Problem H. Hot-keys

Author:A. Klenin   Time limit:5 sec
Input file:input.txt   Memory limit:64 Mb
Output file:output.txt  

Statement

When designing dialog forms for interactive programs, it is important to assign hot-keys (known also as accelerator keys) to each dialog element, so as to facilitate keyboard input.

For better mnemonics, hot-keys are assigned based on the letters of dialog elements' captions, usually favoring letters near the beginning of caption. Manual hot-keys distribution can be tedious and error-prone, as one must be careful not to assign same letter to different elements.

Your program will be given a list of captions. It must assign unique hot-keys to as many captions of possible. Each assigned hot-key must be a letter from the corresponding caption.

For each hot-key, position is the leftmost occurrence of the hot-key letter in the corresponding caption. From all solutions with the same numbers of hot-keys, your program must choose the one with minimal sum of hot-key positions. If there is still more than one optimal solution, output any of them.

Input file format

Input file contains number of captions N followed by N lines with captions.

Output file format

Output file must contain N lines with the same captions as in input. In those captions which have hot-key assigned, leftmost occurrence of hot-key letter must be preceded with '&' (ASCII 38).

Constraints

1 ≤ N ≤ 10, all captions are from 1 to 10 characters in length and consist of small Latin letters.

Sample tests

No. Input file (input.txt) Output file (output.txt)
1
3
yes
no
cancel
&yes
&no
&cancel
2
4
abc
bca
acb
aaaa
&abc
&bca
a&cb
aaaa

0.101s 0.011s 13