After grading too many tests, Mr. DeMello decided to start grading strings instead.

Mr. DeMello has the correct ~4~-letter, lowercase string, ~C~, which he will use to grade the other strings.

Now, Mr. DeMello considers all possible ~4~-letter, lowercase strings and grades them by finding the minimum distance between each letter in the string (e.g., a and z have a distance of ~1~), summing it up for their total score.

Since Mr. DeMello knows all his students will get a score of at most ~K~, can you tell him all the possible strings that his students can get?

Input Specification

The first line will contain ~K~ ~(0 \le K \le 52)~, the maximum score his students can achieve.

The second line will contain ~C~, the intended ~4~-letter string.

Output Specification

Output all possible strings in sorted alphabetical order (e.g., abc should appear before bac).

Sample Input

1
abcd

Sample Output

aacd
abbd
abcc
abcd
abce
abdd
accd
bbcd
zbcd