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In 1948 Claude E. Shannon in "The Mathematical Theory of Communication"' has introduced his famous formula for the entropy of a discrete set of probabilities p1, ... , pn:
We will apply this formula to an arbitrary text string by letting pi be the relative frequencies of occurrence of characters in the string. For example, the entropy of the string "Northeastern European Regional Contest" with the length of 38 characters (including 3 spaces) is 3.883 with 3 digits after decimal point. The following table shows relative frequencies and the corresponding summands for the entropy of this string.
Your task is to find a string with the given entropy.
The input consists of a single real number H (0.00 <= H <= 6.00) with 2 digits after decimal point.
Write to the output file a line with a single string of at least one and up to 1000 characters '0'-'9', 'a'-'z', 'A'-'Z', '.' (dot), and spaces. This string must have the entropy within 0.005 of H.
Northeastern European Regional Contest
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