', '110010000101', '1010001010', '1010001011', '100011010110', '100001110101', '100001110100', '100011001000', '100011001001', '010110100101', '010110100100', '101001000111', '101001000110', '111010111010', '111010111011', '100001011100', '0111111101', '0111111100', '0000001100', '0000001101', '1101110010', '000101010010', '000101010011', '00101111101', '110010100000', '110010100001', '111100100010', '111100100011', '010101001000', '010101001001', '00001110000', '100101001110', '100101001111', '001110100000', '000111111100', '111010010111', '111010010110', '00010100100', '00010100101', '0000010111', '0000010110', '101100010000', '101100010001', '100000011', '01101110110', '01101110111', '00111011011', '011011011000', '101011011011', '101011011010', '110001100110', '110001100111', '0110011000', '10001011111', '10001011110', '1110111010', '10010000100', '10010000101', '110010000000', '0010000', '0010001', '000000100010', '001100011101', '001100011100', '000000100011', '011000011000', '011000011001', '011100000101', '11101101100', '11101101101', '10000101100', '11001111001', '011100001000', '011100001001', '01011011011', '01011011010', '000101101101', '000101101100', '001001101101', '000011001011', '01110111111', '01110111110', '110110010001', '110110010000', '01101011011', '01101011010', '100000110111', '100000110110', '101010000', '101010001', '111001001100', '111001001101', '010000000001', '010000000000', '010010001100', '001101101001', '001101101000', '11001100001', '11001100000', '01001110010', '10001111110', '10001111111', '1100010', '1100011', '001001110000', '001001110001', '010110001110', '010110001111', '01110011101', '01110011100', '1100110010', '1100100111', '11001111101', '000010001000', '000010001001', '1100100110', '000110', '000111', '011000110110', '011000110111', '010011100011', '010011100010', '101100001011', '101100001010', '00100001000', '010011101010', '010011101011', '10010110011', '010111101110', '010111101111', '00000001', '10011110101', '110001111101', '110001111100', '0001001011', '0001001010', '11110110001', '100010110101', '1001001', '1001000', '100010110100', '111001010', '111001011', '1011001011', '1011001010', '111000011', '111000010', '0111010000', '011101', '011100', '011100000', '011100001', '110101001010', '110101001011', '0100011001', '0100011000', '1110011100', '1110011101', '00110000001', '111101000111', '111101000110', '010001010001', '010001010000', '100101100011', '100101100010', '011001111011', '01001110011', '010100001100', '010100001101', '110011100010', '110011100011', '001011000', '001011001', '100100111111', '100100111110', '110000010', '110110101111', '00110000000', '110000011', '1100011101', '1100011100', '111101100011', '111101100010', '010010111010', '010010111011', '111111100010', '111111100011', '01100000010', '01100000011', '0000000000', '00111101011', '00111101010', '1110100100', '10001011', '1001101011', '11010100111', '11010100110', '111000100110', '111000100111', '01100010000', '01100010001', '10011110100', '0100101010', '0100101011', '001111010100', '001111010101', '10111010011', '10111010010', '11101001110', '11101001111', '0011101110', '0011101111', '110101111111', '110101111110', '11001001001', '11001001000', '101100111000', '110100011000', '011100111110', '011100111111', '11111100100', '11111100101', '11110', '011101000', '111110110010', '000010000000', '011110101000', '011110101001', '011010110010', '011010110011', '111100111010', '111100111011', '100101010110', '100101010111', 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'011000001111', '011000001110', '10011111100', '10011111101', '100101101101', '011011011001', '011011111111', '011011111110', '000011011000', '000011011001', '011100011111', '011100011110', '010001011000', '010001011001', '01011001001', '01011001000', '10000011101', '10000011100', '1000110010', '1000110011', '001011110', '10011010', '011011011101', '101001010100', '000111101100', '011011011100', '111010101011', '111010101010', '00001000101', '00001000100', '01011', '0100010111', '1100110', '111101010011', '111101010010', '011011101101', '011011101100', '11101011100', '11101011101', '101101011001', '001000100101', '10100011010', '100011100', '0110111', '001000100100', '011110100010', '010010001', '010010000', '100100001101', '011111010000', '011111010001', '00010001110', '0101100', '0101101', '01000100', '01000101', '011101000101', '011101000100', '11011110111', '100000110', '100000111', '10010101100', '10010101101', '100010101101', '110111111011', '110111111010', '1100010110', '100010101100', '110111110010', '110111110011', '1000000001', '11101000001', '11101000000', '0101111100', '00011101011', '010110101', '010110100', '0100010000', '0100010001', '001000111110', '001000111111', '1011110', '1011111', '0110110011', '0110110010', '10110100100', '0101101000', '1110010', '01100101', '0110111010', '0110111011', '001101010101', '001101010100', '111011101010', '111011101011', '011101011000', '011101011001', '0110101100', '011010100110', '00000010101', '00000010100', '01100100', '000110110011', '000110110010', '01001001011', '000110111010', '000110111011', '00100000101', '00100000100', '000000111010', '00011100101', '00011100100', '11000100110', '11000100111', '000000111011', '001110010011', '001110010010', '011110011110', '110110100011', '11010110010', '111110010101', '111110010100', '100000000100', '100000000101', '110110100010', '11100110101', '1011110010', '1111010', '11100110100', '010000100110', '010000100111', '010001110110', '010001110111', '110011110101', '1010000110', '011111000010', '011111000011', '110110000110', '110110000111', '100000100000', '100000100001', '01110100', '01110101', '100011110111', '000010110100', '000010110101', '111010011001', '10101011', '0010101001', '0010101000', '100010000110', '100010000111', '010001101101', '010001101100', '00000111011', '001000000111', '0011111001', '0011111000', '100100010001', '100100010000', '010010111110', '111110001001', '110001101111', '1101111110', '1101111111', '01110110011', '01110110010', '100110100110', '100110100111', '101010100110', '010011100110', '101101001100', '101101001101', '111100101000', '111100101001', '100010011101', '100010011100', '00000011101', '01010110010', '01010110011', '01010111011', '01010111010', '110001101110', '00000010110', '0101000000', '110010110001', '110010110000', '010110011100', '010110011101', '1100111000', '0111010111', '100110111101', '100110111100', '01111000111', '01111000110', '11110011111', '11000101011', '0100001110', '101101010111', '101101010110', '0010110100', '0010110101', '01010010110', '01010010111', '0101011001', '11010011000', '11010011001', '01001111101', '01001111100', '10101010', '1010011111', '000011010101', '01010000001', '0011010', '0011011', '01101110000', '00101011', '00101010', '000110100111', '00100010', '000100101001', '000110100110', '11110110010', '000100101000', '111010110000', '111010110001', '11110110011', '110111011001', '110111011000', '110110011101', '110110011100', '100000111011', '100000111010', '01101110001', '110100101010', '110100101011', '10111001101', '10111001100', '0001000111', '10111011110', '01011100010', '01011100011', '10111111110', '001010011000', '001010011001', '001101001101', '001101001100', '100001101101', '100001101100', '101101111001', '101101111000', '10100001011', '10100001010', '110100110001', '110100110000', '001101100110', '001101100111', '011101111010', '011101111011', '00101001110', '0101000001', '10011111010', '10010101', '10010100', '111101100101', '111101100100', '000100000010', '000100000011', '00101100100', '000001110010', '000001110011', '00000001010', '11101001101', '01100100111', '010000111000', '010000111001', '110111101010', '110111101011', '000000101101', '000000101100', '1011011111', '11011100101', '01000111010', '01000111011', '010100010010', '010100010011', '010001000000', '110000101111', '000011000000', '000011000001', '111001100010', '111001100011', '101010110010', '101010110011', '00111111100', '01001100011', '01011001010', '01011001011', '010001011011', '010001011010', '000011011011', '000011011010', '00000001101', '00000001100', '1000110001', '1000110000', '000011010010', '000011010011', '101100111110', '101100111111', '110011101000', '110011101001', '011001101100', '011001101101', '010010110011', '10000011110', '10000011111', '11100100011', '010010110010', '000111101111', '000111101110', '0011001010', '0011001011', '0001100100', '111010101', '111111101110', '111111101111', '1001010010', '01000', '01001', '110000101110', '1001010011', '000101111000', '0110100', '100011111', '10011111011', '10000010', '10000011', '111101110010', '111101110011', '00111100001', '00111100000', '00110111000', '011111010011', '011111010010', '011111011010', '011111011011', '1101000010', '1101000011', '001000100110', '001000100111', '11101000010', '11101000011', '001111110110', '001111110111', '110111110001', '110111110000', '0101111111', '0101111110', '0100010011', '0100010010', '0111101111', '0111101110', '100111001', '100111000', '1000011010', '100111110000', '100111110001', '1101100110', '00101110', '1000011011', '01100110', '001011110100', '001011110101', '000110100100', '000110100101', '00100100111', '00100100110', '01010110110', '0110111001', '0110111000', '110111100', '00011111101', '00011111100', '0000010011', '111011101001', '111011101000', '0111011010', '011101011011', '011101011010', '010010110000', '010010110001', '0111011011', '011101010010', '011101010011', '0000101000', '0000101001', '10101011100', '00100010010', '1101100001', '101011011110', '000110111001', '000110111000', '00100000110', '00100000111', '101011011111', '00011100110', '00011100111', '11111101010', '0001010000', '01101100', '01101101', '0111011110', '0001010001', '000001000001', '000001000000', '110110100001', '110110100000', '100000000111', '100000000110', '011110101011', '0111010001', '010111111100', '010111111101', '1011110001', '1011110000', '011101110011', '0110100100', '0110100101', '00000100000', '010000100101', '010000100100', '110011001', '110011000', '010001110101', '010001110100', '011111000001', '011111000000', '10101010100', '10101010101', '100000100011', '100000100010', '100000101010', '100000101011', '000010110111', '000010110110', '00110110000', '100010000101', '100010000100', '01000110', '111100110000', '111100110001', '10111101', '10111100', '10011011', '11000011001', '00000111000', '00000111001', '111110001011', '111110001010', '1101111101', '1101111100', '111110000010', '111110000011', '101110100100', '101110100101', '100110100101', '100110100100', '101101001111', '101101001110', '10010110001', '10010110000', '01000001100', '11000001110', '11000001111', '111100101011', '111100101010', '000100011010', '000100011011', '100100100010', '100100100011', '1001001010', '1001001011', '00000011011', '01010111000', '01010111001', '111111011000', '111111011001', '000001101010', '000001101011', '110111000100', '110111000101', '110110101110', '010110011111', '010110011110', '000010011010', '000010011011', '11110011100', '11110011101', '01101111001', '01101111000', '110110111', '01100010', '0010110111', '0010110110', '001011001110', '001011001111', '11111000', '1000101101', '01110111', '01110110', '110110000101', '110110000100', '101111111011', '101010001110', '101010001111', '101101100100', '101101100101', '01111110011', '001010000000', '001010000001', '000111000', '00100001', '00100000', '01011110101', '10101101100', '10011001011', '101111011010', '111010110010', '10001101010', '1001110010', '111100001', '011011001', '10001110001', '000110010100', '000110010101', '10111001110', '10111001111', '110100101001', '110100101000', '010000001110', '010000001111', '101011111', '101011110', '10010111000', '111111110110', '111111110111', '00010010100', '10010111001', '110011011', '101110111', '10100111010', '10100001000', '10100001001', '001101100101', '001101100100', '100011111110', '100011111111', '1101100100', '0110001010', '0110001011', '011101111001', '011101111000', '0101101011',  C-c C-c '1110101100', '101110110', '000100000001', '000100000000', '111011000100', '001110011', '010000010', '110111101100', '000001110001', '000001110000', '101000', '10100000110', '110111101001', '110111101000', '111011000101', '0000011', '010100010001', '010100010000', '000011000011', '000011000010', '110000101101', '110000101100', '101100100110', '101100100111', '111001100001', '111001100000', '110101100010', '110101100011', '110011110000', '110011110001', '11100011101', '100111000110', '111011010001', '001010011011', '001010011010', '10010010010', '100110011', '100110010', '101100111101', '101100111100', '011101001010', '011101001011', '011001101111', '011001101110', '000011010001', '000011010000', '110011101011', '110011101010', '110101010100', '110101010101', '101111011', '10110001001', '101111010', '0001110100', '0001110101', '0011001001', '0011001000', '111111101101', '111111101100', '11010101110', '11010101111', '001100111110', '10000001', '10000000', '1100111110', '00111100011', '111101110001', '111101110Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
KeyboardInterrupt
>>> def revl(L):
    """Reverse a language.
       revl(set(['ab', 'bc'])) --> set(['cb', 'ba'])
    """
    return set(map(lambda x: x[::-1], L))

def revl(L):
...     """Reverse a language.
...        revl(set(['ab', 'bc'])) --> set(['cb', 'ba'])
...     """
...     return set(map(lambda x: x[::-1], L))
... 
000', '000001000011', '100011110', '01000110000', '010011000', '010011001', '110000001', '110000000', '1101000001', '1101000000', '011111011001', '011111011000', '111011110100', '111011110101', '10100010000', '11010001100', '101000101110', '101000101111', '001011101100', '001011101101', '010111001010', '010111001011', '100101100', '000001000010', '010101011111', '110010011010', '110010011011', '10011100', '111110010010', '001111110101', '001111110100', '110110100100', '011110011001', '100111010', '01100111000', '001011110111', '001011110110', '01101000101', '01101000100', '111110011010', '111110011011', '00100100100', '00100100101', '101110111100', '101110111101', '00011111110', '00011111111', '1111111', '1111110', '11110000111', '11110000110', '00100011110', '00100011111', '101000111100', '101000111101', '110111001101', '100001000110', '100001000111', '00010010', '00010011', '010100110001', '000000110000', '000000110001', '0000101011', '0000101010', '011101010001', '011101010000', '0000100010', '0000100011', '011111001011', '111011011010', '111011011011', '10011000000', '001011010110', '001011010111', '10011000001', '0110011101', '01101111', '01101110', '00001110101', '00001110100', '01100000101', '11011001101', '010111111111', '010111111110', '111011001011', '10001111010', '1000101100', '000110010', '101010111000', '111011001010', '11001111111', '0110011100', '000110011', '101011', '10100101', '00010000110', '000011110110', '000011110111', '010101011110', '010111011010', '100111110011', '100111110010', '11111111010', '01100100110', '000110001100', '000110001101', '011000001', '011000000', '100000101001', '100000101000', '10100100', '010000010110', '010000010111', '111100110011', '111100110010', '101000111', '101000110', '100011000001', '1100111', '101010101011', '110000011110', '110000011111', '111001010010', '111001010011', '111111000000', '111111000001', '011100110100', '011100110101', '111110000001', '111110000000', '101110100111', '101110100110', '10010110010', '11011111110', '00000100001', '11011111111'}
>>> def revl(L):
    """Reverse a language.
       revl(set(['ab', 'bc'])) --> set(['cb', 'ba'])
    """
    return set(map(lambda x: x[::-1], L))

def revl(L):
...     """Reverse a language.
...        revl(set(['ab', 'bc'])) --> set(['cb', 'ba'])
...     """
...     return set(map(lambda x: x[::-1], L))
... 
>>> revl({'aaa', 'aah'})
revl({'aaa', 'aah'})
{'haa', 'aaa'}
>>> revl({'aab', 'aah'})
revl({'aab', 'aah'})
{'haa', 'baa'}
>>> def lcomplem(L,alph,m):
    """Complement L relative to alphabset alph. alph is also given as a set of strings.
       We subtract from the "star up to m" of the alphabet alph, the language L.
    """
    return star(alph,m) - L

def lcomplem(L,alph,m):
...     """Complement L relative to alphabset alph. alph is also given as a set of strings.
...        We subtract from the "star up to m" of the alphabet alph, the language L.
...     """
...     return star(alph,m) - L
... 
>>> {'aaa', 'aba'} - {'aaa', 'ccc'}
{'aaa', 'aba'} - {'aaa', 'ccc'}
{'aba'}
>>> star({'a','b'}, 2)
star({'a','b'}, 2)
{'aa', 'a', 'ab', 'ba', 'bb', 'b', ''}
>>> star({'a','b'}, 10)
star({'a','b'}, 10)
{'', 'aaabbbabb', 'aaabbbaba', 'babbaaaa', 'abbbba', 'bbbabababb', 'bbbabababa', 'abbbbb', 'aaababaa', 'bbabbaabb', 'aaababab', 'baaaaaabbb', 'baaaaaabba', 'bbbbbaabbb', 'baaabbbaa', 'aaabbabaab', 'aaabbabaaa', 'bbbaaabaab', 'bbbaaabaaa', 'aaababbbb', 'abaabbabbb', 'abbabbbaba', 'baaabbaab', 'abaabbabba', 'aaababbba', 'baaaab', 'bbbbabaaab', 'bbbaaabbb', 'bbbaaabba', 'abbabbbabb', 'aabbbbaaba', 'aabbbbaabb', 'bbbaabab', 'abaabaab', 'baabaaaaa', 'aaabbbaa', 'aaabbbab', 'bbbaaaabba', 'abbabbaaaa', 'abbabbaaab', 'aabbbababb', 'bbbaaaabbb', 'aabbbababa', 'abaabbbba', 'bbbabbaba', 'baaaaababb', 'abaabaaa', 'bababbbaa', 'bbabbbabaa', 'bbabbbabab', 'bababbbab', 'baaabbbab', 'aaababaaa', 'ababababa', 'bbbbbbabbb', 'aabbababbb', 'bbaababaab', 'bbaababaaa', 'aabbababba', 'babbbabb', 'bbbbabaaaa', 'bbababab', 'bbabaaaab', 'bbabaaaaa', 'bbabbbbbba', 'abbbab', 'bbabbbbbbb', 'ababaaaaaa', 'ababaaaaab', 'ababaabab', 'ababaabaa', 'bbbabbba', 'aba', 'abb', 'bbbabbbb', 'abaaaabaa', 'abbaabbaba', 'abbaabbabb', 'bbaaababbb', 'bbabbaaaba', 'bbabbaaabb', 'bbaaababba', 'aaaaaabb', 'abbabbbaaa', 'babaaaaaa', 'aaabaab', 'abbabbbbab', 'abbabbbbaa', 'baaabbaaa', 'abbbbbbb', 'bababaab', 'aabbbbabab', 'aabbbaa', 'aabbbab', 'aabbbbabaa', 'abaaaaa', 'abaaaab', 'babaaaaab', 'baabbbaaaa', 'baabbbaaab', 'bbaabbbbab', 'bbaabbbbaa', 'abbaabba', 'baaaaa', 'ababaaaa', 'baabaaaba', 'abbbbbaba', 'abbbbbabb', 'abaabbbaaa', 'babbbababa', 'abaabbbaab', 'abaabbaa', 'abaabbab', 'babbbab', 'aaabaaabaa', 'aaabaaabab', 'abaaabaaba', 'abaaabaabb', 'abbabaa', 'abbabab', 'aaabaabbba', 'aabaaaaaaa', 'aabaaaaaab', 'aaabaabbbb', 'abbbbbaabb', 'abbbbbaaba', 'bababbaab', 'bababbaaa', 'bbbbbbbb', 'bbbbbbba', 'babbbaaba', 'abbbbbbaa', 'aaabaabab', 'aaabaabaa', 'babaaa', 'baaabbaabb', 'baaabbaaba', 'bbbbaa', 'bbbbab', 'baaaaaaaba', 'bbbaabaaba', 'bbbaabaabb', 'baaaaaaabb', 'aaababbaaa', 'aaababbaab', 'babababba', 'bbaaabaab', 'baaabbab', 'bbaaabaaa', 'bbaabbbab', 'bbaabbbaa', 'babbaababb', 'babbaababa', 'bbaabaaaab', 'bbaabaaaaa', 'bbbbbaaaba', 'bbbbbaaabb', 'abbabababb', 'abbabababa', 'aaaabab', 'aaaabaa', 'bbabbaabab', 'abaaaabaab', 'abaaaabaaa', 'bbabbaabaa', 'abbaaaabba', 'bbabbaabba', 'abbaaaabbb', 'baaabaaba', 'aabbbbbaba', 'baaabaabb', 'aabbbbbabb', 'babaaaabbb', 'babaaaabba', 'bbabbabba', 'aababbbbaa', 'aababbbbab', 'abbbbbbaba', 'ababbaba', 'baababaaaa', 'baababaaab', 'aabb', 'aaaa', 'baababba', 'aaab', 'baaabbaa', 'bbababaaab', 'aabaaaabaa', 'babbaaa', 'bbbbaaa', 'bbbbaab', 'babaabaabb', 'babaabaaba', 'baaabb', 'aaabbaaabb', 'aababaaaab', 'aaaabaabab', 'aaaabaabaa', 'aaabaaaaa', 'aaabaaaab', 'bbaaabbb', 'babbbbbbab', 'abbaaabbba', 'abbaaabbbb', 'babbbbbbaa', 'bbaaabaaba', 'bbbbaaaa', 'bbaaabaabb', 'bbbaabbbb', 'bbbaabbba', 'baaaaaabb', 'baaaaaaba', 'abaaabba', 'bbababbaab', 'bbbbaaab', 'bbabbbaa', 'aabababaaa', 'aabababaab', 'aaaaa', 'ababbab', 'bbababbaaa', 'baaaabbaa', 'bbabaabaaa', 'abababbbaa', 'abababbbab', 'bbabaabaab', 'abbbbababa', 'abbbbababb', 'abbbbaaaba', 'abbbbaaabb', 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'bababaabaa', 'baabababba', 'bbbbbaba', 'bbbbbabb', 'aabababbbb', 'bbabbbbb', 'bbabbbba', 'aabababbba', 'babba', 'babbb', 'bbababbba', 'aabaaaaab', 'bbbbaaabab', 'bbbbaaabaa', 'abbabb', 'bbbbbabbab', 'abbaba', 'babbaaabb', 'aababbbbb', 'bbbbbbbba', 'baabbbaba', 'baabbbabb', 'bbababaa', 'babbababbb', 'babbababba', 'bbbbbabbaa', 'babaabbbaa', 'babaabbbab', 'baaabaaab', 'bbbabbabbb', 'ababbbbaa', 'ababbbbab', 'bbbabbabba', 'abababaaab', 'abbbaaaaaa', 'abbbaaaaab', 'abababaaaa', 'babbbbbaaa', 'bbaabaa', 'babbbbbaab', 'aaaabbbabb', 'aaaabbbaba', 'aabbaabaab', 'b', 'bbaabaabaa', 'bbaabaabab', 'abbaababb', 'abbaababa', 'ababbaabbb', 'abbb', 'abba', 'ababbaabba', 'aabbaabaaa', 'bbabababb', 'aaaabbb', 'baaaaabbab', 'baaaabaa', 'baaaaabbaa', 'aaaabba', 'aaaaabaaa', 'aabaaabaaa', 'aabaabbaab', 'aabaaabaab', 'abaabbaab', 'abaabbaaa', 'abaababba', 'aaabbb', 'aabaabbaaa', 'baabbaaaab', 'bbabbabbb', 'aabbaaaaa', 'baabbaaaaa', 'aababba', 'bbabbbb', 'bbbbbba', 'bbababbb', 'aabbbbaba', 'aabbbbabb', 'bbababba', 'bbbb', 'bbbaaabbaa', 'bbbaaabbab', 'aababbb', 'aaaabaaab', 'aaaabaaaa', 'aabbaaaaab', 'aabbaaaaaa', 'bbab', 'bbaa', 'bbabababa', 'bbababaabb', 'abbabbaab', 'bbaaaaaabb', 'bbabbaab', 'bbaaaaaaba', 'babaabbaab', 'babaabbaaa', 'babbbba', 'bbaaaabbaa', 'bbaaaabbab', 'babbbbabab', 'babbbbabaa', 'bbbbaabba', 'babbbabbaa', 'bbbaaaab', 'babaabb', 'abbbbabab', 'abbbbabaa', 'aababbaaa', 'aababbaab', 'babbbabbab', 'aaaabbbaa', 'aaaabbbab', 'abaabbabab', 'baababbaaa', 'baababbaab', 'bbabbbabba', 'aababbaaab', 'aaabaabb', 'aababbaaaa', 'bbabbbabbb', 'aaaaaaaabb', 'abbaaaaabb', 'abbabbabbb', 'abbabbabba', 'abbaaaaaba', 'baaaabbb', 'baaaabba', 'baaababab', 'baaababaa', 'aabbbaaabb', 'aabbbaaaba', 'baaaabab', 'abbabaabba', 'abbabaabbb', 'bbbbbbaab', 'bbbbbbaaa', 'baaaaabb', 'aaabaababb', 'baababbaa', 'abbbabb', 'aaabaababa', 'bbaaabbbab', 'bbbbbaabba', 'bbaaabbbaa', 'abbbabbbaa', 'abbbabbbab', 'bbbabbbaba', 'bbbabbbabb', 'aaaabbab', 'bbbabbaaba', 'aaabaaa', 'bbbabbaabb', 'bbb', 'baaaaabbba', 'aabaaab', 'abbabbba', 'babbababb', 'ababaaaba', 'ababaaabb', 'bbabaabbbb', 'bbabaabbba', 'baaabbabab', 'abbbababb', 'abaababb', 'ababbaaaba', 'bbaabbbaaa', 'bbaabbbaab', 'ababbaaabb', 'aaaaabab', 'abbabaabaa', 'abaabaaaaa', 'aaaaabaa', 'baabbabab', 'baabbabaa', 'bbaababbba', 'bbaababbbb', 'bbbaabaa', 'babbbabbba', 'babaaaabaa', 'bbbbbbabba', 'babbbabbbb', 'abbbabaaab', 'baabbb', 'baabaabbbb', 'baabba', 'bbbabaabb', 'baaaababba', 'bbbabaaba', 'aaabbabbba', 'abbabbbaab', 'baaabbbbaa', 'aabbbbbbbb', 'baaabbbaab', 'baaabbbaaa', 'aabbbbbbba', 'aaaaabbbba', 'baaabbbbab', 'aaaaabbbbb', 'baaaababbb', 'abaabababb', 'aabaaaa', 'babababbb', 'abaabababa', 'aaabababab', 'bbbbbbbaa', 'bbbbbbbab', 'aaabababaa', 'aaaabaaa', 'baaaba', 'baababbb', 'aaaabaab', 'abbabbbbb', 'bbabbbab', 'abaaaaaaab', 'abaaabbb', 'abbaaba', 'baabbaaaa', 'baabbaaab', 'ababaabbab', 'ababaabbaa', 'babaaabbb', 'aababbbabb', 'aababbbaba', 'baabbabaab', 'baabbabaaa', 'bbaaabbaa', 'baababb', 'aabaabbabb', 'aabaabbaba', 'baababa', 'bababbbbaa', 'aaaabbaaab', 'aaaabbaaaa', 'bababbbbab', 'abbba', 'abbaababab', 'abbaababaa', 'aaababaaba', 'aaababaabb', 'bbababbbbb', 'bbaaaaabba', 'aababbbba', 'bbaaaaabbb', 'abbaabbaa', 'baabaaab', 'bbaaabbba', 'bbaaabbbb', 'babbbbbaa', 'bbababbbaa', 'bbaaaaaab', 'bbaaaaaaa', 'bbababbbab', 'abaabb', 'babbbbbab', 'aabbbabab', 'abbbbabbbb', 'abbbbabbba', 'bbabbabbbb', 'aabaabb', 'aabaaba', 'bbabbabbba', 'baaabaabbb', 'baaabaabba', 'abab', 'abaa', 'bbbabbb', 'abaabaaba', 'baabbbaab', 'bbaababbb', 'abaabbaba', 'babbbaaab', 'babbbaaaa', 'abbababba', 'aabaaababa', 'aabaaababb', 'aaaabbabba', 'bbaababba', 'ababbbbabb', 'ababbbbaba', 'bbbbaabbbb', 'bbbbaabbba', 'bababbbba', 'abbaabbbbb', 'babbaaaaab', 'aaaababbbb', 'aaaababbba', 'bbaaabbaab', 'abbaabbbba', 'abbbaaab', 'abababbabb', 'abababbaba', 'bbbbabbabb', 'baabaababb', 'baabaababa', 'bbbbabbaba', 'aaababbab', 'abbabbbab', 'aaababbaa', 'aababaabbb', 'aababaabba', 'aaabbbaab', 'aaabbbaaa', 'bbaabaaba', 'abbbaaaba', 'bbababbbba', 'babbbaaabb', 'babbbaaaba', 'baaabbbbb', 'aaaabaaaaa', 'aaaabaaaab', 'baaabbbba', 'aaaaababa', 'aaaaababb', 'aabbbbaaaa', 'aabbbbaaab', 'baaaabbabb', 'baaaabbaba', 'bbaaaabaa', 'bbaaaabab', 'babbbabaa', 'babbbabab', 'abbbbabbb', 'abbbbabba', 'ababbabb', 'aaaaabbbb', 'aaaaabbba', 'aabba', 'abbabbbaa', 'baababbaba', 'baababbabb', 'aabaaabbab', 'bbbbbbb', 'bababaabbb', 'bbbbbbbaaa', 'aababbbbba', 'abbaaaab', 'aababbbbbb', 'bbaabaabb', 'baaaababaa', 'baaaababab', 'baaababbb', 'baaababba', 'abbabaaba', 'abbabaabb', 'bbaababb', 'aaaabbabaa', 'aaaaaaaaa', 'babbaaaaa', 'babbaaaab', 'aaaabbabab', 'abababaaa', 'abababaab', 'aaaababa', 'aaaababb', 'ababbba', 'bbbbaaabb', 'aaabbabaa', 'aaabbabab', 'babbbbbaba', 'babbbbbabb', 'bbabbaaaaa', 'bbaabaabba', 'bbaabaabbb', 'bbabbaaaab', 'abbaabbaaa', 'babbbbbba', 'babbbbbbb', 'abbaabbaab', 'baaaaaaab', 'baaaaaaaa', 'bbaabbbbb', 'bbbaabbab', 'ababbaaaaa', 'ababbaaaab', 'bbbaabbaa', 'aababababa', 'aababababb', 'abbbaabaa', 'bba', 'baababbab', 'aabbbbba', 'babababb', 'bbabbaaba', 'abbbabaaa', 'aaabbbbbbb', 'aaabbbbbba', 'baababbbab', 'babababbbb', 'babababbba', 'baababbbaa', 'bbbaaaaba', 'babbababa', 'abbbaabaaa', 'abbabbbb', 'abababbbbb', 'aaaaabbbaa', 'aaaaabbbab', 'bbbabaaab', 'bbbabaaaa', 'aabbaaab', 'bbbbbbabaa', 'bbbbbbabab', 'abbbbaaaaa', 'baaaabaaab', 'baaaabaaaa', 'abbbbaaaab', 'aabaaaaaba', 'ababaa', 'aabaaaaabb', 'bbbbbbab', 'bbbbbbaa', 'aaaaaaabab', 'bbaaaabbba', 'bbaaaabbbb', 'aaaaaaabaa', 'baaaaab', 'bbbaaaaabb', 'bbbaaaaaba', 'baaaaaa', 'bababbabb', 'bababbaba', 'abbbbaaaa', 'abbbbaaab', 'baaabaaaa', 'aaababb', 'aaaabaabb', 'aaaabaaba', 'babbbaabb', 'bbbaa', 'bbbab', 'ababababb', 'baabbbbbbb', 'baabbbbbba', 'aaabaabbb', 'baabaaabb', 'bbba', 'aaababbaba', 'aaababbabb', 'babaaaaba', 'babaaaabb', 'bbbaabaaaa', 'abbaaaba', 'bbbaabaaab', 'abbabaaaab', 'abbabaaaaa', 'bbbababaa', 'bbbababab', 'bbbabbbbab', 'bbbbbbaaab', 'bbbbbbaaaa', 'bbbabbbbaa', 'baabaabaa', 'baabaabab', 'baaab', 'aabbbabba', 'aaaabbbbaa', 'bbaaaaabaa', 'bbaaaaabab', 'aaaabbbbab', 'bbabbbbabb', 'bababbbbba', 'bababbbbbb', 'bbabbbbaba', 'bbbbaababa', 'bbbbaababb', 'abababbbba', 'abaaaba', 'abbbababa', 'abbababbb', 'aaaaabbb', 'baaaaaaa', 'baaaaaab', 'aaaaabba', 'aaabaaab', 'abbbaaabab', 'abbbaaabaa', 'aaabaaaa', 'babbaaaaba', 'baababaaba', 'babbbb', 'babbba', 'baababaabb', 'abbbbaba', 'abbbbabb', 'bbbabba', 'abbbaaba', 'bbbbbabba', 'aabaababb', 'babaaaba', 'babaaabb', 'abbbaabb', 'bbbbaba', 'bbbbabb', 'abbaaabb', 'aababbbb', 'ababbabbbb', 'ababbabbba', 'ababab', 'aaaaaabbbb', 'abbbabbbba', 'abbbabbbbb', 'aaaaaabbba', 'bbbbbabbb', 'bbbabbaaaa', 'bbbabbaaab', 'aabbaabaa', 'abbaaabbaa', 'abbaaabbab', 'bbaaabb', 'abbbaabbb', 'bbaaaba', 'ababaaa', 'aabbbaaba', 'aabbaabab', 'abbbbaaba'}
>>> star({'a','b'}, 12)
star({'a','b'}, 12)
{'aabbbabbbaaa', 'aaabbabbaba', 'aaabbabbabb', 'aabbbabbbaab', '', 'abbabbbabba', 'abaabbbbbbba', 'ababaaabbab', 'abaabbbbbbbb', 'aaaaababbbbb', 'abbabbbabbb', 'aaaaababbbba', 'aaabbbaabbb', 'bbaaababbabb', 'bbaaababbaba', 'aabbbabbaab', 'aabbbabbaaa', 'aaabbabaab', 'abaaabaabbab', 'abaaabaabbaa', 'aaabbabaaa', 'abaaabbaabbb', 'abaababaaab', 'abaaabbaabba', 'abababbaaba', 'abaabaabbba', 'abaabaabbbb', 'bbbbaababaa', 'bbbbaababab', 'bbbaabbbaba', 'abbbaaaabaa', 'bbaaaaababab', 'bbaaaaababaa', 'abbbaaaabab', 'abbaababbabb', 'abbaababbaba', 'bbaababbabab', 'bbaababbabaa', 'abaabaababbb', 'bbbabbabbabb', 'bbbabbabbaba', 'abaabaababba', 'abaabbbaabab', 'aaabbbaa', 'aaabbbab', 'abaabbbaabaa', 'bababbaabba', 'aaaabbbabab', 'bababbaabbb', 'bbaabbaaaa', 'baabbbbababa', 'baabbbbababb', 'bbaabbaaab', 'aaaaaaaba', 'baabbabaaaab', 'baabbabaaaaa', 'aababbbaaba', 'baababaaaab', 'aaabbbaabbab', 'baabbabaaab', 'baabbabaaaa', 'aaabbbaabbaa', 'babbbabb', 'baaabbabab', 'babbbaba', 'bbbabaaabba', 'bbbababaaabb', 'bbbababaaaba', 'bbbabaaabbb', 'abaaaabaaaaa', 'aabaababbaba', 'aabaababbabb', 'babbaabbabb', 'abaaabbbabaa', 'abaaabbbabab', 'aababbaabaab', 'aababbaabaaa', 'bababaabaab', 'aabbbabaabba', 'aababaababaa', 'bbaaaabbbb', 'aabbbabaabbb', 'bababaabaaa', 'babbabbbbba', 'aabababbbabb', 'aabababbbaba', 'babbabbbbbb', 'bbabbbbbba', 'bbabbbbbbb', 'ababaaaaaa', 'abbabaaaaaaa', 'baaabbaaaabb', 'baaabbaaaaba', 'bbbbabbbbba', 'baababbb', 'abaaaaabaa', 'abababaaaaab', 'abbbabbbbaaa', 'abbbabbbbaab', 'abaaaaabbabb', 'aaabbbaabaaa', 'aaabbbaabaab', 'bbbbabbaabba', 'bbaabbbbbaa', 'bbaabbbbbab', 'bbbbabbaabbb', 'bbaababbbab', 'aaaaabaabaab', 'aaaaabaabaaa', 'aabbaabbabb', 'abaaaaaababb', 'abaaaaaababa', 'abbbbbbabbaa', 'abbbbbbabbab', 'ababbbbbbab', 'baababbbbb', 'ababbbbbbaa', 'baabbbaaaa', 'bbbaaababab', 'baabbbaaab', 'bbabaababbbb', 'babbbbbaaaba', 'babbbbbaaabb', 'bbabaababbba', 'aaaaaaaabab', 'bbaaababaaa', 'aababaaabaaa', 'aaabaabaaabb', 'bbabaaaa', 'aaabaabaaaba', 'abbbbbaaaaab', 'bbbbaabbbabb', 'bbbbaabbbaba', 'abbbbbaaaaaa', 'abababbaaabb', 'aabaabaaabaa', 'aabaabaaabab', 'abababbaaaba', 'bbaaababaaab', 'abbabab', 'ababbabbbbba', 'bbabababaa', 'bbabababab', 'ababbabbbbbb', 'bababaaaab', 'aaabbaaabba', 'aabbb', 'abbbbbaaba', 'aaabbaaabbb', 'bbaaabbabbab', 'bbaaabbabbaa', 'aaabbababaab', 'aaabbababaaa', 'bbbbbabbbabb', 'ababaaaab', 'bbbbbabbbaba', 'baabbaaaabb', 'bbbbbbbaaabb', 'bbbbbbbaaaba', 'baaabbaabb', 'baaabbaaba', 'aaabbbababba', 'aaabbbababbb', 'aaababaabaaa', 'aaababaabaab', 'baaaabaaaa', 'aaabababbab', 'abababaaabaa', 'baabaaaba', 'abababaaabab', 'aaaaaababbb', 'babbaababb', 'babbaababa', 'baaaaabaabab', 'baaaaaa', 'baaaaabaabaa', 'aabaabaaaba', 'bbabbaabab', 'aabbabaaaaaa', 'aabbabaaaaab', 'bbabbaabaa', 'abbaaaabba', 'baaabbabba', 'abbaaaabbb', 'bbbbaabbabb', 'bbbbaabbaba', 'bbaababbaab', 'bbaababbaaa', 'abbbbaaabbbb', 'babaaaabbb', 'babaaaabba', 'abbbbaaabbba', 'abbabbabbbaa', 'abbabbabbbab', 'abbbabbbaaa', 'abbbbbaaabaa', 'abbbbbaaabab', 'ababbabababa', 'bbbbabaabba', 'baababaaaa', 'baababaaab', 'aaaaaaaabbab', 'abbbabbbaab', 'aaaaaaaabbaa', 'bbbabbbabbb', 'ababbabababb', 'abbbbbaabb', 'aabbbbaaaaba', 'aabbbbaaaabb', 'babaaababbab', 'aaaabaabaabb', 'babaaababbaa', 'bbbbbbbabba', 'aaaaaabababa', 'aaaaaabababb', 'baabbaaabbb', 'baabbaaabba', 'aabbbaabbbbb', 'aabbbaabbbba', 'abbbbaaabab', 'bbbbabbbabb', 'bbbbabbbaba', 'abbbaaababb', 'abbbaaababa', 'abbaaabbba', 'abbaaabbbb', 'baabaababbba', 'baababbbabba', 'baababbbabbb', 'baabaababbbb', 'ababaaabbaab', 'bbbbbbaababa', 'babaaabbaaa', 'abbbbabbaabb', 'bbbabbaabba', 'bbbabbaabbb', 'abbbbabbaaba', 'babbbbbabaaa', 'babbbbbabaab', 'bbaaaabbaaa', 'bbaaaabbaab', 'baaaaabaaaaa', 'aaabaaabbbab', 'aaabaaabbbaa', 'baaaaabaaaab', 'aaaabaaaaa', 'ababbbabaa', 'aababba', 'aababbb', 'abbbbababa', 'ababbbabab', 'abbbbababb', 'ababaabbaab', 'babaabaabbb', 'aabaabbbabab', 'aabaabbbabaa', 'bbbabbbaaaba', 'bbbabbbaaabb', 'babbbabbbaab', 'aaaaaaabbabb', 'bbaabbaabb', 'babaabaabba', 'ababaabbaaa', 'baabaabaaabb', 'baabaabaaaba', 'abbbabab', 'aaaaaaabbaba', 'babaaaabaaa', 'baabababab', 'baabababaa', 'bbaabbbaaaa', 'bbbabbabbaab', 'bbbabbabbaaa', 'bbbababaaaab', 'bbaabbaababb', 'baaababbaba', 'bbababaaaaab', 'bbababaaaaaa', 'bbbbbabbaab', 'babaababaaa', 'baabbaabaaba', 'baabbaabaabb', 'babaababaab', 'aababbaababb', 'abaabbabaab', 'abaabbabaaa', 'aababbaababa', 'bababbaabb', 'baaabbaabaa', 'bababbaaba', 'aaaaaaaa', 'bbabbbaaaaaa', 'abbbaaabbaa', 'abbbabbaab', 'abbbabbaaa', 'bbbaaababaa', 'abbaaabbbbb', 'ababbabaaaaa', 'bbbabbaaaaaa', 'bbbabbaaaaab', 'ababbabaaaab', 'aaabbbbaabab', 'abbbabaaaaab', 'abbbabaaaaaa', 'aaabbbbaabaa', 'baabb', 'baaba', 'bbbbabaabbba', 'abbbaaabbab', 'bbbbabaabbbb', 'bbbaabbabaaa', 'abbaabbaaaba', 'abbaabbaaabb', 'bbbaabbabaab', 'aabaaaaabba', 'aabaaaaabbb', 'abbabbbbbbaa', 'abbabbbbbbab', 'abbabbbaaaaa', 'abbabbbaaaab', 'bbbbbabbbb', 'babbbabaaab', 'aabbabaaaba', 'babababababa', 'babababababb', 'babaababbab', 'babaababbaa', 'aababbaaaaa', 'aababbaaaab', 'aabaabbaabba', 'aabaabbaabbb', 'bababaaabaaa', 'aabbabbbaba', 'bababaaabaab', 'baaaabbabbb', 'baaaabbabba', 'aabbabababba', 'baaaababbaba', 'baaaababbabb', 'aabbabababbb', 'bbabaaabbb', 'abbaabbbabb', 'babaabbabbba', 'bbbbaabbbaab', 'baaaaabbabba', 'baaaaabbabbb', 'bbbbaabbbaaa', 'bbaaababbaab', 'aaaaaababbbb', 'aaabababbaaa', 'bbaaababbaaa', 'bbabaabaaaaa', 'abbabaaaaaa', 'abbabaaaaab', 'bbabaabaaaab', 'bbbababaabaa', 'bbabaaabaab', 'bbabaaabaaa', 'bbbababaabab', 'bbaabaaa', 'aaaaabbabbba', 'aaaaabbabbbb', 'aaabbabbaaa', 'aabaabbbbbb', 'babaababbaaa', 'babaababbaab', 'abbbaaaaaaba', 'aabaabbbbba', 'abbbaaaaaabb', 'aaaabbbabaab', 'aaaabbbabaaa', 'abaaabaabbbb', 'aabbaaaaaab', 'aabbaaaaaaa', 'abaaabaabbba', 'baaaabbaabaa', 'baaaabbaabab', 'bbbabbbaabbb', 'bbbabbbaabba', 'babaaababaaa', 'babaaababaab', 'baabbabaaabb', 'aaabaabab', 'abbbbbbbbbb', 'baabbabaaaba', 'abbaababbaab', 'abbbaaaabbbb', 'abbbaaaabbba', 'abbaababbaaa', 'bbaababbabbb', 'bbaababbabba', 'abaabaabbaa', 'abaabaabbab', 'abaabbaaaab', 'aabbaaa', 'abaabbaaaaa', 'aabbaaabbbbb', 'aabbaaabbbba', 'abbaaaabaa', 'abbaaaabab', 'baaaabbbaa', 'aaababbabaa', 'babbbaaabba', 'aaabaabbabab', 'aaabaabbabaa', 'babbbaaabbb', 'baabbaababbb', 'baabbaababba', 'babbbbbbbab', 'babbbbbbbaa', 'baabbbaaa', 'aaababbabab', 'bababbbaab', 'bababbbaaa', 'aabbbbaabab', 'aabbbbaabaa', 'bababbbabbb', 'abbaaaaabaa', 'bbbbaabbbbaa', 'aababbaabb', 'bbaaabaabbb', 'bbbbaabbbbab', 'abbaaaaabab', 'aaabaaaaab', 'bbabbbbbaa', 'bbabbbbbab', 'aaabaaaaaa', 'aabababbbaab', 'babbaaabbbb', 'babbaaabbba', 'aabababbbaaa', 'abbaaaaabba', 'abbaaaaabbb', 'baaabbaaaaab', 'abaaaabaaa', 'baaabbaaaaaa', 'abbaaaabbba', 'abbaaaabbbb', 'aaaaaba', 'aaabbab', 'aaabbaa', 'bbabbabbbaa', 'bbabbabbbab', 'aababaabab', 'aaaaaabbabaa', 'aaaaaabbabab', 'abbbabbabb', 'abbabbaaaba', 'abbabbaaabb', 'babbaababba', 'baabaaabbb', 'ababaaaaab', 'bbaabbbbbba', 'aabbbaababb', 'bbaabbbbbbb', 'abaaabaabbb', 'abbbaabbbbb', 'bbbabbabab', 'bbbabbabaa', 'abbbaabbbba', 'bbbabbbabbab', 'bbbabbbabbaa', 'bbbaabbabbbb', 'bbbaabbbbbba', 'bbbaabbbbbbb', 'bbbabbaabaa', 'bbbabbaabab', 'aaabaaabbbbb', 'aaabaaabbbba', 'aaaaabbabbb', 'baaabbaaabaa', 'ababbababbab', 'ababbababbaa', 'baaabbaaabab', 'bbbaabbabbba', 'abbbabbbabbb', 'abbbabbbabba', 'bbabaaaaba', 'bbabaaaabb', 'bbaaabbabbbb', 'baaaababbbbb', 'baaaababbbba', 'baabbbabbaba', 'bbbbaabaaab', 'abbbbabaaa', 'abbbbabaab', 'bbbbaabaaaa', 'aabaaaabaab', 'aabaaaabaaa', 'bbbaabaaaba', 'aaabbbaba', 'abbabba', 'aaaaabbababb', 'aaaaabbababa', 'bbbabababab', 'aaabbabababb', 'aaabaaaaa', 'aaabbabababa', 'aaabbbbababa', 'baaaaabbaabb', 'baaaaabbaaba', 'abaabbbaaaab', 'aaabaabbaa', 'aaabaabbab', 'aabaaabbbbba', 'abaabbbbaaa', 'abaabbbbaab', 'aabaaabbbbbb', 'bbbbbbbaaaab', 'babbbabba', 'bbbbbbbaaaaa', 'bbabaaaaaaba', 'bbabbbabbaaa', 'bbabbbabbaab', 'bbabaaaaaabb', 'aaabaaaab', 'abaaaaabbaba', 'baababaabbb', 'aaaaaaaab', 'aabaabbba', 'aabaabbbb', 'baaaaaaaabb', 'bbbabababbba', 'abababaaaaaa', 'aabbababbaa', 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'babbbaaababa', 'bbaabbababab', 'aababbbbaaa', 'aababababa', 'abbbbbababa', 'baabaabbaaa', 'bbaaaaabbab', 'babaabbbba', 'babaabbbbb', 'baababaab', 'abaaaaab', 'baababaaa', 'aabaabbbbaba', 'bbaaabbaba', 'bbaaabbabb', 'aabaabbbbabb', 'bbaaabaabbab', 'bbbbabbaabaa', 'bbbbabbaabab', 'bbaaabaabbaa', 'baabaaaabaa', 'baaaaabaaaba', 'baaaaabaaabb', 'abaaaaaa', 'bbbabaabaa', 'bbbabaabab', 'ababbbbbaba', 'ababbbbbabb', 'baabbbbbaab', 'baabbbbbaaa', 'aaabaabbabb', 'aaabaaaababb', 'aaaabbabbaa', 'aaabaaaababa', 'bbabaaaaaab', 'bbabbaabb', 'bbabaaaaaaa', 'aabbbbab', 'abbbbbbababb', 'abbbbbbababa', 'ababbaaaabbb', 'ababbaaaabba', 'aaabbaabbaa', 'bbbaaababa', 'bbaaaabbaba', 'aaabbababbba', 'bbaaaabbabb', 'aaabbababbbb', 'aabbabbabaa', 'aaabbbaaaab', 'bbbababaabb', 'aabbaaabaab', 'aabbaaabaaa', 'bbabaaabbabb', 'bbabaaabbaba', 'abbaabbaabb', 'abbaaaababb', 'abbaababa', 'aaabaabaabba', 'ababbabbbbaa', 'ababbabbbbab', 'aaabaabaabbb', 'aaaaaaaaaba', 'babbbabbabb', 'baabaabbbaa', 'abababbaabba', 'abababbaabbb', 'ababbbaababb', 'ababbbaababa', 'bbbababaaa', 'babaabaaa', 'bbbaababbb', 'bbbaababba', 'abaaabbaaaba', 'abababaaabba', 'abababaaabbb', 'abaaabbaaabb', 'abaaabbaaa', 'abaaabbaab', 'babbaaabbaaa', 'bbababbaaabb', 'bbababbaaaba', 'bbaaabaaaa', 'abbbbbaaab', 'abbbbbaaaa', 'babbbaaaabb', 'babaabaab', 'babbbaaaaba', 'bbbbbaaaabbb', 'bbaaaaaabaab', 'bbaaaaaabaaa', 'bbbbabaaab', 'aaabbbbbbba', 'aaaaaaabaabb', 'aaaaaaabaaba', 'abaabababbaa', 'bbbabaabaabb', 'aaaaabbaabab', 'ababaaaaabba', 'bbbbbabbaba', 'ababbabaaaba', 'ababbabaaabb', 'bbbbbabbabb', 'bbaaaaabb', 'bbaaaaaba', 'baaaaaabbaa', 'baaaaaabbab', 'baabbbaabbbb', 'bbbbabaabbaa', 'bbbbabaabbab', 'baabbbaabbba', 'babbaabbbba', 'babbbaabaab', 'abbaababaaa', 'abbabbbbbbba', 'abbabbbbbbbb', 'babbbaabaaa', 'bbbaaaababa', 'bbbaaaababb', 'aaabaabba', 'aabbbaababab', 'abbbbbbbaa', 'bbaababbbaa', 'aabbbaababaa', 'abbbbaaababa', 'abbaaababaab', 'bbbaabbababb', 'abbbbaaababb', 'bbababaabb', 'aabbbabbaaab', 'bbababaaba', 'abbbabbb', 'baabaababbaa', 'baabaababbab', 'abbbabba', 'aabaaabaaaaa', 'aabaaabaaaab', 'bbbbaaabbabb', 'baabbaaabab', 'baabbaaabaa', 'bbbbaaabbaba', 'abaabbbaaab', 'babbaaaba', 'abaaabbbab', 'abaaabbbaa', 'abaaaaabaaaa', 'abbbaaabaab', 'babbbabbaaa', 'abaaaaabaaab', 'aabab', 'baaaabbaabba', 'baaaabbaabbb', 'abaaaaaaaaa', 'aabababbaa', 'abaaaaaaaab', 'aabababbaab', 'aabaa', 'bbaaaaaabbaa', 'bbaaaaaabbab', 'aaabbbbbbbba', 'aaabbbbbbbbb', 'aabaaabbabba', 'aaababba', 'aaababbb', 'aabbabbbab', 'aabbabbbaa', 'abbbaaaaaaaa', 'abbbaaaaaaab', 'abbbbabbbbba', 'aabaababaaba', 'aabaaabbabbb', 'abbbbabbbbbb', 'bbabbbaabb', 'bbabbbaaba', 'baaaabbaaaab', 'bbaabbbabaa', 'aabaaabbbabb', 'babaaabababb', 'bbaabbbabab', 'baaabbbaaab', 'babbabbababa', 'baaaabbaaaaa', 'baabababbb', 'babbabbababb', 'abbbbbbaaa', 'baaabbbababb', 'bbbbbabbbbba', 'bbbabaababab', 'bbbabaababaa', 'aabaaabbbaba', 'bababbabbbba', 'aaabbaaaabb', 'aabbaabbaaa', 'aaabbaaaaba', 'bbaabbaabaaa', 'bbaabbaabaab', 'bbabaaabab', 'bababbaba', 'bbabaaabaa', 'bbaaabaaaaba', 'bbaaabaaaabb', 'ababbabaabbb', 'ababbabaabba', 'abbbbaaab', 'abaaaababa', 'bbbaaaabbbbb', 'baabbbabb', 'babbbaaabaab', 'baababababaa', 'abbabaabbbaa', 'babbbaaabaaa', 'abbbabaabba', 'bbabbaababb', 'babaabbbaa', 'babaabbbab', 'baaabaaab', 'bbbabbabbb', 'abbbaabbbab', 'abbbaabbbaa', 'bbbabbabba', 'abbabbbbbabb', 'abbabbbbbaba', 'bbbbbaa', 'aababbaabbb', 'abbaabbaaba', 'aababbaabba', 'baabababb', 'baabababa', 'b', 'bbaabaabaa', 'bbaabaabab', 'bababaaababa', 'bababbababaa', 'aabbaabbaab', 'baababaabbbb', 'baababaabbba', 'bbabbbaabbb', 'bababababaaa', 'bababababaab', 'aababaa', 'babaababbbb', 'babaababbba', 'aaaabbb', 'bbabaaaabaaa', 'aaaabababb', 'aaaabba', 'babbbabbaaba', 'aabaaabaaa', 'aabaaabaab', 'babbbabbaabb', 'bbbaabbbbb', 'bbabaaaabaab', 'aabbaabababb', 'aabbbababaa', 'aabbbababab', 'aabbaabababa', 'aabbaabbaabb', 'aabbabababaa', 'aabbabababab', 'aaaabbbabbba', 'aaaabbbabbbb', 'aabbaaaaaabb', 'bbabbaaaabbb', 'bbabbaaaabba', 'aabbaaaaaaba', 'bbabaabaaaba', 'bbabaabaaabb', 'bbbababaabba', 'bbbababaabbb', 'aabbaabbbbb', 'aabaaabbbbaa', 'aabaaabbbbab', 'abaaabbaaba', 'aaabaabbb', 'aababbbaa', 'ababbabbaabb', 'babbbaabbab', 'ababbbaabaab', 'babbaaababba', 'bbabbbbaaaaa', 'ababbbaabaaa', 'bbba', 'bbabaaabbaab', 'abaaaabaaaab', 'abaabbbaaabb', 'bbabaaabbaaa', 'aabbaabbbba', 'baaaaaabaaab', 'baaaaaabaaaa', 'bbababbaaaab', 'aababab', 'abbbabbabbbb', 'baaaabbaaabb', 'baaaabbaaaba', 'abbababbbaa', 'bbaabaaabaab', 'bbaabaaabaaa', 'baababaaabbb', 'baababaaabba', 'abaababababb', 'bbabbbabbaba', 'abaababababa', 'abaabbaaabb', 'abaabbaaaba', 'baaababbaabb', 'baaababbaaba', 'bbaaaaabaaba', 'bbabaaaaaaaa', 'baabbabaabaa', 'bbaaaaabaabb', 'aaaabbbaa', 'aaaabbbab', 'abbabbabbab', 'aababbaaab', 'bbbbaabbbbba', 'bbbbaabbbbbb', 'aababbaaaa', 'bbaabbabbb', 'baabbaaab', 'abbabaabaaa', 'aaaaba', 'aabbbbaabbb', 'aabbbbaabba', 'aaababbabb', 'abbabaabba', 'abbabaabbb', 'aaabaaaaaaba', 'bbbbbbaab', 'abababbbaab', 'abbaaabababb', 'babaabbbbaa', 'abbaaabababa', 'aaaabb', 'bbbaaaabaaa', 'bbbabaaaabaa', 'bbbabaaaabab', 'bbbaaaabaab', 'bbbabaaaaaaa', 'bbbabbbababa', 'bbbabbbababb', 'bababbbbaab', 'bbbaaab', 'bbbabbaaba', 'baaaaaabb', 'bbbabbaabb', 'aaabbbbbabb', 'bbb', 'bba', 'bbababbaabaa', 'bbababbaabab', 'bbbbbbbaabba', 'bbbbbbbaabbb', 'ababbbbbaaa', 'abbbbaa', 'aaaaaaaaaaa', 'ababbbbbaab', 'abbaaaaaabba', 'bbbabaabbbbb', 'bbbabaabbbba', 'abbaaaaaabbb', 'baaababbab', 'babbaababbb', 'bababaaabbbb', 'bababaaabbba', 'bbaabbbbabb', 'abbbbab', 'bbbaaabaaab', 'bbbaaabaaaa', 'aaabbbaaaaa', 'ababaaabbbaa', 'ababaaabbbab', 'bbbabaabbaaa', 'bbbbaabaaba', 'babaabbabbbb', 'bbabaabaabba', 'babbbaaabbaa', 'baaabbaaabba', 'baaabbaaabbb', 'babbbaaabbab', 'abbbbbbbb', 'baabaaaaabb', 'bbbabaabbaab', 'babaabaabab', 'abbbbbbabaab', 'abbbbbbabaaa', 'aaabbbaabbbb', 'aaabbbaabbba', 'abbbbbbba', 'abaabaababab', 'abaabaababaa', 'babbbbaaaab', 'aaaabaabaaab', 'abaabbbaabba', 'aaaaabbbbaba', 'aaabababab', 'bbbbbbbaa', 'bbbbbbbab', 'aaabababaa', 'bbbbbaaaaaab', 'babaabaabaa', 'abbbbabaaaba', 'bbbbbabbaa', 'aabbbaaabaa', 'abbbbabaaabb', 'abbaabb', 'abbaaba', 'abbaaaaabbaa', 'aabbabababa', 'babbbaab', 'babbbaaa', 'babaaaabbbaa', 'bbaaabbababa', 'abbabaabaaaa', 'baabbbabbbbb', 'babaaaabbbab', 'bababbaabab', 'bbabaaaaabab', 'bbabbaaabaaa', 'bbabbaaabaab', 'bbbabaababbb', 'bbabaaaaabaa', 'bbbabaababba', 'aabbbabbbba', 'aabbbabbbbb', 'abbabaabaaab', 'bbaaabaabaaa', 'bbbabaaaaabb', 'bbaaabaabaab', 'abbbbaabaaa', 'ababaaaaabab', 'ababaaaaabaa', 'aabaabbbbbab', 'aabaabbbbbaa', 'bbbabaaaaaba', 'bbabbbbaaaa', 'bbababbbaa', 'babababbbaab', 'babababbbaaa', 'bbababbbab', 'bbaababaabba', 'bbaababaabbb', 'abbaabaabaaa', 'babbbaabaaaa', 'babbbaabaaab', 'abbaabaabaab', 'abbaaabbbaba', 'abbaaabbbabb', 'aabbbabbbbbb', 'aabbbabbbbba', 'babbaaaabab', 'baaaaaabbba', 'aabbbaaabbaa', 'aabbbaaabbab', 'baaaaaabbbb', 'babbaaaabaa', 'aaabbbbbbab', 'baababaabbab', 'bbabaababbab', 'bbabaababbaa', 'baababaabbaa', 'aaabbbbbbaa', 'aababbabbab', 'baaabbbbbb', 'aaaaaabbabb', 'abaaaaaabaab', 'abaaaaaabaaa', 'aaaaaabbaba', 'babbbabbaa', 'aababbabbaa', 'bbbaabbabbab', 'aabaaababa', 'aabaaababb', 'bababbababba', 'ababaaaaaaaa', 'ababaaaaaaab', 'bbbbaabbbb', 'bbbbaabbba', 'bababbbba', 'aaabaabaaaab', 'aaabaabaaaaa', 'bababbbbb', 'bbabbaaaabab', 'bbaaaabbbbbb', 'aaaababbba', 'bbabbaaaabaa', 'abababbaaaab', 'abababbaaaaa', 'abaababbbbb', 'aabbbababba', 'aabbbababbb', 'ababbaabb', 'abbbababb', 'abaaabbaabab', 'abaaabbaabaa', 'aaabaaabaaab', 'aababaabbb', 'aababaabba', 'aabaaaaaabb', 'aabaaaaaaba', 'abbbbbaaaabb', 'abbbbbaaaaba', 'aabbaabbbbba', 'bbababbbba', 'aaaaaaababaa', 'bbaababbbba', 'bbaababbbbb', 'aaaaaaababab', 'bbababbbbb', 'abaabbbaa', 'bbaabbbbabaa', 'bbaabbbbabab', 'abaabbbab', 'aaaaabaaaba', 'bbbbabaa', 'baabbbaaba', 'aaaaababbbab', 'aaaaababbbaa', 'bbaaaabaa', 'bbaaaabab', 'bababbaaabaa', 'bababbaaabab', 'aaaaabaaabb', 'abbbaaaabba', 'babbabbabab', 'bbabbaaaaaaa', 'ababbaba', 'bbabbaaaaaab', 'baaaaabaabbb', 'baaaaabaabba', 'baababaabaaa', 'baababaabaab', 'bbaabaababa', 'babbbbababb', 'babbbbababba', 'babbbbababbb', 'bbbbbbb', 'bbbbbba', 'bbbbabbaabb', 'baaabba', 'bbaabbabbbb', 'baaabbb', 'bbbaaaaabbaa', 'bbbaaaaabbab', 'abbbbaaabbab', 'abbbbaaabbaa', 'bbaabbabbba', 'ababbabaabab', 'babbaaaaa', 'babbaaaab', 'abbbababbbba', 'abbbaaaababa', 'abbbaaaababb', 'aabbbbabbbaa', 'aabbbbabbbab', 'bbababaaabba', 'aaaaabaaab', 'baaababababa', 'bbababaaabbb', 'abbabaabbbbb', 'babbaaaabbaa', 'babbaaaabbab', 'abbabaabbbba', 'abbbbbabaaa', 'baaaabbbabab', 'abbbbbabaab', 'aabbbaabaaaa', 'aabbbaabaaab', 'aaaaabaaaa', 'abbabbbbbaab', 'abbabbbbbaaa', 'baabbababbab', 'abababaaaabb', 'abababaaaaba', 'abbabbbbb', 'bbaabaabba', 'bbaabaabbb', 'abbbabaaabba', 'babbabbbbaa', 'babbabbbbab', 'abbbabaaabbb', 'bbabbbabaaa', 'baaabbabbab', 'baaabbabbaa', 'bbbabaabbbab', 'aabbaaabbaba', 'aabbaaabbabb', 'bbbabaabbbaa', 'bababaaabbab', 'abbaababbbba', 'abbaababbbbb', 'bababaaabbaa', 'abbababaabba', 'abbbbabbaaab', 'abbbbabbaaaa', 'abbababaabbb', 'aaaababbbbb', 'aaaababbbba', 'aaabbbbbbb', 'aaabbbbbba', 'bbabaabaabab', 'babababbbb', 'babababbba', 'bbabaabaabaa', 'abbbbbabbab', 'bababbbabbaa', 'bababbbabbab', 'abbbbbabbaa', 'bbbabbaaabab', 'bbbbaba', 'abaabaababb', 'abaabaababa', 'bbbbabb', 'aabaabbbabbb', 'aabaabbbabba', 'aabbaababab', 'bbabababba', 'bbbbbabbbaab', 'bbbbbabbbaaa', 'bbabababbb', 'aaabbaaabaa', 'aaabbaaabab', 'aaabababbbba', 'bbbaaaaabb', 'bbbaaaaaba', 'aaabababbbbb', 'bbabbbbaaabb', 'bbabbbbaaaba', 'bbbabbabbbba', 'bbbabbabbbbb', 'baaabaababba', 'abaaaabaaabb', 'abaaaabaaaba', 'aaaabbbabbab', 'abbbabbbba', 'babbbaabb', 'aabbabbbbba', 'abbabbaabbb', 'abbabbaabba', 'ababaabababa', 'baabaaabb', 'bbaabaaababb', 'bbaabaaababa', 'babaaaaba', 'babaaaabb', 'baaaaaabaabb', 'baaaaaabaaba', 'bbbabbbbbabb', 'aabbbabbbaa', 'aabbbababbaa', 'bbbabbaaaa', 'aabaabbbbbbb', 'aabaabbbbbba', 'bbbabbaaab', 'bbababaaaaa', 'bbabbbbabb', 'aaabbbbaabbb', 'aaabbbbaabba', 'bbabbbbaba', 'babbbabbaab', 'aabababbbbba', 'aabababbbbbb', 'babababbbabb', 'abbaaababab', 'abbaaababaa', 'babababbbaba', 'bbabbbaaaaa', 'bbabbbaaaab', 'abaaaabbbba', 'aabbbabbbbab', 'abaaaaaba', 'aabbbabbbbaa', 'abbbabbbaaba', 'abbbabbbaabb', 'aaabaabbaaba', 'aaabaabbaabb', 'baababaaba', 'abaaaaabb', 'aaabbbaaaaaa', 'aaabbbaaaaab', 'bbbbaaaaaaa', 'baababaaabb', 'baababaaaba', 'abababbbabb', 'abababbbaba', 'aaabbbaabab', 'aababaabbbaa', 'aababaabbbab', 'aaababbaabb', 'ababbbabaab', 'babaaababbbb', 'babaaababbba', 'aabbbababbab', 'bbaaababbbba', 'bbaaababbbbb', 'ababbbabaaa', 'abaaabbabab', 'aabbbaabbbab', 'aabbbaabbbaa', 'aabbaabaa', 'abbaaabbaa', 'abbaaabbab', 'bbaaabb', 'aabbaabab', 'bbaaaba', 'abbbaabba', 'abbbaabbb', 'abbbbaaba'}
>>> len(star({'a','b'}, 12))
len(star({'a','b'}, 12))
8191
>>> len(star({'a','b'}, 14))
len(star({'a','b'}, 14))
32767
>>> len(star({'a','b'}, 16))
len(star({'a','b'}, 16))
131071
>>> len(star({'a','b'}, 15))
len(star({'a','b'}, 15))
65535
>>> len(star({'a','b'}, 20))
len(star({'a','b'}, 20))
2097151
>>> exp(Phi(), 0)
exp(Phi(), 0)
{''}
>>> """See that if you take star of 20, it takes forever because
"""See that if you take star of 20, it takes forever because
... it is trying to print something big. But if you take len(..) of
it is trying to print something big. But if you take len(..) of
... that thing, then it only needs to print the length. Compute is
that thing, then it only needs to print the length. Compute is
... much faster than I/O.  Also is there a pattern to the growth
much faster than I/O.  Also is there a pattern to the growth
... of the len of star ?? 
of the len of star ?? 
... """
"""
'See that if you take star of 20, it takes forever because\nit is trying to print something big. But if you take len(..) of\nthat thing, then it only needs to print the length. Compute is\nmuch faster than I/O.  Also is there a pattern to the growth\nof the len of star ?? \n'
>>>