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, ... , p_n:

H=-∑pilog2pi

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.

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.

3.88

Northeastern European Regional Contest