7401번 - Entropy 스페셜 저지다국어

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 $p_1, \ldots, p_n$: $$H = - \sum p_i \log_2 p_i \; .$$

We will apply this formula to an arbitrary text string by letting $p_i$ 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.

Input file consists of a single real number $H$ ($0.00 \le H \le 6.00$) 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 $H$.