Kata

A seven-segment display (SSD), or seven-segment indicator, is a form of electronic display device for displaying decimal numerals.

![alt text][sev_seg]

Above is a diagram of the seven-segment display I am using. However, some of its segments are broken. When I try to display the number a, it becomes the number b instead.

Task

Your task is to find the possible broken segments given the numbers a and b as strings. There will be multiple SSDs forming a number, so you must return the broken segments of an SSD in a set, return an empty set if an SSD does not seem to be broken.

If a can not become b, throw an exception.

Examples

sev_seg('1000','1007') should equal [set(),set(),set(),{'D','E','F'}]
sev_seg('888','123') should equal [{'A','D','E','F','G'},{'C','F'},{'E','F'}]
sev_seg('-23',' 23') should equal [{'G'},set(),set()]
sev_seg('123','123') should equal [set(),set(),set()]
sev_seg('123','888') should throw Exception 'Invalid input'

Important notes

• If an SSD is not displaying anything, it will be ' '.
• If an SSD is displaying '-', only the G segment is working.
• a and b will always be strings of valid characters with the same length.
• You may report to me if the description is too confusing.