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# A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
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#
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# 1/2 = 0.5
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# 1/3 = 0.(3)
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# 1/4 = 0.25
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# 1/5 = 0.2
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# 1/6 = 0.1(6)
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# 1/7 = 0.(142857)
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# 1/8 = 0.125
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# 1/9 = 0.(1)
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# 1/10 = 0.1
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#
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# Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
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#
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# Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
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def longest_permutation(denominator):
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mod_list = []
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modulo = 1.0
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while True:
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modulo *= 10
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if modulo in mod_list:
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break
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mod_list.append(modulo)
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modulo %= denominator
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return len(mod_list)
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longest_perm = 0
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longest_perm_denominator = 0
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for i in range(1, 1000):
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perm_num = longest_permutation(i)
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if longest_perm < perm_num:
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longest_perm = perm_num
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longest_perm_denominator = i
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print(longest_perm_denominator)
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print(longest_perm)
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